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.
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: 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