Centre for High Energy Physics · Physics Vol.1, 4th (1992) and 5th (2002) Edition by Halliday, Resnic and Krane, John Wiley and Sons 2. Fundamental of Physics 5th and 6th Edition

Centre for High Energy Physics

Curriculum B.Sc. (Hons.) Computational Physics Status and Regulations: B.Sc. (Hons.) in Computational Physics will be of four years duration and is divided into eight semesters of full time study. The program will be conducted in accordance with the Punjab University rules and regulations for semester studies. The outlines of the program and courses of reading are specified in the Appendix I and II, and can be changed from time to time by the Academic Council on the recommendation of the Board of Studies

Eligibility for Admission Admission to B.Sc. (Hons.) in computational physics is by competitive entrance examination, which is open to candidates who passed F.Sc./A-Level (with physics & mathematics) and is based on the following merit criteria.

1. 20% Matric 2. 50% F.Sc.. 3. 30% Test + Interview.

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Appendix I Semester 1: Courses Cr. Hr. PHYS 1101: General Physics I 4 MATH 1101: Differential Calculus 4 MATH 1102: Discrete Mathematics 3 COMP 1101: Introduction to Computer Science 3 HUM 1101: English Comprehension 2 Total 16 Semester 2: Courses Cr. Hr. PHYS 1201: General Physics II 4 MATH 1201: Analytical Geometry, Integral Calculus 4 MATH 1202: Linear Algebra 4 STAT 1201: Statistics and Probability 3 HUM 1201: Communication Skill 2 PHYS 1202: Physics Lab I 2 Total 19 Semester 3: Courses Cr. Hr. PHYS 2301: General Physics III 4 MATH 2301: Vector Algebra and Analysis 3 MATH 2302: Infinite Series and Sequences 2 MATH 2303: Applied Differential Equations 4 HUM 2301: Pakistan Study 2 PHYS 2302: Physics Lab II 2 Total 17 Semester 4: Courses Cr. Hr. PHYS 2401: General Physics IV 4 PHYS 2402: Electronics 3 COMP 2401: Computer Programming 4 HUM 2401: Islamic Study 2 PHYS 2403: Physics Lab III 2 PHL 404: Electronics Lab 2 Total 17

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Semester 5: Courses Cr. Hr. PHYS 3501: Classical Mechanics 4 PHYS 3502: Electromagnetic Theory and Special Relativity 4 COMP 3501: Advance Computer Programming 3 MATH 3501: Mathematical Method I 3 COMP 3502: Numerical Linear Algebra 3 PHYS 3503: Physics Lab IV 2 Total 19 Semester 6: Courses Cr. Hr. PHYS 3601: Waves and Optics 3 PHYS 3602: Digital Electronics 3 COMP 3601: Scientific Computation I 3 COMP 3602: Numerical Analysis 3 MATH 3601: Mathematical Method II 3 PHYS 3603: Physics Lab V 2 Total 17 Semester 7: Courses Cr. Hr. PHYS 4701: Quantum Mechanics 4 PHYS 4702: Thermal and Statistical Physics 3 COMP 4701: Scientific Computation II 3 COMP 4702: Computational Physics Simulations I 3 HUM 4701: Fundamentals of Management 3 COMP 4703: Computational Physics Simulations Lab I 2 Total 18 Semester 8: Courses Cr. Hr. PHYS 4801: Solid State Physics 3 PHYS 4802: Applied Nuclear and Particle Physics 3 COMP 4801: Computational Physics Simulations II 3 HUM 4801: Philosophy of Science 2 COMP 4802: Computational Physics Simulations Lab II 2 Project 4 Total 17 Total: 140

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PHYS 1101: General Physics I Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 1st Semester e-mail Name of the Course General Physics I Course no. PHYS 1101 Credit Hours 4

Contact hours: 4 per week Lectures: 4 Duration: 1 hr/Lecture

Pre-requisite F.Sc/A-Level Physics Follow-up General Physics II Category Core course Aim The course will introduce calculus based basic physics and its applications Objectives At the completion of the course student will be able to:

1. Understand basic principles of mechanics and its applications. 2. Be able to solve relevant numerical problems. 3. Be able to use calculus in studying the mechanics systems.

Syllabus Sr. Major Topics Subtopics 1. Preliminary Vector in 3D; Vector products; Review of derivation

and integration with physical importance; Position vector; velocity and acceleration; Newton’s laws of motion; Equations of motion with constant and variable forces

2. Applications of Newton’s law

Nature of forces; Frictional forces; Drag force & motion of projectile; Uniform circular motion (Conical pendulum, Rotor and Banked curve) Non-inertial frame & pseudo forces; Limitation of Newton’s laws

3. Work and Energy

Work Done by a Constant Force and Variable forces; Kinetic Energy and the Work-Energy Theorem; Power

4. Conservation of Energy

Conservative Forces; Potential Energy; Solution of conservative systems

5. System of Particles

System of many particles, Centre of mass of solid objects; Linear momentum of system of particles and its conservation; System of variable mass and rocket motion

6. Collisions Elastic and Inelastic collisions in one and two dimensions

7. Rotational Kinematics

Rotational motion & its variables; Relation b/w linear angular variables

8. Rotational Dynamics

Torque, Angular momentum & KE of system of particles and rigid body; Moment of inertia; Parallel axis theorem; Momentum inertial of solid bodies; Rotational dynamics of rigid body; The tope; Combine rotational and transnational motion

9. Angular Momentum

Angular momentum of a particle and a system of particles; Angular momentum and angular velocity; Law of conservation of angular momentum and its applications

10. Equilibrium of Rigid Bodies

Conditions of equilibrium; Centre of gravity; Examples of equilibrium; Equilibrium of rigid bodies

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in gravitational field 11. Gravitation Gravitational effect of a spherical mass distribution;

Gravitational P.E.; The Motion of Planet and Satellites; Kepler’s Law with derivations; Energy consideration in planetary and satellite motion; Shape of Galaxy

Text Book(s) 1. Physics Vol.1, 4th (1992) and 5th (2002) Edition by Halliday, Resnic and Krane, John Wiley and Sons

2. Fundamental of Physics 5th and 6th Edition by Halliday & Resnic, John Wiley and Sons

Reference Books/Material

1. Physics for Scientists and Engineers, Extended Version by P. M. Fishbane, Prentice-Hall International Editions

2. Classical Mechanics Simulations, CUPS course, John Wiley & Sons

Instructional aids/Resources

1. White board and markers 2. OHP 3. Transparence sheets 4. Multimedia Projector 5. Soft boards 6. Pointer 7. Software (PowerPoint) 8. Photocopy machine/photocopying facility

Teaching Strategies 1. Lecturing 2. Topic discussion 3. Individual project/Assignments 4. Class presentation 5. Questioning and explanation

Categories Weightage Criteria Sessional 25% Assignments

Quiz Mid 25% Paper

Assessment

Final 50% Paper Recommendations

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PHYS 1201: General Physics II Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 2nd Semester e-mail Name of the Course General Physics II Course no. PHYS 1201 Credit Hours 4


Pre-requisite PHYS 1101 Follow-up General Physics III Category Core course Aim The course will introduce calculus based basic physics and its applications Objectives At the completion of the course student will be able to:

1. Understand basic principles of mechanics and its applications. 2. Be able to solve relevant numerical problems. 3. Be able to use calculus in studying the mechanics systems.

Syllabus Sr. Major Topics Subtopics 1. Bulk Properties of

Matter Elastic properties of matter; Elasticity; Tension; Compression & Shearing; Elastic modulus; Elastic limit; Poisson’s ratio; Relation b/w three types of elasticity;

2. Fluid Statics and Dynamics

Fluids; Pressure and density; Variation of pressure in a fluid at rest; Surface tension; Viscosity; Fluid flow through cylindrical pipe (Poisenille’s Law)

3. Oscillations Simple Harmonic Motion; Energy considerations in SHM ; Applications of SHM; Oscillation with two degree of freedom; Spring system and coupled pendulum; Damped Vibrations; forced vibrations; Resonance; Phase of Resonance; Quality Factor

4. Wave in Physical Media

Mechanical waves; Traveling waves; Phase velocity; Group velocity and dispersion; Wave speed; Principle of superposition; Interference of wave; Standing wave; Resonance

5. Sound Waves Beats (analytical treatment); The Doppler effect 6. Light Waves Nature of light; Speed of light in matter; Doppler

effect for light 7. Interference Coherence; double slit interference (analytical

treatment); Interference from thin films, Newton’s ring (analytical treatment); Michelson’s interferometer; Fresnels Biprism

8. Diffraction Single slit diffraction; Intensity in single slit diffraction (analytical treatment); Double slit diffraction & interference combined; Diffraction at circular aperture; Diffraction from multiple slits; Diffraction grating; Dispersion and resolution power

9. Polarization Polarization; polarization by polarizing sheet, by reflection, by double refraction and double scattering; Polarization states (linear, circular & elliptic polarization)

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10. Heat and Temperature

Temperature; Kinetic theory of the ideal gas, Work done on an ideal gas; Intermolecular forces

11. Thermodynamics First law of thermodynamics and its applications; Reversible and irreversible process; 2nd law of thermodynamics; Carnot theorem; Carnot engine; Heat engine; Refrigerators; Thermodynamic temp. scale; Entropy; Entropy and 2nd law; Entropy in reversible and irreversible process; Entropy and probability





2. Classical Mechanics Simulations, CUPS course, John Wiley & Sons





Quiz Mid 25% Paper

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PHYS 2301: General Physics III Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 3rd Semester e-mail Name of the Course General Physics III Course no. PHYS 2301 Credit Hours 4


Pre-requisite PHYS 1101, PHYS 1201 Follow-up General Physics IV Category Core course Aim The course will introduce calculus based basic physics and its applications Objectives At the completion of the course student will be able to:

1. Understand basic principal of electricity and magnetism and its applications.

2. Be able to solve relevant numerical problems. 3. Be able to use calculus in studying the electromagnetic systems.

Syllabus Sr. Major Topic Subtopics

1. Electrostatics Electric Charge; Coulomb’s law; Electric Field; Gauss’s law; ; Application of Gauss’s law; Electric filed due to surface and volume charge distribution; electric field due to dipole;

2. Electric Potential

Electric potential; Potential due to point charge, due to collection of point charges; surface and volume charge distribution; due to dipole; Poisson’s and Laplace equation (without solution)

3. Capacitors & Dielectrics

Capacitance; Calculating capacitance; Energy storage in an electric field; Capacitor with dielectric; Dielectric (an atomic view); Dielectrics and Gauss’s Law

4. Current and Resistance

Electric current & density; Ohm’s law, microscopic view of Ohm’s law; semiconductor and superconductivity

5. DC Circuits Calculating current in a single loop & multiple loops; Voltage at various elements of a loop; Use of Krchoff’s Ist and 2nd law; Thevenin theorem; Norton theorem and superposition theorems; Transient behaviour of RC circuit

5. Magnetic Field Magnetic Field; Definition of B; Magnetic Force on a current; Torque on a Current Loop; The Hall Effect; Circulation Charge; The Cyclotron; The Thomson Experiment;

6. Ampere’s Law The Bio-Savart Law and its applications; Ampere’s Law; Magnetic Lines of induction; Two Parallel Conductors; Solenoids and Toroids;

7. Faraday’s Law Faraday’s Law of Induction; Lenz’s Law; Motional emf; Induced electric field; The Betatron; Induction; LR Circuit (transient behaviour); Inductance and relative motion;

8. Magnetic Gauss’s law for magnetism; atomic and nuclear

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Properties of Matter

magnetism; Magnetization; Magnetic materials

9. AC Circuits AC current; AC current in resistive, inductive and capacitative elements; RLC series and parallel circuits; Power in AC circuits

10 Maxwell’s Equations

Displacement current; Maxwell’s Equations; The wave equation; Energy Transport and Poynting Vector





2. Electromagnetic Simulations, CUPS course, John Wiley & Sons 3. Foundations of Electromagnetic Theory by J. R. Reitz Narosa

Publishing House





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PHYS 2401: General Physics IV Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 4th Semester e-mail Name of the Course General Physics IV Course no. PHYS 2401 Credit Hours 4


Pre-requisite PHYS 1101, PHYS 1201, PHYS 2301 Follow-up Advance Course in Physics Category Core course Aim The course will introduce modern physics and its applications Objectives At the completion of the course student will be able to:

1. Understand basic principal of modern physics and its applications. 2. Be able to solve relevant numerical problems.

Syllabus Sr. Major Topics

Subtopics

1. Special Theory of Relativity

Inertial and non inertial frame; Postulates of Relativity; Lorentz transformation and its consequences (time dilation and length contraction); Transformation of velocity; Variation of mass; relativistic momentum and energy; Energy mass relation

2. Origin of Quantum Theory

Black body radiation; Stefan, boltzmann, Wien and Planck’s law-consequences; Quantization of energy; Photoelectric effect; Einstein’s photon theory; The Compton effect; Line spectra

3. Wave Nature of Matter

Wave behaviour of particle; De Broglie’s hypothesis; Wave packets and particles; Heisenberg’s uncertainty principle; Wave function (its definition and probability interpretation); Trapped particles; The correspondence principle

4. Quantum Mechanic

Linear operators; Eigen values and functions; Postulates of QM; momentum and energy operators; Schrödinger equation and its application to free particle, potential well and step functions

5. Atomic Physics

Bohr’s theory (Review); Frank. Hertz experiment; Atomic spectra; Angular momentum of electron; Orbital angular momentum; Spin quantization; Boh’s Magnetron; X-ray spectrum; Moseley’s law; Pauli Exclusion Principle and its use in building periodic table

6. Nuclear Physics

Laws of radioactive decay; Half life; Mean life; chain disintegration

7. Nuclear Reactions

Basic nuclear reactions; Q-Value; Nuclear fission; Liquid drop model; Nuclear fusion in stars





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2. Modern Physics Simulations, CUPS course, John Wiley & Sons Instructional aids/Resources




Quiz Mid 25% Paper

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PHYS 1202: Physics Lab I Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 2th Semester e-mail Name of the Course Physics Lab I Course no. PHYS 1202 Credit Hours 2 Pre-requisite PHYS 1101 & Accompanying PHYS 1201 Follow-up PHYS 2302 Category Core course Aim The Lab will cover the experiment in Mechanics, Oscillations, Waves and Optics Objectives At the completion of the Lab student will be able to:

1. Verify the various laws of mechanics, wave and oscillation and optics. 2. Learns different techniques of analyzing and presenting scientific data.

Syllabus 1. Modulus of Rigidity by Static & Dynamics Methods (Maxwell’s needle, Barton’s Apparatus)

2. To study the damping features of an oscillating system using simple pendulum of variable mass.

3. Measurement of viscosity of liquid by Stoke’s/Poiseulli’s method. 4. Surface tension of water by capillary tube method. 5. To determine the value of “g” by compound pendulum/Kater’s

Pendulum. 6. To study the dependence of Centripetal force on mass, radius, and

angular velocity of a body in circular motion. 7. Investigation of phase charge with position in traveling wave and

measure the velocity of sound by CRO. 8. Determination of moment of inertial of a solid/hollow cylinder and a

sphere etc. 9. To determine thermal emf and plot temperature diagram. 10. Determination of temperature coefficient of resistance of a given wire. 11. To determine Horizontal/Vertical distance by Sextant. 12. The determination of wavelength of Sodium lines by Newton’s Rings. 13. The determination of wavelength of lingh/laser by Diffraction grating. 14. Determination of wavelength of sodium light by Fresnel’s bi-prism. 15. The determination of resolving power of a diffraction grating.

Text Book(s) 1. Physics Vol.2, 4th (1992) and 5th (2002) Edition by Halliday, Resnic and

Krane, John Wiley and Sons 2. Fundamental of Physics 5th and 6th Edition by Halliday & Resnic, John

Wiley and Sons





Teaching Strategies 1. Lecturing

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2. Topic discussion 3. Individual project/Assignments 4. Class presentation 5. Questioning and explanation


Quiz Mid 25% Paper

Assessment


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PHYS 2302: Physics Lab II Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 3rd Semester e-mail Name of the Course Physics Lab II Course no. PHYS 2302 Credit Hours 2 Pre-requisite PHYS 1201 & Accompanying PHYS 2301 Follow-up PHYS 2303 Category Core course Aim The Lab will cover the experiment in electricity and magnetism. Objectives At the completion of the Lab student will be able to:

1. Verify the various laws of electricity and magnetism. 2. Learns different techniques of analyzing and presenting scientific data.

Syllabus 1. Measurement of resistance using a Neon flash bulb and condenser. 2. Conversion of galvanometer into Voltmeter & an Ammeter. 3. Calibration of an Ammeter and a Voltmeter by potentiometer 4. Charge sensitivity of a ballistic galvanometer. 5. Comparison of capacitance by ballistic galvanometer 6. To study the BH curve & measuring the magnetic parameters. 7. Measurement of low resistance coil by a Carey Foster Bridge. 8. Resonance frequency of an acceptor circuit. 9. Study of the parameter of wave i.e. Amplitude, phase and time period of

a complex signal by CRO. 10. Measurement of self/mutual inductance 11. Study of electric circuits by black box. 12. Determining resistances using a Wheatstone bridge









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PHYS 2403: Physics Lab III Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 4th Semester e-mail Name of the Course Physics Lab III Course no. PHYS 2402 Credit Hours 2 Pre-requisite PHYS 2301 & Accompanying PHYS 2401 Follow-up Advanced Lab in Physics Category Core course Aim The Lab will cover the experiments modern physics Objectives At the completion of the Lab student will be able to:

1. Verify the laws which are basis of modern physics. 2. Learns different techniques of analyzing and presenting scientific data.

Syllabus 1. Determination of e/m of an electron 2. Ionization potential of mercury. 3. To study the characteristic curves of a G.M. counter and use it to

determine the absorption co-efficient of Beta particle in Aluminum. 4. Determination of range of Alpha particles 5. Mass absorption coefficient of Pb for gamma using G.M. counter.

Text Book(s) 1. Physics Vol.2, 4th (1992) and 5th (2002) Edition by Halliday, Resnic and

Krane, John Wiley and Sons 2. Fundamental of Physics 5th and 6th Edition by Halliday & Resnic, John

Wiley and Sons Reference Books/Material






Quiz Mid 25% Paper

Assessment


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PHYS 2402: Electronics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 4th Semester e-mail Name of the Course Electronics Course no. PHYS 2402 Credit Hours 3


Pre-requisite PHYS 2301 Follow-up Advance Courses in Physics Category Core course Aim The course will introduce basic principle of electronics Objectives At the completion of the course student will be able to:

1. Understand basic principal of electronics. 2. Be able to solve relevant numerical problems.

Syllabus Sr. Major Topic Subtopics 1. Semiconductors Classification of conductor, semiconductors and

insulators by Band Theory; P-type & N-type; Doping; PN junction;

2. Diode theory and Circuit

Characteristics of diode; Ideal Diode; Models of diode; The diode as rectifier; Surge current; The zener diode; Optoelectronic devices; The schottkydiode

3. Bipolar Transistors

PNP and NPN transistors; Characteristics of transistors; Model of transistor; Transistor biasing

4. Transistor as amplifier

Transistor as voltage, current and power amplifier

5. Field-Effect transistors

The JFET; The biased JFET; Characteristics of JFET; FET circuits

6. Frequency effects Frequency response of an amplifier; Miller’s theorem; High Frequency FET analysis

7. OP-AMP OP-AMP theory; OP-AMP negative feedback; Linear OP-AMP circuits; Non-linear OP-AMP circuits;

Text Book(s) 1. Electronic Principles by Paul Malvino, McGraw-Hill International


1. Electronics Circuits and Systems by J.D. Ryder (1976) 2. Electronics Devices by T.L. Floyd, Prentice-Hall (1996) 3. Electronic Devices and Circuit Theory by Boylestad and Nashhelsky,

Prentice-Hall (1997) Instructional aids/Resources


Teaching Strategies 1. Lecturing 2. Topic discussion 3. Individual project/Assignments

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4. Class presentation 5. Questioning and explanation


Quiz Mid 25% Paper

Assessment


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PHYS 2404: Electronics Lab Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 4th Semester e-mail Name of the Course Electronics Lab Course no. PHYS 2404 Credit Hours 2 Pre-requisite Accompanying PHYS 2402 Follow-up Advance Courses in Physics Category Core course Aim The Lab covers experiments in electronics Objectives At the completion of the course student will be able to:

1. Develop and study characteristics of different electronics circuits. 2. Be able to use different instrument in the study of electronics circuits.

Syllabus 1. Characteristics of a semiconductor Diode. 2. To construct a power supply and study the rectified wave form, ripple

factor and regulation (without regulator). 3. To construct a voltage-regulated power supply with Zener diode. 4. Characteristics of Transistors. 5. To construct a single stage CE transistor voltage amplifier and study

gain, input impedance, output impedance, half power points by sine/square wave testing and effect of bias on the output and measurement of distortion.

6. To construct a source follower FET voltage amplifier and study gain, input impedance, output impedance, half power points by sine/square wave testing.

7. To construct an R-C oscillator and compare it with a standard frequency. 8. To construct a Hartley or Colpitts oscillator and measure it frequency. 9. To construct and study the wave forms at the base and collector of the

transistors of a free running a multivibrator. 10. To construct and study of the height, duration and time period of the

output pulses in a monostable and bistable multivibrators with reference to the input trigger.

11. To construct from discrete components OR, AND, NOT, NAND, NOR, exclusive OR circuits and verify their truth tables.

12. Study of wave shaping circuits of diode, integrators and differentiators. 13. To construct the operational amplifier (741) by using discrete

components and study its frequency response.

Text Book(s) 1. Electronic Principles by Paul Malvino, McGraw-Hill International



Prentice-Hall (1997) Instructional aids/Resources


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Quiz Mid 25% Paper

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PHYS 3501: Classical Mechanics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 5th Semester e-mail Name of the Course Classical Mechanics Course no. PHYS 3501 Credit Hours 4


Pre-requisite PHYS 1101, PHYS 1201 Follow-up PHYS 3502 Category Core course Aim The course introduces Classical Mechanics at graduate level. Objectives At the completion of the course student will be able to:

1. Solve advance problems of mechanics. 2. Learn different formalism of classical mechanics. 3. Learn basis principles of non linear dynamics

Syllabus Sr. Major Topics Subtopics 1. Newtonian

Mechanics in Moving Coordinate system

Introduction to operator D; Newton’s equation in rotating coordinate system and in system with arbitrary relative motion; Free Fall on the rotating earth; perturbation calculation; Method of successive approximation; Exact solution; Foucault’s pendulum; Solution of its DEs and discussion of solution

2. Mechanics of systems of particles

Degree of freedom; Degree of freedom of rigid body; Linear and angular momentum of many-body system; Energy law of many body system;

3. Mechanics of Rigid Bodies

Rotation about fixed axis & moment of inertial (Review); The physical pendulum; Rotation about a point; Tensor of inertia; KE of rotating rigid body; Principle axes of inertia; Tensor of inertial in the system of principle axes; Ellipsoid of inertial Theory of top; Heavy symmetrical top; The Euler angles

4. Lagrange Formalism

Constraints; Generalized coordinate; Quantities of mechanics in generalized coordinates; D’Almbert Principle and Derivation of Lagrange equations; Lagrange equations for nonholonomic constraints

Central Force Problem

Two body problem and its reduction to one body problem; equation of motion solution of one body problem; Kepler’s laws; Lab and CM systems; Rutherford scattering

5. Hamilton’s Formalism

Legendre transformation and Hamilton’s equations of motion; Calculus of variation and Hamilton’s principle; Derivation of Lagrange’s equation from Hamilton’s principle; Phase space and Liouville’s theorem

6. Canonical Transformations

The canonical transformation and its examples; Lagrange’s and Poisson bracket; Integrals of motion; Poisson’s theorem

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7. Hamilton_Jacobi Theory

Hamilton-Jacobi theory; Solution of Hamilton-Jacobi DE for some elementary systems

8. Non linear Dynamics

Dynamics systems; Stability of Time-Dependent Path; Bifurcation; Lyapunov exponents and Chaos; Systems with Chaotic dynamics

Text Book(s) 1. Classical Mechanics, by H. Goldstein, Addison-Wesley, Reading (1950) 2. Classical Mechanics by Greiner, Springer (2003)


1. Classical Mechanics Simulations, John Wiley & Sons (1996) 2. Classical Mechanics, by V.D. Barger and M. G. Olsson, McGraw-Hill,

(1995) 3. Classical Mechanics, by Atam and P. Arya, Prentice Hall Int. Inc.

(1998)





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PHYS 3502: Electromagnetic Theory Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 5th Semester e-mail Name of the Course Electromagnetic Theory Course no. PHYS 3501 Credit Hours 4


Pre-requisite PHYS 2301, MATH 2301 Follow-up PHYS 3502 Category Core course Aim The course introduces electromagnetic theory at graduate level. Objectives At the completion of the course student will be able to:

1. Solve advance problems of electromagnetism. 2. Apply Maxwell’s equation to explain various wave phenomena. 3. Solve simple problems of electrodynamics 4. Introduce covariant form of Maxwell’s equations

Syllabus Sr. Major Topics Subtopics 1. Fundamental

Concept Recapitulation of the fundamental concepts;

2. Electrostatics Poisson’s and Laplace’s equations; Properties of solution of Laplace’s equation; Solution of Laplace’s equation in spherical, cylindrical and Cartesian coordinates; Conducting sphere in a uniform electric field; Electrostatic images; Point charge and conducting sphere; Line charge and line images; system of conducting spheres;

2 Electrostatic Field in Dielectric Media

Polarization; Field outside a dielectric medium; Electric field inside a dielectric; Gauss’s law in a dielectric; Electric susceptibility and dielectric constant; Point charge in a dielectric fluid; Boundary conditions on the field vector at the interfaces b/w different medium;

4. Electrostatic energy

PE of a group of point charges; Electrostatic energy of a charge distribution; Energy density of an electrostatic field; Energy of system of charged conductors; Coefficients of capacitance

5. Magnetostatics Field

Current & current density; equation of continuity; Ohm’s law; steady current in a continuous media; Electrostatic equilibrium; Magnetic induction; Forces on a current carrying conductors; Biot and Savart law and its applications; Ampere’s law; Magnetic vector potential; Magnetic field of a distant circuit;

6. Magnetic properties of Matter

Magnetization; Magnetic field produced by magnetized material; magnetic scalar potential and magnetic pole density; Magnetic intensity; The field equations; Magnetic susceptibility and permeability; Hysteresis; Boundary conditions on the field vector at the interfaces b/w different medium

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7. Electromagnetic Induction and Magnetic energy

Electromagnetic induction; Magnetic energy of coupled circuits; Energy density in the magnetic field

8. Maxwell’s Equations and their Applications

Generalization of Ampere’s law; Maxwell’s equations; Electromagnetic energy; The wave equations; Boundary Conditions; The wave equation with sources; Plane wave solution in non-conducting media; Polarization; Plane waves in conducting media; Spherical waves; Reflection and refraction at the boundary of two non-conducting media (normal and oblique incidence); Brewster’s angle; Reflection from a conducting plane; The radiation from an oscillating dipole; Covariant formulation Maxwell’s equation; The field uniformly moving point charge

Text Book(s) 1. Classical Electrodynamics by Jackson, John Wiley & Sons, (1975) 2. Foundations of Electromagnetic Theory by J. R. Reitz, Narosa

Publishing House (1979) Reference Books/Material

1. Introduction to Electrodynamics by D. Griffiths Prentice Hall, (1989) 2. Electromagnetic Simulations, John Wiley & Sons (1996)





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PHYS 3601: Wave and Optics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 6th Semester e-mail Name of the Course Wave and Optics Course no. PHYS 3601 Credit Hours 3


Pre-requisite PHYS 3501 Follow-up Category Core course Aim The course introduces wave theory and optics at graduate level. Objectives At the completion of the course student will be able to:

1. Solve advance problems of oscillations. 2. Study of refraction, reflection, Interference, diffraction and polarization. 3. Learn fundament principles of geometric optics 4. Study of different wave equation in physics

Syllabus Sr. Major Topics Subtopics 1. Vibrations of

Coupled Mass Points

The vibrating chain; Eigen frequencies of the vibrating chain; Vibration of two coupled mass points in 2D; Three masses on a string;

2. The Vibrating String

Wave equation of vibrating string; solution of the wave equation; KE and PE of vibrating string; Normal vibrations; Fourier series

3. The Vibrating Membrane

The vibrating membrane; Derivation of differential equations; Solution of DE (rectangular membrane); Inclusion of the boundary conditions; Eigen frequency; Degeneracy; Nodal lines; General solution (inclusion of the initial conditions); Superposition of node line figures; The Circular membrane

4 Reflection and Transmission

Reflection and Transmission of Waves on Strings; Huygen’s Principle; Huygen’s Principle and Laws of Reflection and Refraction; Total Internal Reflection; Fermat’s Principle

5 Interference, Diffraction and Polarization

Analytical Treatment of Interference; Typical Cases of Interference Phenomena; Interferometers; Analytical Treatment of Diffraction; Resolving Power; Double Slit Diffraction Pattern; Diffraction Grating; X-ray Diffraction; Bragg’s Law; Polarization; Linear, and Elliptical Polarization of Standing and Traveling Waves;

6. Geometric Optics

The fundamental Principle of Fermat; Ray Tracing in Geometrical Optics; Applications of ray tracing in geometrical optics.

7. Wave equations Classical; Schrödinger, Diffusion; Klein-Gordan wave equations; General Solution of wave equation in 1-dimensions; Initial and Boundary conditions

Text Book(s) 1. Classical Mechanics by Greiner, Springer (2003) 2. Wave and Optics Simulations, John Wiley & Sons (1995)

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1. te board and markers 2. OHP 3. Transparence sheets 4. Multimedia Projector 5. Soft boards 6. Pointer 7. Software (PowerPoint) 8. Photocopy machine/photocopying facility



Quiz Mid 25% Paper

Assessment


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PHYS 3602: Digital Electronics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 6th Semester e-mail Name of the Course Digital Electronics Course no. PHYS 3602 Credit Hours 3


Pre-requisite PHYS 2402 Follow-up Advance Courses in Physics Category Core course Aim The course will introduce basic principles of digital electronics Objectives At the completion of the course student will be able to:

1. Fundamental principles of digital electronics 2. Basic components of combinational and sequential logic. 3. Understand the components and functioning of processors


Subtopics

1. Digital electronics

Binary and other number systems; Logic gates; Boolean algebra; combinational logic; sequential logic; Registers; counters and memory units; Register transfer logic

2. Processor logic design

Processor organization; Arithmetic logic unit; Status register; Shifter; Accumulator

3. Control logic design

Control organization; Hard-Wired Control; Control of processor unit

4. LabView Introduction to LabView Package Text Book(s) 1. Digital Logic and Computer Design by M. M. Mano, Prentice-Hall Inc

(1995). 2. Digital Fundamental by T.L. Floyd, Prentice-Hall (1994)



Prentice-Hall (1997)




2. Topic discussion 3. Individual project/Assignments 4. Class presentation 5. Questioning and explanation

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PHYS 4701: Quantum Mechanics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 7th Semester e-mail Name of the Course Quantum Mechanics Course no. PHYS 4701 Credit Hours 4


Pre-requisite PHYS 2401, MATH 3501, MATH 3601 Follow-up PHYS 4801, PHYS4701 Category Core course Aim The course introduces Quantum Mechanics at graduate level. Objectives At the completion of the course student will be able to:

1. Understand the fundament principles of Quantum Mechanics. 2. Solve basic problems of quantum mechanics in 1D and 3D 3. Understand the theory of angular momentum 4. Study of system of identical particles. 5. Work in approximation methods in quantum mechanics.

Syllabus Sr. Major Topics Subtopics

1. Breakdown of Classical Concepts

Qualitative study of the concepts of classical mechanics; Double slit electron beam experiment and failure of concepts of classical mechanics

2. Formulation of QM

Mathematical preliminaries (Hilbert space; operators; eigen values and vectors; operators algebra; Representation theory; related theorem without proof); Postulates of QM; position and momentum representation; Quantum Dynamics; Schrödinger and Heisenberg picture; stationary states;

3. One Dimensional systems

The potential step; potential well and bound states; Potential barrier; tunneling; alpha decay; Delta function potential; Kronig-Penny model; Harmonic oscillator and number representation

4. Angular Momentum

Angular momentum operator; Eigen value and eigen functions of L2 and Lz

5. Central Potential

Solution of stationary states in central potential

6. Identical Particles

Indistinguishability of identical particles; systems of identical particles; quantum dynamics of identical particles

7. Perturbation Theory

Time independent perturbation theory and its applications; Damped harmonic oscillator; hydrogen like atom in magnetic field; Time dependent perturbation theory; Transition probability

Text Book(s) 1. Understanding Quantum Physics, Vol. I & II, by M. A Morison Prentice Hall Inc. (1990)

2. Quantum Mechanics by J. L. Powell and B. Crasemann, Addision-Wesley, (1961)


1. Quantum Mechanics Simulations, John Wiley & Sons (1996) 2. A Text Book of Quantum Mechanics by P.M. Mathew & K. Venketeson

(1991)

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3. Quantum Mechanics by S. Gasiorowicz, Wiley (1996)





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PHYS 4702: Thermal and Statistical Physics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 7th Semester e-mail Name of the Course Thermal and Statistical Physics Course no. PHYS 4702 Credit Hours 3


Pre-requisite PHYS 2401, MATH 3501 Follow-up Category Core course Aim The course introduces Thermal and Statistical Physics at graduate level. Objectives At the completion of the course student will be able to:

1. Basic principles of equilibrium thermodynamics. 2. Basic principles of statistical mechanics. 3. Study of partition function and different statistical systems


1. Equilibrium Thermodynamics

Basic postulates; Fundamental equations and equation of states; response functions; Maxwell’s relation; reduction of derivative;

2. Elements of Probability Theory

Probabilities; Distribution functions; Statistical interpretation of entropy; Bolzmann H-theorem

3. Formulation of Statistical Mechanics

Ensembles; Counting of states (in classical and quantum mechanical systems) Boltzmann distribution

4. Partition Function Relation with thermodynamics variables; Examples (collection of simple harmonic oscillators, Pauli and Van Vleck paramagnetic); Theorem of equipartition of energy

5. Statistical Systems Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac and Planck statistical systems; Example of these systems (Back body radiations, Gas of electrons in solids)

Text Book(s) 1. Fundamental of Statistical and Thermal Physics by R. Reif (1988) Reference Books/Material

1. Berkley Physics Course on Statistical and Thermal Physics by R. Reif (1988)

2. Elementary Statistical Physics by C. Kittle 3. Thermal and Statistical Physics Simulations, John Wiley & Sons (1996)




2. Topic discussion

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3. Individual project/Assignments 4. Class presentation 5. Questioning and explanation


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PHYS 4801: Solid State Physics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 8th Semester e-mail Name of the Course Solid State Physics Course no. PHYS 4701 Credit Hours 3


Pre-requisite PHYS 3502, PHYS 4701 Follow-up Category Core course Aim The course introduces Solid State Physics at graduate level. Objectives At the completion of the course student will be able to:

1. Learn the theory of crystal structure. 2. Study the origin of thermal properties of solids. 3. Study the band theory. 4. Semiconductor physics. 6. Computation techniques in solid states physics.


1. Crystal Structure Periodic arrays of atoms; Fundamental types of lattices; Index system for crystal planes; Simple crystal structure; Direct imaging of atomic structure; Nonideal crystal structure

2. Reciprocal Lattice Diffraction of waves by crystal; Scattered wave amplitude; Brillouin zones; Fourier analysis of the basis

3. Crystal Binding and Elastic Constants

Crystal of inert gases; Ionic crystals; Covalent crystals; Metals; Hydrogen bonds; Analysis of elastic strains; Elastic compliance and stiffness constants; Elastic waves in cubic crystal

4. Crystal Vibrations Vibrations of crystals with monatomic basis; Two atoms per primitive basis; Quantization of elastic waves; Phonon momentum; Inelastic scattering by phonons;

5. Thermal Properties Phonon heat capacity; Inharmonic crystal interactions; Thermal conductivity; electronic heat capacity

6. Free Electron Theory

Energy levels in 1D; Effect temperature on the Fermi-Dirac distribution; Free electron gas in 3D; Heat capacity of electron gas; Electrical conductivity and Ohm’s law; Motion in magnetic field; Thermal conductivity of metals

7. Band Theory Nearly free electron model; Bloch function; Krnig-Penney model; Wave equation of electron in a periodic potential. Number of orbital in a band

8. Semiconductors Theory of semiconductors; Extrinsic semiconductors; Mobility of current carriers; Minority carriers; Life time; Surfaces; Contacts; Semiconductor devices;

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9. Computational Techniques

Density functional theory, Hartee Fock Methods, LAPW method

Text Book(s) 1. Introduction to Slid State Physics by C. Kittle, 7th Edition, John Wiley & Sons, Inc. (1996)

2. Solid State Physics by J. S. Blakemore, Cambridge University Press, (1991)


1. Solid State Physics Simulations, John Wiley & Sons (1996)





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PHYS 4802: Nuclear and Particle Physics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 8th Semester e-mail Name of the Course Nuclear and Particle Physics Course no. PHYS 4802 Credit Hours 3


Pre-requisite PHYS 4701 Follow-up Category Core course Aim The course introduces Nuclear and Particle Physics at graduate level. Objectives At the completion of the course student will be able to:

1. Learn different nuclear models and explain the nuclear properties. 2. Theory of nuclear forces and its application to different nuclear

reactions. 3. Theories of radioactive decay 4. Study of different mechanics of particles acceleration and detections. 5. Introduction of reactor physics 6. Introduction of elementary particles and their interaction


1. Nuclear Properties Size and mass of the nucleus; nuclear spin; magnetic dipole moment; quadrupole moment; parity and statistics

2. Nuclear Model Liquid drop model; Shell model; Collective model

3. Nuclear Forces Central and non central forces; Nuclear potential (Exponential, square-well, Gaussian and Yukawa); Yukawa’s theory of nuclear forces

4. Nuclear Reactions Direct reactions; Reaction involving the formation of compound nucleus; Stripping reactions; Resonance reactions; Bohr’s theory of compound nucleus and its limitations; Breit-Wigner one level formula including the effect of angular momentum

5. Theories of Radioactive Decay

Alpha Decay; Energy; range; ionization power and stopping power of alpha particles; QM theory of Alpha decay; Alpha particle spectra; Long range particles and fine structure; Nuclear energy level Beta Decay; Energy; velocity and range of beta particles; Fermi theory of beta decay; Neutrino hypothesis; Direct evidence of anti-neutrino; Non conservation of parity Gamma Decay; Energy; range and nature of gamma rays; Theory of gamma decay; Classification of gamma decays

6. Particle Accelerators

Van de Graff generator; Cyclotron; Synchrocyclotron; Betatron; Electron-Synchrotrons; Proton-Synchrotron; Alternating-Gradient Synchrotron; Linear Accelerator

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7. Nuclear Radiation Detection and Measurements

Interaction of nuclear radiation with matter; Photographic emulsions; Gas-filled detectors; Scintillation counters and solid state detectors;

8. Reactor Physics Nuclear fission and its characteristics; Energy release; Fission products; The chain reaction; Controlled fission reactions; Types of nuclear reactors

9. Elementary Particles

Elementary particles classification; ; Strong, electromagnetic and weak interactions; Conservation laws; The quark model

Text Book(s) 1. Nuclear and Particle Physics by Burcham, E. E. and Jobes, M., Longman, (1995)

2. Introduction to Nuclear and Particle Physics by Das, A. and Ferbel, T. John Wiley and Sons, (1994)

3. Nuclear and Particle Physics by Williams, W.S.C., Oxford University Press, (1995)


1. Nuclear and Particle Physics Simulations, John Wiley & Sons (1996) 2. Elementary Particle Physics by D. Griffiths, John Wiley and Sons,

(1987)





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PHYS 3503: Advance Physics Lab I Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 2th Semester e-mail Name of the Course Advance Physics Lab I Course no. PHYS 3503 Credit Hours 2 Pre-requisite PHYS 2301, PHYS 2401 Follow-up PHYS 3603 Category Core course Aim The Lab covers the advance experiments in modern physics and optics Objectives At the completion of the Lab student will be able to:

1. Verify the various laws in modern physics and optics. 2. Learns different techniques of analyzing and presenting scientific data.

Syllabus 1. Measurement of wavelengths of sodium light, difference of wave lengths and thickness of thin film e.g. mica using Michelson interferometer

2. The study of spectra using Fabry-Perot interferometers 3. The determination of Cauchy’s constants using spectrometer 4. To study some aspects of Ferromagnetism by drawing B-H curve. 5. Measurement of speed of light using laser source rotating mirror

method. 6. To measure the wave length of light by Fresnel biprism 7. Study of sound with help of Noise-Level meter. 8. To determine e/m of an electron using a fine beam tube 9. To study the Hall effect in an n-type/p-type semiconductor or a metal

Text Book(s) Reference Books/Material





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PHYS 3603: Advance Physics Lab II Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 6th Semester e-mail Name of the Course Advance Physics Lab II Course no. PHYS 3603 Credit Hours 2 Pre-requisite PHYS 2301, PHYS 2401 Follow-up Category Core course Aim The Lab covers the advance experiments in modern physics. Objectives At the completion of the Lab student will be able to:

1. Verify the various laws in modern physics. 2. Learns different techniques of analyzing and presenting scientific data.

Syllabus 1. To measure the critical potential of mercury by Frank-Hertz Method. 2. To measure the Planck’s constant by studying photoelectric effect. 3. To measure work function of metal and verification of Rihardson’s

equation. 4. Determination of dielectric constant of liquid and solid. 5. To determine the characteristic of G. M. tube and measure the range and

maximum energy of beta particles. 6. Measurement of half-life of radioactive source. 7. Characteristics of G. M. counter and study of fluctuations in random

process. 8. To determine the charge of an electron by Millikan’s oil drop method.

Text Book(s) Reference Books/Material





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MATH 1101: Differential Calculus Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 1st Semester e-mail Name of the Course Differential Calculus Course no. MATH 1101 Credit Hours 4


Pre-requisite F.Sc/A-Level Physics Follow-up MATH 1201 Category Core course Aim The course introduces the subject of differential calculus at undergraduate level. Objectives At the completion of the course student will be able to:

1. Understanding the concepts of functions, limit and differentiation. 2. Study the application of differentiation 3. Be able to solve relevant numerical problems. 4. Be able to use calculus in physics and advance courses in mathematics

Syllabus Sr. Major Topic Subtopic 1. Preliminaries Real Number and Real line; Properties of Real

Numbers; Absolute value and inequalities; Solution of equation containing inequalities

2. Functions Function; Bounded sets and functions; Graphs of functions; Shifting Graph; Trigonometric functions;

3. Limit and Continuity

Limits; Rules for finding limits; Target value and formal definition of limit; Continuity; Properties of continues functions

4. Derivatives Derivation of a function; Rules of differentiations; Derivatives of algebraic and transcendental functions; Implicit Differentiation and Rational exponent; Higher Derivatives; Leibniz theorem; Rolle’s theorem; Mean Values theorems

5. Applications of Derivatives

Increasing and Decreasing Functions; Maxima and Minima; Test of Local extreme values; Concavity; Graphing in Cartesian and Polar coordinates; Arc length Intrinsic and Pedal equations; Curvature; Evolute; Envelope; Optimization; Linearization and differentials; Newton’s Method;

6. Multivariable function and partial derivations

Functions of Several variables; Limits and Continuity; Partial Derivatives; Differentiability; Linearizations; Chain rules; Implicit functions; Directional derivatives; Partial derivatives with constrained variables

Text Book(s) 1. Calculus 5/e by Howard Antony, John Wiley and Sons


1. Calculus with Analytic Geometry by E. W. Swokowski, PWS Publishers, Boston

2. Calculus and Analytic Geometry by G.B. Thomas and R.L. Finney, Addison-Wesley Publishing Company (1996)

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MATH 1102: Discrete Mathematics Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 1st Semester e-mail Name of the Course Discrete Mathematics Course no. MATH 1102 Credit Hours 3


Pre-requisite F.Sc/A-Level Physics Follow-up COMP 2401 Category Core course Aim The course introduces the subject of Discrete Mathematics at undergraduate

level. Objectives At the completion of the course student will be able to:

1. Introduce the concepts of Calculus of proposition, set theory and functions

2. Study the methods of mathematical reasoning 3. Learn the concepts of relations and their properties 4. Learn the concepts of Graphs and Trees

Syllabus Sr. Major Topic Sub topic

1. The Foundations

Calculus of Propositions; Simple and compound propositions; Connectives (AND, OR, XOR); truth tables; Tautologies and contradictions; Logical Equivalence; Propositional Functions and Quantification

2. Sets and Functions

Set Operations; Venn’s Diagrams; De Morgan’s Laws; Functions for set of integers to set of integers; Injective; Subjective and Bijective functions; Ceiling and floor functions and their applications

3. Sequences and Summations

Sequences from set of non-negative integers to set of integers; Summations; Summation indices

4. Mathematical Reasoning

Methods of proof; Mathematical induction; Recursive definitions and recursive algorithms

5. Counting The basics of counting; The pigeonhole principle; Permutations and Combinations

6. Relations Relations and their properties; Representing Relations; Equivalence relations; Partial ordering

7. Graphs Introduction to graphs; Graph terminology and Graph isomorphism; Connectivity; Euler’s and Hamilton’s path; Shortest Path Problems

8. Trees Introduction to Trees; Application of Trees Text Book(s) 1. Discrete Mathematics and Its Applications (4th Edition) by Kenneth H.

Rosern


1. Discrete Mathematics by K.A. Ross & C.R.B. Wright, Prentice-Hall 2. Discrete Mathematical Structures with Application to Computer Science

by J.P. Trembley & R.Manoher


1. White board and markers 2. OHP

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3. Transparence sheets 4. Multimedia Projector 5. Soft boards 6. Pointer 7. Software (PowerPoint) 8. Photocopy machine/photocopying facility



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MATH 1101: Differential Calculus Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 1st Semester e-mail Name of the Course Differential Calculus Course no. MATH 1101 Credit Hours 4


Pre-requisite F.Sc/A-Level Physics Follow-up MATH 1201 Category Core course Aim The course introduces the subject of differential calculus at undergraduate level. Objectives At the completion of the course student will be able to:

5. Understanding the concepts of functions, limit and differentiation. 6. Study the application of differentiation 7. Be able to solve relevant numerical problems. 8. Be able to use calculus in physics and advance courses in mathematics

Syllabus Sr. Major Topic Subtopic 1. Preliminaries Real Number and Real line; Properties of Real

Numbers; Absolute value and inequalities; Solution of equation containing inequalities

2. Functions Function; Bounded sets and functions; Graphs of functions; Shifting Graph; Trigonometric functions;

3. Limit and Continuity

Limits; Rules for finding limits; Target value and formal definition of limit; Continuity; Properties of continues functions

4. Derivatives Derivation of a function; Rules of differentiations; Derivatives of algebraic and transcendental functions; Implicit Differentiation and Rational exponent; Higher Derivatives; Leibniz theorem; Rolle’s theorem; Mean Values theorems

5. Applications of Derivatives

Increasing and Decreasing Functions; Maxima and Minima; Test of Local extreme values; Concavity; Graphing in Cartesian and Polar coordinates; Arc length Intrinsic and Pedal equations; Curvature; Evolute; Envelope; Optimization; Linearization and differentials; Newton’s Method;

6. Multivariable function and partial derivations

Functions of Several variables; Limits and Continuity; Partial Derivatives; Differentiability; Linearizations; Chain rules; Implicit functions; Directional derivatives; Partial derivatives with constrained variables





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MATH 1201: Analytical Geometry and Integral Calculus Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 1st Semester e-mail Name of the Course Analytical Geometry and Integral Calculus Course no. MATH 1201 Credit Hours 4


Pre-requisite MATH 1101 Follow-up MATH 2301 Category Core course Aim The course introduces the subject of Analytical Geometry and Integral Calculus

at undergraduate level. Objectives At the completion of the course student will be able to:

1. Introduce plane analytical geometry and analytical geometry of 3D 2. To study the concept of integration, relevant theorems and techniques of

evaluating integrals. 3. Study definite integrals and its applications 4. Study multiple integrals and its applications.

Syllabus Sr. Major Topics Sub topics

1. Plane Analytical Geometry

Translation and rotation of rectangular axes; General equations of second degree; Polar coordinates; Polar equations of conics; Properties of parabola, ellipse and hyperbola; Tangents and normals; Parametric representations of Curves

2. Analytic Geometry of 3D

Rectangular coordinate system in space; Direction angles; Direction numbers; Equations of lines and planes in scalar and vector form; Skew lines; Shortest distance b/w skew lines; Cylindrical and spherical coordinates; Surfaces; Equation of sphere, cylinder, cone, ellipsoid paraboloid and hyperboloid ; Tangent planes and normal of surfaces;

3. Integration Antiderivative and indefinite integral; The definite integral as limit of a sum; Fundamental theorem of integral calculus; integration of various mathematical functions;

4. Techniques of Evaluating in Definite Integrals

Basic Integration Formulas; Integration by Parts; Trigonometric substitution;

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5. Definite Integral

Properties of definite integral; Substitution in Definite integral; Improper Integrations

6. Application of Integration

Area under the curve; Area between the curves; Finding volumes by slicing; Volumes of solids of Revolution; Length of plane curves; Area of surface of Revolution

7. Multiple Integral

Double and Triple Integrals; Area and Volume; Moment of Inertial; Centre of Mass









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MATH 1202: Linear Algebra Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 2nd Semester e-mail Name of the Course Linear Algebra Course no. MATH 1202 Credit Hours 4


Pre-requisite F. Sc/A-Level Follow-up MATH 3501 Category Core course Aim The course introduces the subject of linear algebra at undergraduate level. Objectives At the completion of the course student will be able to:

1. Learn the concept of vector spaces and related theorem 2. Studying representation theory, theory of matrices and determinants 3. Studying groups, related theorems and representations of groups

Syllabus Sr. Major Topic Subtopic

1. Linear Vector Spaces

Definition and examples of LVS; Linear independence; Basis Vector; Subspace; Linear functional on a LVS; Dual spaces

2. Inner Product LVS Definition of inner product spaces; examples; Orthogonality; The Gram-Schmidt process; The Schwarz inequality; Length of a vector;

3. Linear Operator Definition and examples Linear transformation; Related Theorems; Operator algebra; polynomial of operators; Functions of operators; Commutations; Operator valued function and derivative of operators; Conjugation of operators; Hermitian and unitary operators; Projection operators;

4. Representation Theory and Matrices

Representation of linear operators by matrices; Related theorems for the translation of operator algebra into Matrix algebra; Operations on Matrices; Change of bases and similarity transformations (Definition of Matrix; Algebra of matrices; some types of matrices; Determinate of a square matrix; Evaluation of determinates; Equivalence; Adjoint and inverse of a matrix)

5. Determinants and Traces

Determinant of a Matrix; Related Theorem; Inverse of a Matrix; Related Theorems; Elementary operations; Row-echelon form; Determinants of Products of Matrices; The Trace; Related Theorems; Direct sums and invariant subspaces; Solution of linear algebraic (homogeneous and non-homogeneous) systems of equations by the use of matrices.

6. Spectral Decomposition and Diagonalizations

Eigenvalues and Eigenvectors; Related Theorems; Eigen values of Hermitian Operators; Related Theorems;

7. Group Theory Group; Subgroup; Cyclic group; Permutations;

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Group of permutations; homomorphism and isomorphism, Group representations; Reducible and Irreducible representations

Text Book(s) 1. Elementary Linear Algebra by Howard Anton, John Wiley & Sons (1997)

2. Foundations of Mathematical Physics by Sardi Hassani, Prentice-Hall International (1991)

3. Linear Algebra by G. Hadley, Addison-Wesley (1987)






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MATH 1201: Statistics and Probability Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 2nd Semester e-mail Name of the Course Statistics and Probability Course no. MATH 1201 Credit Hours 3


Pre-requisite MATH 1101 Follow-up PHYS 2401 Category Core course Aim The course introduces the subject of statistics and probability at undergraduate


1. Learn the concept of descriptive statistics 2. Studying the theory of probability. Its fundamental concepts and

probability distributions 3. Learning the concepts of statistical inference 4. Learning the theory of error.

Syllabus Sr. Major Topic

Subtopic

1. Descriptive Statistics

Tabular representation of samples; Frequency; Graphical representation of samples; Mean and variance of a sample

2. Probability Theory

Fundament Concepts; Random experiments, Sample space, Events, Union and intersection of Events, Mutually exclusive events, Classical concept of Probability, Concept of Probability is statistics, Conditional probability, Independent events, Permutations and Combinations Probability Distributions; Random variables, Discrete distribution, Continuous distributions, Mean, Variance, and skewness of a distribution, Binomial, Poisson and Gaussian distributions, Probability distributions of several random variables

3. Statistical Inference

Estimations of parameters; Confidence Intervals; Testing of Hypotheses; Goodness of Fit; Analysis of variance; Regression analysis; Correlation analysis

4. Theory of Error

Types of errors; Causes of errors, Correlated and un-correlated errors, Propagation of errors

Text Book(s) 1. Introductory mathematical statistics by Erwin Kreyszig, John Wiley & Sons (1970)

2. Modern Mathematical Statistics by Edward J. Dudewicz John Wiley & Sons (1988)



1. White board and markers 2. OHP 3. Transparence sheets 4. Multimedia Projector

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5. Soft boards 6. Pointer 7. Software (PowerPoint) 8. Photocopy machine/photocopying facility



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MATH 2301: Vector Algebra and Analysis Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 3rd Semester e-mail Name of the Course Vector Algebra and Analysis Course no. MATH 2301 Credit Hours 3


Pre-requisite MATH 1101, MATH 1201 Follow-up PHYS 3501, PHYS 3502 Category Core course Aim The course introduces the subject of Vector Algebra and Analysis at

undergraduate level. Objectives At the completion of the course student will be able to:

1. Learn the basis concepts of vector algebra and its application 2. Studying vector differentiation and integration 3. Studying vector differential operator (Gradient, Divergence and Curl) 4. Studying integral theorem. 5. Introducing curvilinear coordinates and Cartesian tensor.

Syllabus Sr. Major Topic Sub topic

1. Vector Algebra Vectors in the Plane; Cartesian coordinates; Vectors in space; Dot and Cross Product; Lines and Planes in Space; Cylinder and Quadric Surfaces; Cylindrical and spherical coordinates

2. Vector functions and Motion in Space

Vector valued function and Space curves; Modeling projectiles motion; Arc length and the unit tangent vector; curvature; torsion and TNB frames; Planetary motion and Satellite

3. Vector Differentiations

Ordinary Derivatives of Vectors; Space curves; Continuity and differentiability; Differentiation formulas; Partial Derivatives of Vectors; Differential of vectors; Applications in Physics

4. Gradient, Divergence and Curl

The vector differential operator del. Gradient. Divergence. Curl. Physical interpretation of these operators

5. Vector Integrations

Ordinary integral of vectors. Line integral. Surface integral; Volume integrals

6. Divergence and Stokes’ theorem

The divergence theorem of Gauss; Stokes’ theorem; Green’s theorem in the plane; Related integral theorems

7. Curvilinear Coordinates

Transformation of coordinates; Orthogonal curvilinear coordinates; unit vectors in curvilinear systems; Arc length and volume element; gradient, div. and Curl; Special Orthogonal coordinate systems, Cylindrical coordinates and Spherical coordinates

8. Cartesian Tensor Introduction to Cartesian Tensors; Tensor Algebra Text Book(s) 1. Foundations of Mathematical Physics by Sardi Hassani, Prentice-Hall

International (1991) 2. G. D. Smith Vector Analysis, Oxford University Press (1962)

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1. Vector Analysis Schaum’s outlines by Frank Ayrees, McGrw-Hill International

2. Calculus 5/e by Howard Antony, Johg Wiley and Sons 3. Calculus and Analytic Geometry by G.B. Thomas and R.L. Finney,

Addison-Wesley Publishing Company (1996)





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MATH 2302: Infinite Series and Sequences Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 3rd Semester e-mail Name of the Course Infinite Series and Sequences Course no. MATH 2032 Credit Hours 2


Pre-requisite MATH 1101, MATH 1201 Follow-up MATH 3501, MATH 3601 Category Core course Aim The course introduces the subject of infinite series and sequences at

undergraduate level. Objectives At the completion of the course student will be able to:

1. Learn the concepts sequence and series 2. Studying various tests of convergence of series 3. Studying power and Fourier series

Syllabus Sr. Major

Topic Sub Topic

1. Sequences Sequence; Limits of sequences of Number; Theorems for calculating the limits of sequences

2. Series Series; Infinite series; Convergence of infinite series; Integral test; Comparison test; Ratio and Root tests; Alternative series; Absolute Convergence; Conditional Convergence

3. Power Series

Power Series; Taylor’s Series; Maclaorin Series; Convergence of Taylor series; Error Estimate; Applications of Power Series

4. Fourier Series

Fourier Theorem; Fourier Series; Fourier Transformation

Text Book(s) 1. Calculus 5/e by Howard Antony, Johg Wiley and Sons


1. Calculus and Analytic Geometry by G.B. Thomas and R.L. Finney, Addison-

Wesley Publishing Company (1996) 2. Calculus with Analytic Geometry by E. W. Swokowski, PWS

Publishers, Boston (1983)



Teaching Strategies 1. Lecturing 2. Topic discussion 3. Individual project/Assignments

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4. Class presentation 5. Questioning and explanation


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MATH 2303: Applied Differential Equations Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 3rd Semester e-mail Name of the Course Applied Differential Equations Course no. MATH 2303 Credit Hours 4


Pre-requisite MATH 1101, MATH 1201, MATH 1202 Follow-up MATH 3501, MATH 3601, PHYS 3501, PHYS 3502 Category Core course Aim The course introduces the subject of Differential equations at undergraduate


1. Learning the classification of differential equations. 2. Techniques of solving various differential equations. 3. Getting familiarize with different differential equations used in physics. 4.

Syllabus Sr. Major Topic Subtopic 1. Classification of

Differential equations

Ordinary and Partial Differential equations; Classification of ordinary differential equations; Linear and Nonlinear differential equation; Initial value and Boundary value problem; Formation of a differential equations

2. ODE’s of First Order and First Degree

General FODE; Normal form of FODE; Integrating factor & exact FODE; General FOLDE (homogeneous and inhomogeneous) Application of FOLDE (Simple Electric Network, Linear Rate Equations, Fluid Flow, Radioactive Decay, Population Growth, Compound Interest, Newton’s law of cooling); NLFODE; (1) Separable FODE (2) Homogeneous FODE (3) Exact FODE (4) Bernoulli’s FODE (5) Lagrange FODE

3. ODE’s of FO and Higher Degree

DE’s of FO and HD; Methods of solution; (1) Equation solvable for y` (2) Equation solvable for x (3) Equation solvable for y (4) Clairaut’s equations

4. Orthogonal Trajectories

Family of curves and trajectories; Orthogonal trajectories in Cartesian form; Orthogonal trajectories in polar form

5. SOLDE General properties of SOLDE; Linearity; Superposition & uniqueness & related theorems; The Wronskian; ISOLDE, Exact HSOLDE; The Riccati

6. HOLDE with constant coefficients

Homogeneous NOLDE; Inhomogeneous NOLDE and transfer function; Application to Undamped and damped motion; Electric circuit; Spring-Mass system (Forced and damped)

7. Cauchy-Euler Differential Equation

Cauchy-Euler Differential Equation

8. Simultaneous Linear system of equations; Euler’s method for

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DE’s in two variables with constant coefficients;

homogeneous linear system; Linear independence of solutions

9. SODE’s with variable Coefficients

Whet a part of the complementary function in know; Variation of parameters; Changing the independent variable; changing the dependent variable; Exact differential equations

10. Power Series Solutions

Power series solutions of first and second order; recursion formula

11. Laplace transform Laplace transform for simple functions; inverse Laplace transform; Application of Laplace transformation to ODEs

Text Book(s) 1. Differential Equations, A system Approach by Jack Goldberg, Prentice-Hall International (1998)

2. Differential Equations with Applications and Programs by S B Rao, Universities Press, India (1996)


1. Foundations of Mathematical Physics by Sardi Hassani, Prentice-Hall International (1991)

2. Elementary Differential Equation and Boundary Value Problems, by C.H. Edward, Prentice-Hall International (1996)





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MATH 3501: Mathematical Methods I Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 5th Semester e-mail Name of the Course Mathematical Methods I Course no. MATH 3501 Credit Hours 4


Pre-requisite MATH 1101, MATH 2302 Follow-up MATH 3601 Category Core course Aim The course introduces the subject of Mathematical Methods at graduate level. Objectives At the completion of the course student will be able to:

1. Learning vector analysis in curvilinear coordinate systems and tensor analysis.

2. Studying finite and infinite dimensional vector spaces. 3. Studying Fourier series and transforms. 4. Studying the theory of complex variable and analysis.

Syllabus Sr. Major Topics Subtopics 1. Vector

Analysis

Gradient, Divergence and Curl, Divergence and Stokes’ theorem, Curvilinear Coordinates

2. Tensors Analysis

Cartesian tensors, coordinate transformation, covariant and contravariant tensors, tensor algebra, metric tensor

3. Finite Dimensional Vector Spaces

Vector spaces, Inner product, Linear operators, Operator algebra, Eigen Values and Vectors, Operator function and derivative, Hermitian and unitary operators and related theorems, Representation theory

4. Infinite Dimensional Vector Spaces

Convergence issue, Hilbert space, space of square-integrable functions, Generalized functions, Dirac delta function

5. Fourier Series and Transforms

Fourier series and its complex form, Applications of Fourier series, Fourier transforms, Fourier integral theorem, Applications of Fourier transforms. Laplace transform

6. Complex Variables

Complex functions; Analytic functions; Properties of analytic functions; Derivative of analytic functions, Cauchy-Riemenn equations, Laplace equation, Line integral in the complex plane, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor and Laurent series, Residues, The residues theorem and its applications

Text Book(s) 1. Foundations of Mathematical Physics by S. Hassani, Allyn and Bacon (1999)

2. Mathematical Methods for Physics by G. Arfken, Academic Press, NY (1995)


3. Vector Analysis, L. L. Mir, 3rd edition 2001, Ilmi Kitab Khana, Lahore 4. Advanced Engineering Mathematics, by E. Keyszig 8th Edition, J. Wiley 5. An Introductory Course in Differential Equations by K.L. Mir

56

6. Differential Equations and their Application, G. D. Zill, National Book Foundation Islamabad

7. Mathematical Physics by E. Butkov, Addison-Wesley, (1973)





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57

MATH 3601: Mathematical Methods II Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 6th Semester e-mail Name of the Course Mathematical Methods II Course no. MATH 3601 Credit Hours 3


Pre-requisite MATH 3501 Follow-up PHYS 4701, PHYS 4702 Category Core course Aim The course introduces the subject of Mathematical Methods at graduate level. Objectives At the completion of the course student will be able to:

1. Studying the partial differential equations of physics 2. Studying complex differential equations 3. Studying special functions. 4. Studying the Sturm-Liouville systems and the theory of green functions


Subtopics

1. Partial Differential Equations in Physics

Common partial differential equations (Wave, Laplace, Poisson, Diffusion and Helmholtz equations); Separation in time; Separation in Cartesian coordinates; separation in cylindrical coordinates; Separation in spherical coordinates;

2. Complex DEs

(Review Continuation principle; general analytical properties of CDE, Complex SOLDE and related theorems; Fuchsian DE; Riemann DE; The hyper geometric functions; Jacobi functions;

3. Special functions

The hyper geometric functions; Jacobi functions; Bessel function; Spherical Bessel functions; Neumann functions; Hermit polynomial; Legendre polynomials; Associated Legendre functions and spherical harmonics; Gamma and Beta functions

4. The Sturm-Liouville Systems

The Sturm-Liouville equation; Properties of Sturm-Liouville systems; Expansion in term of eigenfunctions

5. Green’s Functions

Operators in Hilbert space; Integral transform and DEs; Green’s functions in one dimension (as inverse of differential operators in homogenous/inhomogeneous boundary conditions) and related theorem; Green’s functions for second-order linear differential operators; Properties of Green’s functions; Eigen function expansion of Green’s functions; Introduction to Green’s functions in higher dimensions

Text Book(s) 1. Foundations of Mathematical Physics by S. Hassani, Allyn and Bacon (1999)

2. Mathematical Methods for Physics by G. Arfken, Academic Press, NY (1995)


3. Vector Analysis, L. L. Mir, 3rd edition 2001, Ilmi Kitab Khana, Lahore 4. Advanced Engineering Mathematics, by E. Keyszig 8th Edition, J. Wiley

58

1. An Introductory Course in Differential Equations by K.L. Mir 2. Differential Equations and their Application, G. D. Zill, National Book

Foundation Islamabad

3. Mathematical Physics by E. Butkov, Addison-Wesley, (1973)





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59

COMP 1101: Introduction to Computer Science Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 1st Semester e-mail Name of the Course Introduction to Computer Science Course no. MATH 1101 Credit Hours 3


Pre-requisite F.Sc./A-Level Follow-up COMP 2401 Category Core course Aim The course introduces the subject of Computer Science Objectives At the completion of the course student will be able to:

1. Studying the history of computer and its applications. 2. Studying the architects of computer and various operating systems. 3. Learn to use the word processor and graphics packages. 4. Learning the basic concepts of data base management systems.

Syllabus Brief history of computers and its applications, Architects of computer; Introduction to various operating systems (Windows, Linux, Unix etc.), Coding schemes, Office automations tools such as word processing, graphic packages, spreadsheet, Database, data base management systems, types of databases, data concept and modeling, Information management with ACCESS/SQL. Data sharing and computer networks.

Text Book(s) 1. Introduction to Computer Science by P. K. Sinha


1. Introduction to Computer Science by Peter Norton 2. Mastering Office 2000, Microsoft Press





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60

COMP 2401: Computer Programming Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 4th Semester e-mail Name of the Course Computer Programming Course no. COMP 2401 Credit Hours 4


Pre-requisite COMP 1101 Follow-up COMP 3502, COMP 3602 Category Core course Aim The course introduces the subject of Computer Programming Objectives At the completion of the course student will be able to:

1. Studying the basic concepts of computer programming 2. Learning to develop algorithms and its translation into programs. 3. Get familiar with programming Languages like C, FORTRAN 90 etc. 4. Learning Debugging and testing programs and its documentation

Syllabus Programming and problem analysis, Development of basic algorithms, translation of algorithms into programs, Standard Data types, Basic control structures, Structured data types, arrays, Pointers and files, String processing, Introduction to data structures, Separate Compilations, Debugging and testing programs, Documentations, Programming languages C, FORTRAN 90

Text Book(s) 1. C Programming Using C++, by Robert Lafore 2. Programming with C, Sharm’ OutLines Series C by Examples by

Kalicharan, Noel, Cambridge University Press 3. Theory and Problem of Programming with FORTRAN 90, by W. E.

May McGraw Hill Co.






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61

COMP 3501: Advance Computer Programming Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 5th Semester e-mail Name of the Course Advance Computer Programming Course no. COMP 3501 Credit Hours 4


Pre-requisite COMP 2401 Follow-up COMP 4702, COMP 4801 Category Core course Aim The course introduces the subject of object oriented programming. Objectives At the completion of the course student will be able to:

1. Learning the difference between structured and modular programming 2. Learning the concepts of object oriented programming

Syllabus Advance programming techniques using C/C++; Structured and modular programming, Structured data types such as arrays, records, lists; Dynaics Variables; File managements; Memory Managements; Classes in C++; Concepts of expert systems; Concepts of object oriented programming

Text Book(s) 1. C Programming Using C++, by Robert Lafore 2. Programming with C, Sharm’ OutLines Series C by Examples by

Kalicharan, Noel, Cambridge University Press 3. Theory and Problem of Programming with FORTRAN 90, by W. E.

May McGraw Hill Co.






Quiz Mid 25% Paper

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62

COMP 3502: Numerical Linear Algebra Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 5th Semester e-mail Name of the Course Numerical Linear Algebra Course no. COMP 3502 Credit Hours 3


Pre-requisite COMP 2401 Follow-up COMP 3602, COMP 3601 Category Core course Aim The course introduces the subject of numerical linear algebra Objectives At the completion of the course student will be able to:

1. Studying the fundamental concepts of numerical methods 2. Learning different numerical methods of solving non-linear equations 3. Learning different methods of solving set of equations 4. Learning methods of interpolation and curve fitting 5. Get experience of developing computer programs to implement various

numerical methods

Syllabus Sr. Main Topics Subtopics 1. Fundamentals of

Numerical Methods Introduction; Basic; Recursion Formulas; Successive Approximation; Steps of Problem-to-Solution Process; Errors in Computations

2. Solution of Non-linear Equations (Algebraic and transcendental)

Non-Linear equations; Bisection Method; Linear interpolation method; Newton’s Method; Muller’s Method; Fixed Point Iteration Method; Newton’s Method for Polynomials; Bairstow’s Method for quadratic factors; Multiple roots; Error estimation and convergence rates of roots;

3. Solution of Set of Equations System equations; Matrix notation; Elimination

method; Gauss and Gauss-Jordan Methods; Other Direct Methods; Pathology in Linear Systems; Determinants and matrix inversion; Norms; Condition Numbers and error in solutions;

4. Interpolation and Curve Fitting Interpolation Problem; Lagrangian polynomials;

Divided differences; Evenly spaced data; Interpolation with a Cubic Spline; Bezier Curves and B-Spline Curves; Least-Squares Approximations

Text Book(s) 1. Applied Numerical Analysis by Curtis F. Gerald, Addison-Wesley (1994)


1. Introduction to Numerical Methods and FORTRAN Programming by

Thomas Richard McCalla, John Wiley & Sons (1964) 2. Elementary Numerical Analysis, An Algorithmic Approach by Samuel

63

D. Conte, McGraw-Hill International Edition (1981)





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64

COMP 3602: Numerical Analysis Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 6th Semester e-mail Name of the Course Numerical Analysis Course no. COMP 3602 Credit Hours 3


Pre-requisite COMP 3502 Follow-up COMP 4701, COMP 4702, COMP 4801 Category Core course Aim The course introduces the subject of numerical analysis Objectives At the completion of the course student will be able to:

6. Studying different methods of numerical differentiation and integrations. 7. Learning different numerical methods of solving ordinary differential

equations and partial differential equations 8. Numerical study of boundary and characteristic value problems 9. Get experience of developing computer programs to implement various

numerical methods

Syllabus Sr. Major Topic Subtopics

1. Numerical Differentiation and Numerical Integration

Getting Derivatives and Integrals Numerically; Derivatives from difference tables; Higher-Order derivatives; Extrapolation techniques; Newton-Cotes Integration Formulas; The Trapezoidal; Simpson’s; Gaussian Quadrature; Adaptive Integration; Multiple Integrals; Applications of Cubic Splines

2. Numerical Solution of Ordinary Differential Equations

Taylor-Series Method; Euler and Modified Euler Methods; The Runge-Kutta Methods; Multistep Method; Milne’s Method; The Adams-Moulton Method; Multivalued Methods; Convergence Criteria; Errors and Error Propagations; Systems of Equations and Higher-Order Equations; Comparison of Methods

3. Boundary-Value Problems and Characteristic-Value Problems

Introduction; The ‘Shooting Method’; Solution Through a Set of Equations; Derivative Boundary conditions; Rayleigh-Ritz, Collocation, and Galerkin Methods; The Finite-Element method; Characteristic-value problems; Eigenvalues by Iteration-The Power Method; Eigenvalues by the QR method; Applications of Eigenvalues

4. Numerical Solution of Partial-Differential Equations

Finite difference method; Representation as a difference equation; Laplace’s equation on a rectangular region; The Poisson Equation; Finite-element method;

Text Book(s) 1. Applied Numerical Analysis by Curtis F. Gerald, Addison-Wesley (1994)

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66

COMP 3601: Scientific Computing I Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 6th Semester e-mail Name of the Course Scientific Computing I Course no. COMP 3601 Credit Hours 3


Pre-requisite COMP 3502 Follow-up COMP 4701, COMP 4702, COMP 4801 Category Core course Aim The course introduces the subject of scientific computing Objectives At the completion of the course student will be able to:

1. Studying the concepts of computer arithmetic and approximations in computing.

2. Getting experience of working with different problem solving environments.

3. Getting experience of working with different Scientific Libraries Syllabus Sr.

Major Topic Subtopics 1. Approximations in

Scientific Computations

Sources of approximations; Data error and rounding error; Absolute error and relative error; Sensitivity and conditioning; Backward error analysis; Stability and accuracy

2. Computer Arithmetic Floating-Point Numbers; Normalization; Properties of Floating-point systems; Rounding; Machine Precision; Subnormal and Gradual underflow; Exceptional values; Floating-point arithmetic; Cancellation

3. Mathematical Software Mathematical Softwares; Libraries; Scientific computing Environments;

4. Building Blocks of Mathematica

Arithmetic; Variables; Expressions; Patterns; Replacement Rules; Programming; Scoped expression; Functions

5. Visualization in Mathematica

Graphics; Plotting Functions; Plotting Data; Graphics Programming; Animating Graphics; Sound

6. Symbolic Calculations Operation with polynomials; Rational expressions; Differentiations; Integration; Power Series; Solutions of equations; Simplifying Algebraic Expressions using Patterns; Units

7. Numerical Calculations Types of Numbers; Precision and Accuracy; Numerical Functions; Root finding; finding the minimum of a function numerical integration; line integration; Contour integration; Sums and Products; Interpolations functions;

Text Book(s) 1. Scientific Computing, An Introductory Survey by M. Heath, McGraw-Hill International Edition (1997)

2. Mathematica for Scientists and Engineers by Thomas B. Bahder,

67

Addison-Wesley Publishing Company (1995) 3. Introduction to Scientific Computing by Brigitte Lucquin, John Wiley &

Sons (1998)









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Recommendations

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68

COMP 4701: Scientific Computing II Program B.Sc. (Hons.) in Computational Physics Course

Instructor

7th Semester e-mail Name of the Course Scientific Computing II Course no. COMP 4701 Credit Hours 3


Pre-requisite COMP 3601 Follow-up COMP 4801 Category Core course Aim The course introduces the subject of scientific computing Objectives At the completion of the course student will be able to:

1. Learning to do computation in different problems solving envoirments and scientific libraries.

2. Learning to methods of storing and retrieving and communicating scientific data

3. Learning the basic concepts of parallel computing. Syllabus Sr.

Major Topic Subtopics 1. Computation with

Vectors; Matrices and Tensors

Vector and Matrix Algebra; Creating Vectors and Matrices; Operations on Vectors and Matrices; Symbolic vs. Numerical Computations; Solution of linear systems of equations; Eigen values and Eigen vectors

2. Computation in Vector Field Theory

Vector analysis; Gradient; Divergence; Curl; Laplacian;

3. Computation in Differential Equations

Symbolic Solutions; Variation of Parameters; Series approximations; Solutions by Laplace transforms; Numerical solutions; Perturbation solutions;

4. Boundary Value Problems

Inhomogeneous boundary values problem; Shooting Method; Finite difference method

5. Input and Output Operations;

Output formats; I/O of expressions; I/O of Graphics and Large expressions; Reading and Writing files; Formatting numbers;

6. MathLink Communications;

Introduction to MathLink Communications; Calling C, Fortran and VB from Mathematica and visa versa;

7. Parallel Computing Introduction to Parallel computing; Parallel computing using MPI and Gridmathematica

Text Book(s) 1. Scientific Computing, An Introductory Survey by M. Heath, McGraw-Hill International Edition (1997)

2. Mathematica for Scientists and Engineers by Thomas B. Bahder, Addison-Wesley Publishing Company (1995)

3. Introduction to Scientific Computing by Brigitte Lucquin, John Wiley & Sons (1998)

Years/Semester

69









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70

COMP 4702: Computational Physics Simulations I Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 7th Semester e-mail Name of the Course Computational Physics Simulations I Course no. COMP 4702 Credit Hours 3


Pre-requisite COMP 3502, COMP 3601, COMP 3602 Follow-up COMP 4801 Category Core course Aim The course introduces the subject of simulations of physical systems on

computers Objectives At the completion of the course student will be able to:

1. Learning different techniques of simulating physical systems. 2. Get experience of simulating complicated systems. 3.

Syllabus Sr. Major Topics Subtopics 1. Realistic

Projectile Motion

The Effect of Air Resistance; Projectile Motion; Motion of a Batted Ball; The Effects of Spin

2. Oscillatory Motion and Chaos

Simple Harmonic Motion; Chaos in the Driven Nonlinear Pendulum; Lorenz Model; The Billiard Problem; Bouncing Balls; Chaos and Noise

3. The Solar System

Kepler’s Laws; The Inverse-Square Law and the Stability of Planetary Orbits; Precession of the Perihelion of Mercury; The Three-body Problem and the Effect of Jupiter on Earth; Resonances in the solar systems; Chaotic tumbling of Hyperion

4. Potentials and Fields

Electric potentials and fields; potentials and fields near electric charges; magnetic field produced by a current; Magnetic field of a solenoid

5. Waves Waves; Frequency spectrum of waves on a string; Motion of realistic string; spectral methods

Text Book(s) 1. Computational Physics: Problem Solving with Computers by Rubin H. Landau, John Wiley & Sons (2000)

2. Computational Physics by Nicholas J. Giordano, Prentice Hall (1997)




Teaching Strategies 1. Lecturing 2. Topic discussion

71

3. Individual project/Assignments 4. Class presentation 5. Questioning and explanation


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72

COMP 4801: Computational Physics Simulations II Program B.Sc. (Hons.) in Computational Physics Course

Instructor

Years/Semester 8th Semester e-mail Name of the Course Computational Physics Simulations II Course no. COMP 4801 Credit Hours 3


Pre-requisite COMP 4702 Follow-up Project Category Core course Aim The course introduces the subject of simulations of physical systems on

computers Objectives At the completion of the course student will be able to:

1. Learning different techniques of simulating physical systems. 2. Get experience of simulating complicated systems.

Syllabus Sr. Major Topics Subtopics 1. Random Systems Introduction; Generation of random

numbers; Monte Carlo methods; Random walks; Self-avoiding walks; diffusion, entropy and the arrow of time; Cluster growth models

2. Statistical Mechanics, Phase Transitions, and the Ising Model

The Ising Model and Statistical Mechanics; Mean-Field theory; The Monte Carlo Method; The Ising model and second-order phase transitions; First-order phase transitions;

3. Molecular Dynamics Properties of a Dilute Gas, The melting transition

4. Quantum Mechanics 1D (Shooting and Matching Methods); Variational approach; Time-Dependent Schrödinger Equation (Direct solutions); Spectral Methods

5. Interdisciplinary Topics Protein Folding; Earthquakes and Self-Organized criticality; Neural network and the brain

Text Book(s) 1. Computational Physics: Problem Solving with Computers by Rubin H. Landau, John Wiley & Sons (2000)

2. Computational Physics by Nicholas J. Giordano, Prentice Hall (1997)



1. White board and markers 2. OHP 3. Transparence sheets 4. Multimedia Projector 5. Soft boards 6. Pointer

73

7. Software (PowerPoint) 8. Photocopy machine/photocopying facility



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74

Documents

Centre for High Energy Physics · Physics Vol.1, 4th (1992) and 5th (2002) Edition by Halliday, Resnic and Krane, John Wiley and Sons 2. Fundamental of Physics 5th and 6th Edition