MTH 621-3: DIFFERENTIAL AND INTEGRAL EQUATIONS - Fall 2008
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General information
Assignments

In the schedule below [GL *] means a section from Guenther/Lee text, [S *] means sections from Strauss' text. Material marked with E means additional reading is available there.
Assignments and schedule
  1. 9/30: Introduction and overview. [S 1.1], [GL 1.1]
  2. 10/1-10/6: Solving PDEs of first order: [S 1.2], [GL 2.1-2.2, E 2.4-2.5],
    Assignment 1 is due Wednesday 10/15.
  3. 10/8-10/10: Introduction to basic models of flow, diffusion, and heat conduction. [S 1.3], [GL 1.2-1.5,1.7].
    Assignment 1': Please read about mechanical vibrations: [S 1.3], [GL 1.2, 1.6].
  4. 10/13-10/15: Initial and boundary conditions. Well-posedness, [S 1.4-1.5], [GL 1.8]
  5. 10/17-20: Type of second order equations: [S 1.6], [GL 2.6]
    Assignment 2 is due Wednesday 10/29.
  6. 10/22-24: Solving wave equation, d'Alembert's solution: [S 2.1-2, 3.2, 3.4], [GL 4.1, some of 4.2-4.5]
    You can use MATLAB function wave.m to play with different profiles.
    Also, check out a more physics oriented exposition on reflections Acoustics and Vibration Animations - Dan Russell, Kettering University
  7. 10/27: Wave equation on semi-infinite spatial domain and on an interval: nethod of reflections/images.
  8. 10/29: Solving boundary value problems for wave equation using separation of variables.
  9. 10/31-11/3: Constructing solutions to non-homogeneous problems: Duhamel's principle for first order ODEs, and second order ODEs.
  10. 11/5: Review for exam. Assignment 3 (do not turn in, use as practice for exam).
  11. 11/7: Midterm.
  12. Due 11/14: solve Problem 5 from midterm.
  13. 11/10-14, 17: Fourier series [S 5.1-5.3, some of 5.4-5,5], [GL 3.1-3.3]
    Assignment 4 (Part I) due Monday 11/24. ( Note: the assignment has been modified on Monday 11/17 afternoon)
  14. 11/19-24: Solving diffusion equation on (0,L) with separation of variables. Homogeneous and inhomogeneous initial boundary value problems. Maximum principle. [S 2.3-2.4, 3.2, 3.4], [GL 5.1-5.4].
  15. 11/24-12/3: Diffusion equation on R. Green's function (fundamental solution, diffusion kernel). See for a few MATLAB commands that may be useful in plotting the solutions.
    Assignment 5 is due Monday 12/8 by 9:00am in my mailbox.
  16. 11/26: No class.
  17. 12/5: Wrap-up and review.