Phys603 — Graduate Math Methods in Physics
Purpose of this course
To develop your ‘toolbox’ of mathematical techniques, ready to apply to the problems you’ll encounter in physics research.
Books
There is no single recommended book for this class. Here are some
that i'm familar with:
- Byron & Fuller Mathematics of Classical and Quantum Physics.
A cheap Dover reprint containing all the material we'll cover.
- Mary L. Boas Mathematical Methods in the Physical
Sciences. The best undergraduate level book. Currently in third edition, older editions are just as good.
- Riley, Hobson & Bense Mathematical Methods for Physics
and Engineering. Technically an undergraduate level book, but
long and rather complete.
- Arfken et al. Mathematical Methods for Physicists. Used at
both the undergraduate and graduate levels.
Topics
- Complex analysis
- Linear vector spaces
- Integral transforms
- Green's functions
- Introductory group theory
Grading
Problem Sets: 20%, Midterm Exam: 20%, Final Exam: 60%.
Lecture Notes
| 1. |
Complex analysis |
[pdf]
|
| 2. |
Vector spaces I |
[pdf]
|
| 3. |
Vector spaces II |
[pdf]
|
| 4. |
Green's functions |
[pdf]
|
| 4.5 |
The wave equation |
[pdf]
|
| 5. |
Group theory |
[pdf]
|
Problem Sets
| 1. |
Complex numbers and Analytic Functions |
[pdf]
|
due Sep. 13 |
| 2. |
Riemann and Cauchy say "hi" |
[pdf]
|
due Sep. 20 |
| 3. |
Complex integration |
[pdf]
|
due Sep. 27 |
| 4. |
Complex expansions and mappings |
[pdf]
|
due Oct. 4 |
| 5. |
Matrices |
[pdf]
|
due Oct. 25 |
| 6. |
Vector spaces |
[pdf]
|
due Nov. 1 |
| 7. |
Fourier and other integral transforms |
[pdf]
|
due Nov. 8 |
| 8. |
Ordinary Differential Equations |
[pdf]
|
due Nov. 15 |
| 9. |
Green's functions |
[pdf]
|
due Nov. 22 |
| 10. |
Groups and their representations |
[pdf]
|
due Dec. 6 |
|
