Mathematics 4348             Partial Differential Equations II             Spring, 2000

Current reading and homework assignments

Due Friday, 28 April

  • Reading:
  • H&H, Chapter XIX will be our last chapter, although I will say some things about series solutions for Green functions on Wednesday.
  • NEWS FLASH, Those new things I said are now available as a preliminary version of a Chapter XX!
  • Exercises:
  • No new exercises - dead week.

    • Past homework assignments

    Due Friday, 21 January

  • Reading:
  • H&H, Chapters I, II, XIII; begin with the first half of XIII, through Model Problem XIII.4.
  • Exercises:
  • H&H, Chapter II, Exercises 1, 3, and 7 a)
    • Due Friday, 14 January
  • Reading:
  • H&H, Chapter XIII, Exercises 1,2,4.
  • H&H, Chapter I, Exercises 2,5,6.
    • Test preparation for Friday, 28 January
  • Reading:
  • H&H, Chapters XIII
  • H&H, Chapters XIV through Example Example XIV.2
  • H&H, Chapters XVI through the first Example.
  • Exercises:
  • Do the problems in the reading assigned. Click here to download the first problem of the test (a take-home problem).

    • Due Friday, 4 February

  • Reading:
  • H&H, Chapter XIV
  • Exercises:
  • Problem A2 of the Appendix on Green functions in Rn
  • H&H, Chapter XIV, Exercise XIV.3.
    • Due Friday, 11 February
  • Reading:
  • H&H, Chapter XIV
  • Exercises:
  • H&H, Chapter XIV, Exercises XIV.4, XIV.13.
    • On Friday, 18 February, there was a test.
  • Reading:
  • H&H, Chapters XIV and XV
  • Exercises:
  • Some of the test problems were quite close to the ones in H&H, Chapters XIV and XV
  • Show that the derivative of the function |x| is 2H(x)-1, and find the second derivative of |x| using the delta function.
  • Find the first and second derivatives of sin(2|x|) by using the chain rule.
  • show that the delta function is an even function in the sense that the integral of delta(-x) f(x) is equal to the integral of delta(x) f(x) for all continuous functions f(x).
    • Due Friday, 25 February:
  • Reading:
  • H&H, Chapters XV and XVI
  • Exercises:
  • H&H, Chapter XV, Exercise 12
  • H&H, Chapter XVI,
    • Due Friday, 4 March:
  • Reading:
  • H&H, Chapters XV and XVI
  • Exercises:
  • Show that for any function f(z) of one variable, f(x-2t) is a weak solution of the partial differential equation partial f/ partial t + 2 partial f/ partial x = 0.
    Is this true even if f is the delta function?
  • H&H, Chapter XVI, Exercises 1,2.
    • There was a test on Friday, 17 March:
  • Reading:
  • H&H, Chapters XIV through XVI
  • Exercises:
  • Do the exercises in those chapters and redo the extra ones already assigned.
    • Due Friday, 24 March
  • Reading:
  • H&H H&H, Chapter XVI
  • Exercises:
  • H&H H&H, Chapter XVI Exercise 19
    • Due Friday, 31 March
  • Reading:
  • H&H H&H, Chapters XVI and XVII
  • Exercises:
  • In some of the exercises of Chapter 16, you constructed Green functions for different boundary conditions but the same differential equation of the form LxG = f. Verify in each such case that if you define y := G(a)(x,t) - G(b)(x,t) then y solves the homogeneous differential equation Lxy = 0.

    Do this for Problems 13 (a) and (b) and 5 (d) and (e) as currently on-line, i.e.:
    13.     Find a formula for u if u'' = f and

    (a) u(0) = u(1) = 0.
    (b) u(0) = u'(0) = 0.     5.     Construct L*, B*, and G for the following : (d) L(y) = y'' + 4 pi 2y, B1(y) = y(0), B2(y) = y'(1).
    (e) L(y) = y'' + 4 pi 2y, B1(y) = y(0) + y'(0), B2(y) = y(1) - y'(1).
    • Due Friday, 7 April
  • Reading:
  • H&H, appendices with derivations of the
  • heat equation
  • wave equation for the vibrat ing string
  • wave equation for electromag netic waves
  • Look at the appendix on
  • Continue with Chapter XVII
  • Chapter XVIII
  • Exercises:
  • Verify the vector identity for the gradient of the dot product of two vector fields
  • Solve the problem -uxx -uyy + u = delta (x- xi) for 0 < x < 2, 0 < y < 1, and the following boundary conditions:
    u(0,y) = u(2,y) = 0,
    uy(x,0) = uy(x,1) = 0
    • There was a test on Friday, 14 April
  • Reading:
  • H&H, appendices and recent material through Chapter XVIII
  • Exercises:
  • Look at the exercises in CHapters XVII and XVIII
    • Due Friday, 21 April
  • Reading:
  • H&H, Chapter XIX
  • Exercises:
  • H&H, Chapter XIX, Exercises 1,3,6
    Link to:
  • The 4348 home page
  • Evans Harrell's home page 
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