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Course Syllabus

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6

North Carolina Agricultural and Technical

State University

Course Syllabus

Course Information

Course Number/Section

PHYS 405

Course Title

Mathematical Physics

Term

Spring 2015

Days & Times

2-3:15 PM

Marteena 310

Professor Contact Information

Professor

Solomon Bililign

Office Phone

336-285-2328

Other Phone

336-285-3259 (Lab)

Email Adresse

Bililign@ncat.edu

Office Location

Marteena 306/Gibbs 302

Office Hours

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

Math 231

Course Description

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

Required Texts

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

Lecture

Date

Topic

Book section (BOAS)

1

1/13/15

Complex Variables: Complex plane, Complex Algebra

Chapter 2, section 1-5

2

1/15/15

Complex Variables: Elementary functions of complex numbers, powers, roots, exponential and trigonometric functions

Chapter2, section 8,9,10,11

3

1/20/15

Complex Variables: Logarithms, hyperbolic functions, Applications in mechanics, circuits, optics,

Chapter 2, sections 12-16

4

1/22/15

Vector Analysis: Vector dot, cross and triple products with applications in mechanics, electrodynamics

Chapter 3 section 4, Chapter 6 sections 1,2,3

5

1/27/15

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

1/29/15

Exam 1- Complex Variables

6

2/3/15

Vector Analysis: Line integrals with applications in mechanics and electrodynamics

Chapter 6, section 8

7

2/5/15

Vector Analysis: Divergence and the divergence theorem with applications in electrodynamics

Chapter 6, section 10

8

2/10/15

Vector Analysis: Curl and stokes theorem, conservative fields- applications in Mechanics and electrodynamics

Chapter 6, section 11

9

2/17/15

Linear Algebra: Matrices, Determinants, Cramers Rules; matrix operations

Chapter 3, sections 1-3,6

10

2/19/15

Linear Algebra: Linear Operators, Linear dependence and linear independence- applications in quantum mechanics

Chapter 3, sections 7,8

11

2/24/15

Linear Algebra: Special matrices, Linear Vector Spaces- Applications in quantum mechanics

Chapter 3, section 9, 10

2/26/15

Exam 2- Vector Analysis

12

3/10/15

Linear Algebra: Eigen values and Eigen Vectors, Diagonalization

Chapter 3 section 11 and 12

13

3/12/15

Linear Algebra: Applications of matrix diagonalization in mechanics (moment of inertia, coupled vibrations, quantum mechanics

Chapter 3, section 12

14

3/17/15

ODE: Separable equations, Linear First order equations,

Chapter 8, sections 1-3

15

3/19/15

ODE: second order linear equations with constant coefficients equal to zero

Chapter 8, section 5

16

3/24/15

ODE: second order linear differential equations with constant coefficients and equal to non-zero

Chapter 8, section 6

17

3/26/15

ODE: Applications in mechanics, quantum mechanics, circuits, electrodynamics

3/31/15

Exam 3- Linear Algebra and ODE

18

4/2/15

Partial Differentiation: Total differentials

Chapter 4, section 1-3

19

4/7/15

Partial Differentiation: Approximation using differentials, chain rule or differentiating a function,

Chapter 4, sections 4 and 5

20

4/9/15

Partial Differentiation: Change of variables Applications in mechanics, quantum mechanics, statistical physics and thermodynamics

Chapter 4 section 11

21

4/14/15

PDE: Laplace and Poisson equations-applications: Heat transfer, Electric potentials in Cartesian coordinates

Chapter 13, section 1 and 2

22

4/16/15

PDE: Diffusion or heat flow equation, Schrodinger equation

Chapter 13, section 3

23

4/21/15

Probability and Statistics: Sample space, probability theorems,

Chapter 15, sections1-3

24

4/23/15

Probability and Statistics: Methods of counting, Random variables,

Chapter 15, sections 4 and 5

25

4/28/15

Probability and Statistics: Distributions, Binominal, Normal and Gaussians, Poisson

Chapter 15, sections 6,7,8 and 9

26

4/30/15

Probability and Statistics: Error Analysis

Chapter 15, section 10

Final Exam: Comprehensive

Grading Policy

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

50%

Three Exams 10% each

30%

Final Exam

20%

Grade Scale

Course Policies

Make-up exams

Make up exams are given only with valid excuses

Extra Credit

Attendance of all departmental seminars is a requirement and students will earn extra credit.

Late Work

No late work is accepted

Class Attendance

A student is not allowed to miss a class without reasonable excuse and justification.

Classroom Citi