Math 331: Partial Differential Equations


March 8, 2026


Midterm Review Topics


  1. Boundary value problems for ODEs; eigenvalue problems

  2. Singular boundary value problems for ODEs

  3. Periodic functions; odd and even functions

  4. Fourier series; derivation of coefficients; using orthogonality

  5. Odd and even extensions of functions; Fourier sine series and Fourier cosine series

  6. Expanding functions in FS, FSS, and FCS

  7. Convergence of Fourier series: types of convergence; pointwise and uniform convergence theorems

  8. Applying Fourier series to find "cute" formulas for sums of series

  9. Fourier integral: informal derivation

  10. Applying Fourier integral to find definite integrals

  11. Fourier sine and cosine integral representations

  12. Complex form of Fourier series

  13. Introduction to PDEs: IBVPs

  14. Steady-state solutions of the heat equation; the transient component

  15. Solving the fixed end temperatures case of heat equation IBVP: separation of variables; eigenvalues and eigenfunctions; superposition of solutions

  16. Various cases of heat equation IBVPs

  17. Sturm-Liouville Problem: statement and proof, Sturm-Liouville Theorem

  18. Expanding functions in generalized Fourier series

  19. Solving the semi-infinite and infinite cases of heat equations

  20. Introduction to wave equation; method of separation of variables