**MATHEMATICAL PHYSICS**

** Class: **Tuesdays and Thursdays, 12:30-1:45, Room 122 (Meyer Building)

** Instructor: **Roman Scoccimarro

** Office Hours: **Tuesdays 2-3PM, Room 506 Meyer.

** Grades: ** Your grade will be determined by the BEST of the following three combinations:

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: **Alex Breitweiser (sabreitweiser AT nyu.edu) is the TA for the course. Recitation times are Mondays 5-6:15 (Meyer 264) or Wednesdays 5:-6:15 (Meyer 425B)

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, 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}.

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

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.

HMW7, HMW8, HMW9, HMW10, HMW11, HMW12

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

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

- Subscript/Summation Notation

- Vector Calculus (in cartesian and curvilinear coordinates)

- Tensors

- Dirac Delta function,

that is, the material in homeworks 1-6 (thus, no complex variables!).

Practice Midterm 1 Practice Midterm 2

Midterm Solutions

Practice Final 1 Practice Final 2

Practice Problems

handout on special functions Final 1 Solutions Final 2 Solutions

Final 2016 w/Solutions

- 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 Function: singular distributions

- Complex Analysis: Analytic Functions, Derivatives, Cauchy Theorem, Contour Deformation

- Complex Analysis: Laurent Series, Residues, Residue Theorem, Contour Closure

- 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