MATHEMATICAL PHYSICS
Class: Monday and Wednesdays, 12:30-1:45, Room 102 (Meyer Building)
Instructor: Roman Scoccimarro
Office Hours: Thursdays 11AM-12 noon, Room 506 Meyer.
Grades: Homework (30%), Midterm (30%), Final Exam (40%)
Recitations: Luca Grisa (luca.grisa AT nyu.edu) [Thursdays 2-3:15, Meyer 122]
Office Hours of Luca Grisa: Mondays 1:30-2:30PM, Room 518 Meyer.

### Midterm Exam

Will be on Monday, March 26, in class. Sections from the book that will be in the test are,
Chapter 1 through 6, except sections 3.4,4.5,4.6,5.7,6.7-6.12. An old midterm is available here, with solution.
solution for 2007 midterm

### Final Exam

Will be on Wednesday, May 2, 12:00-1:50PM. Topics covered by the final can be found here. An old final is available here with solution.

### Textbook

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

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

• HMW1 [26Jan]: Problems 1 through 10 in Chapter 1
• HMW2 [02Feb]: Problems 3,4,5,6,8,9,10,11,13 in Chapter 2
• HMW3 [09Feb]: Problems 1 through 7 in Chapter 3
• HMW4 [23Feb]: Problems 1,10,11,15,18,19 in Chapter 4
• HMW5 [02Mar]: Problems 1,2,8,9,14,15,22(i-ii) in Chapter 5
• HMW6 [09Mar]: Problems 2,3,6,7 in Chapter 6, plus the following:
Integrate along a circle of radius |z|=3 the following integrands,
a) cos(pi z)/(z-1), b) cos(pi z)/(z-pi), c) cos(pi z)/(z-1)^2, d) 1/(z^2-4)
• HMW7 [23Mar]: Problems 2,3,4,7,10,11 in Chapter 7
• HMW8 [30Mar]: Problems 1,2,3 in Chapter 8
• HMW9 [06Apr]: Problems 1 through 8 in Chapter 10
• HMW10 [13Apr]: Problems 9,10,13,21,28,29, in Chapter 10 plus

7) 4 y'' + 4 y' + 5 y = exp(-x) sin(2x)
8) x^2 y'' + 3 x y' -3 y = 0

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

• HMW11 [20Apr]: Problems 1,2,3,4,5 in Chapter 11
• HMW12 [27Apr]: Problems 21,23,28(a and d parts only) in Chapter 11, plus

Solve for the steady state temperature distribution inside 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.

### Homework Solutions

HMW1, HMW2, HMW3, HMW4, HMW5, HMW6
HMW7, HMW8, HMW9, HMW10, HMW11, HMW12

### 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)

Jan17[L1] Jan22[L1,L3] Jan24[L3,L6] Jan29[L6,L7] Jan31[L7,L8] Feb05[L8] Feb07[3.2,3,5] Feb12-14[Tensors]
Feb21[L9] Feb26[Dirac] Feb28[ComplexV] Mar5[L10] Mar7[L10,L11] Mar19[L11,L12] Mar21[L12]
Mar28[L13] Apr02[L14] Apr04[L15] Apr09[L16] Apr11[L16-L17] Apr16[L17-L18] Apr18[L18] Apr23[L19] Apr25[L20]

### Course Outline

• Vector Calculus [4 weeks]
- Summation Convention: Scalar, Vector Products, Determinants
- Gradient, Divergence, Curl, Gauss and Stokes Theorems
- Laplacian, Potential and Rotational Fields, Helmholtz Theorem
- Coordinate Systems, Tensors, Eigenvalues, Eigenvectors

• Complex Analysis and Fourier Analysis [4 weeks]
- Dirac Delta Function
- Functions of Complex Variable: Derivatives
- Functions of Complex Variable: Cauchy Integral
- Fourier Series, Fourier Transforms

• Differential Equations [5 weeks]
- Ordinary Differential Equations: First Order, Second Order
- Frobenius Method, Legendre Polynomials, Fuch's Theorem, Bessel Functions
- Partial Differential Equations: Laplace, Diffusion and Wave Equations
- Separation of Variables in Cartesian, Cylindrical and Spherical Coordinates

### 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