**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