MATHEMATICAL PHYSICS
Class: Monday and Wednesdays, 12:30-1:45, Room 122 (Meyer Building)
Instructor: Roman Scoccimarro
Office Hours: Mondays 2-3PM, Room 506 Meyer.
Grades: Homework (30%), Midterm (30%), Final Exam (40%)
Recitations: Jarrett Lancaster (jll419 AT nyu.edu) [Mondays or Thursdays 2-3:15, Meyer 264]

### Midterm Exam

Will be on Wednesday March 25 during class.
There will be a review session March 23rd during lecture
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.
Old midterms: 2003, 2007 Solutions:2003,2007
2009 Midterm with solution

### Final Exam

Will be on Wednesday May 6 12PM-1:50PM. Topics covered in the final can be found here. Old finals 2002, 2003, 2007. Example of formula sheet you'll get during final exam here. Solutions: 2002, 2003, 2007.

2009 Final: Solution

### Textbook

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

### Homework [Due on Fridays, 3PM, Meyer 424, look for "Math Physics" yellow folder next to mailboxes]

• HMW1 [30Jan]: Problems 1 through 10 in Chapter 1
Errata Problem 4: should read [D] [V] = ( [V]^t [D] )^t
Errata Problem 8c: should read delta_ij T_ij A_k (i.e. replace A_i by A_k)
• HMW2 [06Feb]: Problems 4,5,10,13 in Chapter 2
• HMW3 [13Feb]: Problems 6,8,9,11 in Chapter 2
• HMW4 [20Feb]: Problems 1-5,6a,7 in Chapter 3
• HMW5 [27Feb]: Problems 1,10,11,15,18,19 in Chapter 4
• HMW6 [06Mar]: Problems 1,2,8,9,14,15,22(i-ii) in Chapter 5
• HMW7 [13Mar]: 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)
• HMW8 [10Apr]: Problems 1 through 8 in Chapter 10 (in 6c set v(t)=delta(t-ep) where ep>0 is very small, i.e. the pulse is right *after* the initial condition)
• HMW9 [17Apr]: Problems 9,10,13,21,28,29, in Chapter 10 plus
7) 4 y'' + 4 y' + 5 y = exp(-x) sin(2x) with BC's: y(0)=1,y'(0)=0
8) x^2 y'' + 3 x y' -3 y = 0 with BC's: y(1)=0,y'(1)=1
• HMW10 [24Apr]: Problems 1,2,3,4,5 in Chapter 11
• HMW11 [01 May]: 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.

### Extra Examples from Lecture (April 29)

Extra Examples

### Homework Solutions

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

### 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)

Jan21-26[L1] Jan28[L3] Feb02[L6] Feb04[L7] Feb09[L7-L8] Feb11[3.2,3,5] Feb18-23[Tensors]

Feb25[L9] Mar02[Dirac] Mar04-09[ComplexV] Mar11 [L10] Mar23 [review] Mar25 [midterm] Mar30 [L13]

Apr01 [L14] Apr08 [L15]

### 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 [3 weeks]
- Dirac Delta Function
- Functions of Complex Variable: Derivatives
- Functions of Complex Variable: Cauchy Integral

• Differential Equations [6 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