MATHEMATICAL PHYSICS
Class: Monday and Wednesdays, 12:30-1:45, Room 264 (Meyer Building)
Instructor: Roman Scoccimarro
Office Hours: Fridays 10-11AM, Room 506 Meyer.
Grades: Homework (30%), Midterm (30%), Final Exam (40%)
Recitations: David W. Hogg (david.hogg@nyu.edu ) [Thursdays 12:15-1:15, Meyer 421]

### Final Exam

Will be on Wednesday, May 7, 12-1:50PM, Meyer 264
Spring 2002 Final Exam

### Textbook

• B. Kusse and E. Westwig, Mathematical Physics, 1998, John Wiley & Sons

### Homework [Due on Fridays, 3PM, Meyer 424]

• HMW1 [31Jan]: Problems 1 through 10 in Chapter 1
• HMW2 [07Feb]: Problems 3,4,5,6,8,9,10,11,13 in Chapter 2
• HMW3 [14Feb]: Problems 1 through 7, plus 19 and 20 in Chapter 3
• HMW4 [28Feb]: Problems 1,10,11,15,18,19 in Chapter 4
• HMW5 [07Mar]: Problems 1,2,8,9,14,15,22(i-ii),24 in Chapter 5
• HMW6 [14Mar]: Problems 2,3,4,7,10,11 in Chapter 7
• HMW7 [04Apr]: Problems 1 through 5 in Chapter 8
• HMW8 [11Apr]: Problems 1 through 8 in Chapter 10
• HMW9 [18Apr]: Problems 9,10,13,20(a-c),21,28,29, in Chapter 10 plus

8) 4 y'' + 4 y' + 5 y = exp(-x) sin(2x)
9) y'' - 2 y'- 3 y = 24 exp(-3x)
10) x^2 y'' + 3 x y' -3 y = 0

Solve all 3 problems with boundary conditions y(0)=1,y'(0)=0

• HMW10 [25Apr]: Problems 1,2,3,4,5,8 in Chapter 11
• HMW11 [02May]:
Solve steady state temperature distribution insidea a cylinder of radius a for the following two cases
1) Cylinder has height L, and T=0 at the bottom and at the walls, and T=100 at the top.
2) Cylinder extends from z=0 to infinity, T=0 at walls, but T=rho sin(phi) at the bottom.

Plus Problems 21,23,28(a and d only) in Chapter 11

### Lecture Notes

[These are from Spring 2002, but I will follow them (not necessarily in the same order)]

L1,L2,L3,L4,L5,L6,L7,L8,L9,L10,L11,L12,L13,L14,L15,L16,L17,L18,L19,L20

Lecture Schedule (L# refers to notes above, #.# refers to sections in Book)

Jan22[L1] Jan27[L3] Jan29[L6] Feb3[L7] Feb5[L8] Feb10[3.2-3] Feb12[L5]

Feb19 [L4] Feb24 [4.4] Feb26[L9] Mar3[5.4-6] Mar5[L10] Mar10[L10-11] Mar12[review]

Mar31[L11-L12] Apr2[L12] Apr7[L13] Apr9[L14-L15] Apr14[L15-L16] Apr16[L17]

Apr21[L18] Apr23[L18-L19] Apr28[L19-L20] Apr30[L20] May5[review]

### Course Outline

• Linear Algebra and Vector Calculus [4 weeks]
- Linear Equations, Matrices, Determinants
- Eigenvalues, Eigenvectors, Tensors
- Gradient, Divergence, Curl, Gauss and Stokes Theorems
- Laplacian, Conservation Laws, Scale Analysis

• Fourier Analysis, Complex Analysis [3 weeks]
- Dirac Delta Function, Fourier Series
- Fourier Transforms
- Analytic Functions and Complex Integration

• Differential Equations [6 weeks]
- Ordinary Differential Equations
- Green Functions, Normal Modes
- Partial Differential Equations
- Potential Theory, Perturbation Theory

### Other Recommended Textbooks

• M.L. Boas, Mathematical Methods in the Physical Sciences , 1983, John Wiley & Sons
• R. Snieder, A Guided Tour of Mathematical Methods for the Physical Sciences , 2001, Cambridge Univ. Press