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)



Textbook

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

    Homework [Due on Fridays, 3PM in Meyer 639]

  • HMW1 [05Feb]: 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, 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 [12Feb]: Problems 4,5,10,13 in Chapter 2
  • HMW3 [19Feb]: Problems 6,8,9,11 in Chapter 2
  • HMW4 [26Feb]: Problems 1-5,6a,7 in Chapter 3
  • HMW5 [04Mar]: Problems 1,10,11,15,18,19 in Chapter 4
  • HMW6 [11Mar]: Problems 1,2,8,9,14,15,22(i-ii) in Chapter 5
  • HMW7 [01Apr]: Problems 2,3,6,7 in Chapter 6
  • HMW8 [08Apr]: Problems 25,27,28,30,38(i-iv) in Chapter 6
  • HMW9 [15Apr]: 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 [22Apr]: 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 [29Apr]: Problem 21 in Chapter 10 plus Problems 1,2,3,4,5 in Chapter 11
    HMW12 [06May]: 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

    Maxwell

    Check out Maxwell's notation!


    Midterm Exam

    Will be on Thursday March 24 in class. It includes

    - 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


    Final Exam

    Will be on Thursday May 12, 12PM-1:50PM (same room as Lectures).
    Practice Final 1 Practice Final 2

    Practice Problems

    handout on special functions Final 1 Solutions Final 2 Solutions

    Final 2016 w/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