| Lecture | Date | Topic | References |
| 1 | Oct 17 | ODE preview | |
| 2 | Oct 19 | Discrete spectrum: computable examples | Strauss Ch. 4 (esp. Robin BC) and Sec. 10.2 (disk) |
| 3 | Oct 21 | Computable examples for Schroedinger | Strauss Section 9.4 and Gustafson & Sigal Section 7.5 (harmonic oscillator) |
| 4 | Oct 24 | Computable examples, continued | Strauss Sections 9.5, 10.7 and Gustafson & Sigal Section 7.7 (hydrogen atom), and Showalter Section III.7 (discrete spectrum and eigenfunction expansions) |
| 5 | Oct 26 | Discrete spectral theorem | Showalter Section III.7 (discrete spectrum and eigenfunction expansions) |
| 6 | Oct 31 | Applications to the Dirichlet, Neumann and Robin Laplacians. BiLaplacian is covered in notes (omitted in class). | |
| 7 | Nov 2 | Natural boundary conditions Application to Schroedinger potential wells | |
| 8 | Nov 4 | Variational characterizations of eigenvalues | Bandle Section III.1.2 |
| 9 | Nov 7 | Weyl’s asymptotic law | |
| 10 | Nov 9 | Weyl’s asymptotic law, and Polya’s conjecture | |
| 11 | Nov 11 | Case study: thin film stability | |
| 12 | Nov 14 | Case study: thin film stability | |
| 13 | Nov 16 | Case study: reaction-diffusion stability | |
| 14 | Nov 18 | Case study: reaction-diffusion stability | |
| 15 | Nov 28 | Case study: free Schröedinger | |
| 16 | Dec 2 | Case study: free Schröedinger, and Schröedinger with -2 sech^2 potential | |
| 17 | Dec 5 | Case study: Schröedinger with -2 sech^2 potential | |
| 18 | Dec 7 | Spectral theory of unbounded operators |
References
Bandle – C. Bandle, “Isoperimetric Inequalities and Applications” (on reserve at Math Library)
Farlow – S. J. Farlow, “Partial differential equations for scientists and engineers” (on reserve at Engineering Library, or e-copy through library catalog)
Gustafson & Sigal S. J. Gustafson and I. M. Sigal, “Mathematical concepts of quantum mechanics” (one reserve at Math Library)
Henrot – A. Henrot, “Extremum Problems for Eigenvalues of Elliptic Operators” (e-copy through library catalog)
Mathews & Walker – J. Mathews and R. L. Walker, “Mathematical Methods of Physics”, 2nd edition (on reserve at Math Library)
Showalter – R. E. Showalter, “Hilbert Space Methods for Partial Differential Equations” (available free electronically)
Strauss – W. A. Strauss, “Partial Differential Equations: An Introduction” (on reserve at Math Library)