MTH 623: DIFFERENTIAL AND INTEGRAL EQUATIONS - Spring 2016
Links
Assignments and schedule
Assignments
Assignments and schedule
  1. 3/28/2016: Introduction and overview.
  2. 3/30/2016: Solving first order PDEs with the method of characteristics. Burgers equation and conditions on initial data that guarantee existence/uniqueness of solutions.
    [Review Chapter 2]. Read 12.3]
  3. 4/1/2016: Worksheet on plotting the solutions and characteristics for Riemann problem and Burgers equation. Shock (speed) and rarefaction.
  4. 4/4/2016: Integral conservation laws and weak solutions to conservation laws.
  5. 4/6/2016: Complete part of worksheet. Rankine-Hugoniot condition for shock speed.
  6. 4/8/2016: Lax-Oleinik construction of shock and rarefaction solutions.
    Worksheet 1 due Friday 4/8/16.
  7. 4/11/2016: Cole-Hopf transformation. Entropy conditions (general)
  8. 4/13/2016: Continue entropy conditions (Oleinik chord condition, and Lax condition)
  9. 4/15/2016: Nonconvex flux function: Welge tangent.
    Worksheet 2 due Friday 4/15/16.
  10. 4/18/2016: Models of physical phenomena which result in conservation laws with convex and concave flux functions. Handout on models.
  11. 4/20/2016: Continue models; signoid flux functions.
  12. 4/22/2016: wrap-up scalar conservation laws. Plotting characteristics and snapshots.
    Worksheet 3 due Friday 4/29/16.
  13. 4/25/2016: Solving systems (of ODEs)
  14. 4/27/2016: Solving systems of conservation laws; linear constant coefficient case.
  15. 4/29/2016: Solving systems. Intermediate values qmfrom Rankine-Hugionior condition
  16. 5/2/16: Examples of systems (genuinely nonlinear). Shallow water and Euler equations.
  17. 5/4/16: Analyzing nonlinear systems (examples).
  18. 5/6/16: Stokes and Navier-Stokes equations. Poiseille flow.
    Homework 4 on hyperbolic systems due Friday May 20.
  19. 5/9/16: Asymptotic/perturbation techniques. An algebraic example and a ODE example.
  20. 5/11/16 [RS]: Stefan problem
  21. 5/13/16: Continue asymptotic techniques; introduction to homogenization for elliptic problems.
  22. 5/16/16: [JR] KdV (Guest lecture)
  23. 5/18/16: No class today.
  24. 5/20/16: Complete asymptotic expansions: homogenization in 1d.
    Homework 5 on asymptotic problems (assigned in class) and integral equations ([Glee 7.5-5]) due Friday June 3 in class.
  25. 5/23/16: Integral equations. Applications: [GLee Chapter 8]. Theory: [Glee Chapter 7].
  26. 5/25/16: Linear operators: continuous and bounded. Fredholm alternative.
  27. 5/27/16:
  28. 6/1/16:
  29. 6/3/16: LAST CLASS DAY: Review.