**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