MATHEMATICAL PHYSICS
Class: Monday and Wednesdays, 12:30-1:45, Room 102 (Meyer Building)
Instructor: Roman Scoccimarro
Office Hours: Mondays 2-3PM, Room 506 Meyer.
1) Average of the best 9 Homeworks (30%) + Midterm (30%) + Final Exam (40%)
2) Average of the best 10 Homeworks (45%) + Final Exam (55%)
3) Average of all 12 Homeworks (60%) + Midterm (40%)
Recitations: Watee Srinin (ws907 AT nyu.edu) is the TA for the course. Recitation times are Mondays 5-6:15 or Wednesdays 3:30-4:45 (Meyer 264)

### Textbook

• B. Kusse and E. Westwig, Mathematical Physics, 2006 (2nd ed), John Wiley & Sons

### Homework [Due on Fridays, 3PM at Meyer 639B]

• HMW1 [07Feb]: 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)
Problem 9: In lecture we wrote the det A = epsilon_{ijk} a_{1i} a_{2j} a_{3k}.
Write this result in terms of arbitrary components of the matrix A, i.e. det A= (?) a_{ij} a_{kl} a_{mn}.
• HMW2 [14Feb]: Problems 4,5,10,13 in Chapter 2
• HMW3 [21Feb]: Problems 6,8,9,11 in Chapter 2
• HMW4 [28Feb]: Problems 1-5,6a,7 in Chapter 3
• HMW5 [07Mar]: Problems 1,10,11,15,18,19 in Chapter 4
• HMW6 [14Mar]: Problems 1,2,8,9,14,15,22(i-ii) in Chapter 5
• HMW7 [04Apr]: Problems 2,3,6,7 in Chapter 6
• HMW8 [11Apr]: Problems 25,27,28,30,38(i-iv) in Chapter 6
• HMW9 [18Apr]: 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)
• HMW10 [25Apr]: Problems 9,10,13,28,29, 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
• HMW11 [02May]: Problem 21 in Chapter 10 plus Problems 1,2,3,4,5 in Chapter 11
• HMW12 [09May]: 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

L1,L2,L3,L4,L5,L6,L7,L8,L9,L10,

L11,L12,L13,L14,L15,L16,L17,L18

### Midterm Exam

Will be on Monday March 31 in class
There will be a review session March 26 during lecture
Midterm with Solutions

### Final Exam

Will be on Wednesday May 14 12PM-1:50PM.
Final with Solutions

### Course Outline

• Vector Calculus, Tensors [4-5 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

• Dirac Delta and Complex Analysis [3 weeks]
- Dirac Delta Function: singular distributions
- Complex Analysis: Analytic Functions, Derivatives, Cauchy Theorem, Contour Deformation
- Complex Analysis: Laurent Series, Residues, Residue Theorem, Contour Closure

• Differential Equations [5-6 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

• K.F. Riley, M.P. Hobson, S.J. Bence, Mathematical Methods for Physics and Engineering, Cambridge
• R. Snieder, A Guided Tour of Mathematical Methods for the Physical Sciences , Cambridge