North Carolina Agricultural and Technical
Days & Times
Professor Contact Information
Marteena 306/Gibbs 302
W 2-5 PM
Other InformationYou can make appointments if you cannot make it during the office hours
Course Pre-requisites, Co-requisites, and/or Other Restrictions
This is a course in the applications of mathematics to solutions of physical problems. It covers selected topics in vector analysis, differential equations, special functions, calculus of variations, eigenvalues and eigenfunctions, and matrices, complex variables, linear algebra. Prerequisite: MATH 231.
NOTE: The course will cover some mathematical techniques commonly used in physics. This is not a course in pure mathematics, but rather on the application of mathematics to problems of interest in the physical sciences. Knowledge of physics at the level of Phys 241-Phys 242 is required.
At the conclusion of the course a student must be able to apply basic mathematical concepts in solving problems in junior and senior electrodynamics, classical mechanics and quantum mechanics and other upper level physics courses.
Objective 1: Effectively use information technology to find, interpret, evaluate, and use information discerningly.
Outcome: Students will demonstrate the ability to use information technology tools to conduct literature survey, and do research
Objective 3: Effectively employs critical thinking skills in written and oral communication.
Outcome: Students will demonstrate the ability to employ critical thinking in solving problems which are very complicated and mathematically challenging
Objective 4: Effectively relate ideas and concepts, as well as modes of inquiry, across disciplines
Outcome: Students will demonstrate the ability to relate ideas and concepts from physics to chemistry, atmospheric sciences, geosciences and materials science and engineering
Objective 5 : Use analytical thinking skills to evaluate information critically.
Outcome: Students will demonstrate the ability to use analytical thinking skills to evaluate the content of the course as it applies to real life problems.
Objective 6: Apply multiple modes of inquiry, including quantitative and qualitative analysis, to formulate, describe, evaluate, and solve problems
Outcome: Students will demonstrate the ability to apply multiple modes of inquiry, including quantitative analysis, to formulate, describe, evaluate, and solve problems.
Objective 7: Apply scientific reasoning skills to model natural, physical, social, and aesthetic phenomena using multiple modes of inquiry:
Outcome: Students will develop skills to use the different mathematical techniques to solve problems in physical sciences- physics, chemistry engineering and geosciences.
Required Textbooks and Materials
Mathematical Methods in the Physical Sciences
Mary L. Boas, Third Edition
Suggested course reference books
Schaum's Outlines series on Matrix Algebra, Vector Analysis, Linear Algebra, Complex Variables, Ordinary and Partial Differential Equations
Assignments & Academic Calendar
Topics, Reading and problems to work on Assignments
Book section (BOAS)
Complex Variables: Complex plane, Complex Algebra
Chapter 2, section 1-5
Complex Variables: Elementary functions of complex numbers, powers, roots, exponential and trigonometric functions
Chapter2, section 8,9,10,11
Complex Variables: Logarithms, hyperbolic functions, Applications in mechanics, circuits, optics,
Chapter 2, sections 12-16
Vector Analysis: Vector dot, cross and triple products with applications in mechanics, electrodynamics
Chapter 3 section 4, Chapter 6 sections 1,2,3
Vector Analysis: Differentiation of vectors, fields and directional derivative: Gradient; Curl and divergence of a vector: Applications in electrodynamics and mechanics
Chapter 6,sections 4,5,6,7
Exam 1- Complex Variables
Vector Analysis: Line integrals with applications in mechanics and electrodynamics
Chapter 6, section 8
Vector Analysis: Divergence and the divergence theorem with applications in electrodynamics
Chapter 6, section 10
Vector Analysis: Curl and stokes theorem, conservative fields- applications in Mechanics and electrodynamics
Chapter 6, section 11
Linear Algebra: Matrices, Determinants, Cramers Rules; matrix operations
Chapter 3, sections 1-3,6
Linear Algebra: Linear Operators, Linear dependence and linear independence- applications in quantum mechanics
Chapter 3, sections 7,8
Linear Algebra: Special matrices, Linear Vector Spaces- Applications in quantum mechanics
Chapter 3, section 9, 10
Exam 2- Vector Analysis
Linear Algebra: Eigen values and Eigen Vectors, Diagonalization
Chapter 3 section 11 and 12
Linear Algebra: Applications of matrix diagonalization in mechanics (moment of inertia, coupled vibrations, quantum mechanics
Chapter 3, section 12
ODE: Separable equations, Linear First order equations,
Chapter 8, sections 1-3
ODE: second order linear equations with constant coefficients equal to zero
Chapter 8, section 5
ODE: second order linear differential equations with constant coefficients and equal to non-zero
Chapter 8, section 6
ODE: Applications in mechanics, quantum mechanics, circuits, electrodynamics
Exam 3- Linear Algebra and ODE
Partial Differentiation: Total differentials
Chapter 4, section 1-3
Partial Differentiation: Approximation using differentials, chain rule or differentiating a function,
Chapter 4, sections 4 and 5
Partial Differentiation: Change of variables Applications in mechanics, quantum mechanics, statistical physics and thermodynamics
Chapter 4 section 11
PDE: Laplace and Poisson equations-applications: Heat transfer, Electric potentials in Cartesian coordinates
Chapter 13, section 1 and 2
PDE: Diffusion or heat flow equation, Schrodinger equation
Chapter 13, section 3
Probability and Statistics: Sample space, probability theorems,
Chapter 15, sections1-3
Probability and Statistics: Methods of counting, Random variables,
Chapter 15, sections 4 and 5
Probability and Statistics: Distributions, Binominal, Normal and Gaussians, Poisson
Chapter 15, sections 6,7,8 and 9
Probability and Statistics: Error Analysis
Chapter 15, section 10
Final Exam: Comprehensive
Homework: Assigned homework problems for each day are listed and collected at the next class following the assignment. You are urged to try to solve the problems before we solve them in class. Homework carries a major weight in the evaluation. Solutions will be provided after the homework is collected. No homework is accepted after the solutions are distributed. Last day to submit home works is 5PM of the Friday of the week they are assigned.
You can work collaboratively and discuss homework with your peers; however the material you turn in should be your own work. I will file a report of Academic Integrity Violations for any student who turns in homework that is copied from another source or cheats in any other manner. The student will get a zero for the homework.
Quizzes:Daily or once a week, you will have a quiz based on the material to be covered. This quiz could be at the beginning of the class or towards the end. You are expected to read the section for the class before coming to class.
Exams: There will be three exams and a final. The exams schedules are announced in the outline
Grading: Home works + quizzes
Three Exams 10% each
Make up exams are given only with valid excuses
Attendance of all departmental seminars is a requirement and students will earn extra credit.
No late work is accepted
A student is not allowed to miss a class without reasonable excuse and justification.