Physics 116A

Mathematical Methods in Physics.

Winter 2007

TuTh 12PM-1:45 PM

Physical Sciences 110

Instructor: Josh Deutsch, josh@physics.ucsc.edu, 219 ISB
Office Hours: Tues 2:00-4:00PM

T.A. Jeff Jones, jeff@physics.ucsc.edu, 314 ISB
Discussion Sections: Wed 5:00-6:30PM ISB 235
Office Hours: Wed 2-3PM 314 ISB

Textbook: Mary Boas
"Mathematical Methods in the Physical Sciences, 3rd Edition'' (Required).

Evaluations

Student evaluations will be based on their performance in the following three tasks. These tasks and their relative weights in determining the students' ultimate ranking are given below:

  • Weekly homework: Due every Thursday starting January 11. Seven homework sets must be completed and handed in as a requirement to pass the course. To count, 80% of the assigned problems in a homework set must be attempted. Each attempt must constitute a serious effort to solve a problem.
  • Midterms: Two midterms exams February 1 and March 1. Weight: 60% (30% each)
  • Final: In class closed book final exam on Wednesday, March 21 8:00-11:00AM. Weight: 40%

Each midterm will be closed book but will contain at least one problem closely related to a homework problem. For the final exam students will be allowed to bring an 8.5 by 11 inch sheet of paper containing any information they please. In all exams, no calculators or computers are allowed.

Outline (subject to modification) 


   
    
   
  • Infinite Series, Power Series 
   Boas Chapter 1             Jan 4 - Jan 11 
    
   
    • 

   
  • Complex Numbers 
   Boas Chapter 2             Jan 16-23
   
    • 

   
  • Linear Algebra and Linear Vector Spaces
   Boas Chapter 3             Jan 23-Feb 27
   
    • 

   
  • Tensor Analysis
   Boas Chapter 10             Mar 6-8
   
    • 

   
  • Special Functions
   Boas Chapter 11             Mar 8-13
   
    • 

   
  • Review                         March 15
   
    •

Note about computers

Because physics majors are not required to know a computer language, this course will not require the use of a computer. Some of the assigned homework problems have parts to them that need a computer. Those parts are strictly optional. You are not required to turn any of those parts in. However if you are able to program, you may wish to do some of these problems out of your own interest.

Web demos

Nice demo of matrix eigenvectors

and another one here

Homework 1 due on 1/11/07

Boas, Chapter 1, problems 1.4, 1.15, 2.2, 2.5, 2.8, 2.9, 4.1, 5.3, 5.6, 6.1, 6.4, 6.5, 6.6, 6.11, 6.15, 6.20, 6.21, 6.29, 6.31, 6.34, 7.5, 7.7

solutions (password protected, email josh if you don't know the username and password.)

Homework 2 due on 1/18/07

Boas, Chapter 1, problems 9.1, 9.4, 9.5, 9.6, 9.19, 9.21, 9.22, 10.18, 13.5, 13.7, 13.8, 13.12, 13.41, 14.1, 14.7, 15.5, 15.6, 15.9, 15.10, 15.16, 15.18, 15.24, 15.28, 15.33

solutions (password protected, email josh if you don't know the username and password.)

Homework 3 due on 1/25/07

Boas, Chapter 2, problems 4.1, 5.20, 5.25, 5.34, 5.45, 5.57, 5.64, 5.68, 6.7, 8.2, 9.29, 10.1, 10.8, 10.27, 11.17, 12.23, 14.1, 14.4, 15.13

solutions

Additional problems (not turned in):

These problems are assigned for extra practice. Those who have already had a lot of this material and found the homework quite straightforward, may not need to do these. On the other hand, if learning the material for the first time, it is highly recommended that these problems be completed as well, as this material is essential to many physics courses. These problems are not handed in.

Boas, Chapter 2, problems 5.1, 5.3, 5.4, 5.9, 5.19, 5.27, 5.28, 5.29, 5.35, 5.37, 5.43, 5.45, 5.49, 5.65, 5.53, 5.59, 5.61, 5.53, 6.2, 6.4, 7.5, 9.1, 9.2, 9.19, 9.22, 9.28, 10.12, 11.11, 12.1, 12.10, 14.8, 14.11

Homework 4 due on 2/1/07

Boas, Chapter 2, problem 16.8

Boas, Chapter 3, problems 2.3, 2.4, 2.5, 3.4, 3.10, 3.14, 3.17, 4.7, 4.20, 4.21

Additional problems (not turned in):

These problems are assigned for extra practice. This is the same idea as last week's additional problems. Those who have already had a lot of this material and found the homework quite straightforward, may not need to do these. On the other hand, if learning the material for the first time, it is highly recommended that these problems be completed as well, as this material is essential to many physics courses. These problems are not handed in.

Boas, Chapter 3, problems 2.1, 2.7, 3.1, 4.3, 4.22, 4.24

solutions

Practice midterm for midterm on 2/1/07

Boas Chapter 1: 9.7, 9.11, 15.8, 1.15.11, 15.23(d)

Boas Chapter 2: 10.19, 16.12 (note typo, left parentheses are missing), 17.15, 17.32

Boas Chapter 3: 3.2

solutions (erratum: For 2.16.12, in the final answer, the term "+r2+" should be "+r4+").

midterm 1 and solutions average=63 out of 110

Homework 5 due on 2/8/07

Boas, Chapter 3, problems 4.24, 5.7, 5.44, 6.1, 6.6, 6.14, 6.18, 6.30, 6.32, 7.3, 7.5, 7.10, 7.12, 7.13

solutions

Homework 6 due on 2/15/07

Boas, Chapter 3, problems 7.22, 7.31, 8.8, 8.14, 8.21, 9.5, 9.9, 9.20, 9.23, 9.24, 9.25

solutions

Homework 7 due on 2/22/07

Boas, Chapter 3, problems 10.2(a), 10.4(a), 10.10, 11.9, 11.10, 11.12, 11.13, 11.17, 11.27, 11.34, 11.41

solutions

Homework 8 due on 3/1/07

Boas, Chapter 3, problems 11.57, 11.58, 11.62, 12.2, 12.3, 12.15, 14.2, 14.4, 14.15

solutions

Practice midterm for midterm on 3/1/07

solutions

Homework 9 due on 3/8/07

Boas, Chapter 10, problems 2.6, 2.7, 3.2, 3.3, 3.6, 3.13, 4.5, 4.8 (it's easier to do this after having read section 10.5, and also using eqn 10.7.8), 5.3, 5.6

solutions

midterm 2 for all four versions with the answer key to the multiple choice and solutions. average=104 out of 120

Homework 10 due on 3/15/07

Read the whole of Boas Chapter 11. A lot of it is merely the definition of special functions which you may encounter later.

Do Boas, Chapter 11, problems:

3.16 (Don't write the Lagrange equation, but use conservation of energy),

6.1, 7.1, 7.5, 8.3, 9.1,

10.2 (you don't need to integrate by parts. You can change variables so that the limits of integration are from 0 to infinity and then use the binomial expansion on the integrand).

11.4, 11.6, 11.7(b), 11.8

solutions

final and solutions

Problems from 116A last year, taught by Howie Haber

Sample practice problems for the first midterm and solutions.

Sample practice problems for the last third of the course and solutions.

Sample practice problems focusing on expansions and solutions.

Final exam and solutions.

Web Book

Amazing 2321 page book in Applied Math from Sean Mauch of Caltech.

Notes on diagonalization of Hermitian matrices, clarifying some remarks of Boas at the end of 3.11.

Peter Young's notes on the method of steepest descent and