MTH 482- 582: APPLIED PARTIAL DIFFERENTIAL EQUATIONS
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Assignments
Assignments
  1. 1/5/15: Class introduction and overview. Notation on partial derivatives and change of variables.
    Assignment 1 .
  2. 1/7/15: Continue notation, chain rule etc.
  3. 1/9/15: Quiz 1.
    Transport model in 1D (concentration transport in a tube)
    First order PDEs and method of characteristics. Read PDE Primer (Introduction) by Prof. R.E.Showalter; pages 8-12.
    Assignment 2: from PDE Primer, do problems 1-5. Extra: do Pbm 6.
  4. 1/12/15: Homogeneous examples with constant coefficients.
  5. 1/14/15: Non-homogeneous examples with variable coefficients. What happens if you have characteristic auxiliary data.
  6. 1/16/15: Quiz 2.
    Non-smooth initial data. Nonlinear examples (Burgers' equation).
  7. 1/19/15: No class (MLK Holiday)
  8. 1/21/15: (Start Chapter 10 of textbook). Boundary value problems for second order PDEs. Types of boundary conditions. Examples of nonexistence, nonuniqueness, or of only trivial solutions. (Section 10.1)
    Assignment 3: practice using problems 10.1/1-10, 14-19.
    Extra: 10.1/21. (You may want to re-read 5.4).
    Solve 10.2/10,14-15, 19-20, 29.
    Solve 10.3/7,9,11,13,17.
    Solve 10.4/TBA.
  9. 1/23/15: Fourier series. (Section 10.2). Inner product function space L^2(-L,L). Orthogonality of sine and cosine functions in that space. How to find Fourier coefficients=coefficients of expansion of any function in the Fourier basis.
    MATLAB function fourier.m
  10. 1/26/15: Examples how to compute Fourier coefficients. Why are sine and cosine the basis. Why THIS basis is useful for differential equations. Fourier convergence theorems. (Read 10.3-10.4).
  11. 1/28/15: More examples and analyses of Fourier series.
    Extra office hours: Wed 11:00-12:00.
  12. 1/30/15: MIDTERM 1. Scope: everything we covered until now.
  13. 2/2/15: Heat equation: derivation (read Chapter 10. Appendix A). Separation of variables for a one-dimensional problem (Read 10.5-10.6).
    Assignment 4: 10.5/1-6, 7-8, 9-10, 20.
    10.4/1,5,7,9,13,17-18.
    10.6/1,4,8, 15, 21.
  14. 2/4/15: Continue separation of variables for heat equation.
  15. 2/6/15: Examples of solutions to heat equations. Other boundary conditions than homogeneous Dirichlet.
  16. 2/9/15: Quiz 3.
    Solving problems with inhomogeneous booundary conditions and source terms. (See pbms 10.6/21-23).
  17. 2/11/15: worksheet. Given u(x,t), find the heat equation it satisfies, and BC and IC. Then solve it and confirm you got what was expected.
    Take home Quiz 4: use worksheet on nonhomogeneous problems (due Friday 2/13/15)
  18. 2/13/15: Wave equation (read 10.7 and Apppendix B for derivation). On R, use method of characteristics. On (0,L), use separation of variables.
    Extra credit opportunity: verify and/or derive d'Alembert's solution to the wave equation.
  19. 2/16/15: Energy conservation in the wave equation, and dissipation in the heat equation. (Proof directly from the equation, and via Parseval's identities).
  20. Review of heat and wave equation. Heat and wave equations with extra terms and in multiple spatial dimensions.
    Extra office hours W 11:00-11:50.
    Assignment 5: 10.7/1,4,5,8,9-10,13-14, 16, 19. Also, 10.5/21-23.
  21. Midterm 2 on Friday, Feb. 20
  22. 2/23/15: Laplace equation on rectangular and circular regions. Harmonic functions.
  23. 2/25/15: Continue Laplace equation, via separation of variables.
  24. 2/27/15: Laplace eqn with nonhomogeneous Dirichlet b.c.. (Answers to "verify/derive" d'Alembert's solution).
    Assignment 6: 10.8/2,4,7,10,15. Extra: 10.8/16
  25. 3/2/15: Solve Laplace eqn in circular domain via S.O.V. The case of angle-independent interior/exterior Dirichlet problem. Applications: potential equation (water and electrostatic). Recall solving Euler equations (Section 5.4)
  26. 3/4/15: Wrap up Laplace equation.
  27. 3/6/15: Quiz 5. Solving Poiseille problem (flow in a pipe). Laplace equation in a semi-infinite pipe.
  28. 3/9/15: [Read 11.1-11.3]. Eigenvalues and eigenfunctions for Sturm-Liouville problems. (Focus on constant coefficients p(x), q(x), r(x).)
  29. 3/11/15: Solve inhomogeneous heat equation with variable coefficients using SOV and Sturm-Liouville eigenfunctions. Solve the inhomogeneous Laplace equation with eigenfunctions.
    (Please check CANVAS for your midterm/quiz scores)
  30. 3/13/15: Handout on Greens functions.
    Classification of second order PDEs in 2D. Review.
    Assignment 7: 10.8/12; 11.1/7-10,11,12-15,22, 23; 11.5/1,7,8; 11.3/19, 20. Extra: 11.3/35, 36.
  31. Office hours Finals week: TUESDAY 3/17, 3:30pm-5:00pm.
  32. Final Exam: Wed 3/18, 6:00pm in class. Open books nd notes.