PHY 330 – Mathematical Methods of Physics

 

Syllabus Fall 2007

 

 

Class Time:       10:20- 11:20 M-W-F, Olin 109

 

Text:                 Advanced Engineering Mathematics, 9th edition, Erwin Kreyszig.

 

Instructor:         André Wehner, Olin 111, Ph. 238-5919, e-mail wehner@centre.edu,

                        Office Hours: 3:00-5:00 M-Th, 10:00-12:00 Tu and Th, or by appointment.

               

Grading:           3 tests @ 15% each = 45%

Final 30%

Homework 25%

 

 

Course Description

 

This course is meant to familiarize you with various methods of advanced mathematics that are essential in physics and engineering, especially in classical mechanics, electromagnetism, thermal physics, and quantum mechanics. A solid background in multivariable calculus and differential equations is expected.

 

We will not follow our text in order. We will start with chapters 9 and 10 on vector calculus. Most of this is material you have seen before in MAT 230. This is probably the hardest and most work-intensive part of the course, and is needed especially in mechanics and electromagnetism. We will then briefly talk about complex numbers (parts of Ch. 13), which should prepare us for the two chapters on linear algebra (7 and 8). The rest of the course will be dedicated to differential equations. We will first elaborate on the methods developed in MAT 360 (topics from chapters 1-5 and appendix 3) and put them in their physics context with emphasis on the special functions that arise as solutions of the Sturm-Liouville type equations. Finally, we will cover Fourier analysis (Ch. 11) and, as time permits, topics from Ch. 12 on partial differential equations.

 

Homework is an essential part of this class. You are encouraged to cooperate on the assignments, but you should only turn in your own work. The homework problems from the book are listed below. The due dates will be announced in class. Late homework will be marked down (of course, exceptions can be made for emergencies). I also encourage you to use the computer algebra system Maple where appropriate. There exists a Student Solutions Manual and a Maple Manual for our textbook. Also note the accompanying website .

 

Problems on the exams will closely mirror the homework assignments. If you do the homework, you should do fine on the tests. They are closed everything, with calculators permitted. You must show all work.

 

The solutions you present in both the homework and the tests must be complete, coherent, and well-organized. Expect to be graded on a 90-80-70 scale, depending on the class average.

 

You are expected to be present for all classes. Please let me know in advance if you must be absent for a scheduled college activity. Three inexcused absences will result in a lowering of the grade.

 

This syllabus can be found at http://web.centre.edu/wehner/courses/p330f07.htm .

 

Schedule Fall 2007

 

Day

Material Covered

Homework

 

 

 

8/27

Vectors and Vector Fields

9.2: 3, 5, 15-18, 31-36, 42

8/29

 

9.3: 9, 10, 24, 31-37 (odd)

8/31

Vector Differential Calculus

9.4: 1, 3, 5, 9-18; 9.5: 1-13, 27-30, 35

9/3

 

9.7: 1, 2, 7, 8, 13, 14, 19, 20, 29, 30, 33, 39-42

9/5

 

9.8: 1, 2, 12-15,

9/7

 

9.9: 3-5, 9, 11, 16-20,)

9/10

 

handout 1 (vector calculus in curvilinear coordinates)

9/12

Vector Integral Calculus

10.1: 1-5, 14-16; 10.2: 1, 2, 11-14

9/14

 

10.3: 2, 3, 11, 12, 14, 15; 10.4: 2-4

9/17

 

10.5: 1-19; 10.6: 1-9 (odd), 15, 25

9/19

 

10.7: 1-7 (odd), 17-21 (odd),

9/21

 

10.8: 1-5 (odd); 10.9: 1-13 (odd)

9/24

 

handout 2 (delta functions)

9/26

Test 1

 

9/28

Complex Numbers

13.1: 7-19; 13.2: 1-27 (odd); 13.3: 1-9 (odd);

10/1

 

13.5: 3, 7, 9,  13, 14; 13.6: 3-13 (odd); 13.7: 1, 3, 5, 23, 25, 27

10/3

Matrices

7.2: 1-5, 19-21; 7.3: 6-9, 23

10/5

 

7.7: 5-8; 7.8: 1-5 (odd)

10/8

Linear Transformations

7.9: 1-10

10/10

Eigenvalue Problem

8.1: 3-6, 11, 13, 21; 8.2: 1-6

10/15

 

8.3: 4-8, 11-14

10/17

 

8.4: 1-7 (odd), 13; 8.5: 5-9, 12, 16

10/19

Important Integrals

 

10/22

 

handout 3 (important integrals and special functions)

10/24

Test 2

 

10/26

Linear DEs

1.3: 23, 29; 2.1: 23, 24; 2.2: 21, 23; 2.4: 1, 3

10/29

 

2.5: 11, 13; 2.8: 15, 17; 2.9: 13, 17; 3.3: 1

10/31

Systems of DEs

4.3: 1-4, 11

11/2

 

4.6: 11, 12

11/5

Series Solutions

5.1: 1-6; 5.2: 1-5

11/7

 

5.3: 7, 8, 14, 15

11/9

 

5.4: 1-5, 18, 19

11/12

Sturm-Liouville

5.5: 5-9, 21, 25

11/14

 

5.7: 5, 7-10

11/16

Test 3

 

11/19

Fourier Analysis

11.1: 13-17

11/26

 

11.3: 1-4, 11-13, 17-19

11/28

 

11.4: 7-9

11/30

 

11.9: 2-4

 

 

 

12/3

Final (comprehensive)