| Lecture | Date | Topic | References |
| 1 | Mar 6 | Ch. 1 – ODE overture | |
| 2 | Mar 8 | Ch. 2 – Laplacian — computable spectra, and qualitative properties | Strauss Ch. 4 (especially good for Robin BC) and Sec. 10.2 (Laplace eigenvalues on the disk) |
| 3 | Mar 10 | Ch. 3 – Computable examples for Schroedinger | Strauss Section 9.4 and Gustafson & Sigal Section 7.5 (harmonic oscillator) |
| 4 | Mar 13 | Ch. 4 – Discrete spectral theorem for sesquilinear forms | Blanchard and Brüning Section 6.3 |
| 5 | Mar 15 | Ch. 5 – Applications to the Dirichlet and Neumann Laplacians (The Robin Laplacian is covered in the online notes – omitted in class.) | |
| 6 | Mar 17 | Ch. 5 – Neumann Laplacian, continued Ch. 6 – Natural boundary conditions Discussion of exercises | |
| 7 | Mar 27 | Ch. 8 – Application to confining Schrödinger potentials | |
| 8 | Mar 29 | Ch. 11 – Variational characterizations of eigenvalues | Bandle Section III.1.2 |
| 9 | Mar 31 | Ch. 12 – Monotonicity properties of eigenvalues | |
| 10 | Apr 10 | Ch. 18 – Case study: reaction-diffusion stability | |
| 11 | Apr 12 | Ch. 18 – Case study: reaction-diffusion stability | |
| 12 | Apr 14 | Ch. 19 – Case study: thin film stability | |
| 13 | Apr 17 | Ch. 19 – Case study: thin film stability | |
| 14 | Apr 19 | Ch. 15 – Heat trace | |
| 15 | Apr 21 | Ch. 16 – Spectral zeta | |
| 16 | Apr 24 | Ch. 16 – Spectral zeta, cont. | |
| 17 | Apr 26 | Ch. 20 – Case study: free Schrödinger | |
| 18 | Apr 28 | Ch. 20 – Case study: free Schrödinger Ch. 21 – Schrödinger with -2 sech^2 potential | |
| 19 | May 1 | Spectral theory of unbounded operators | |
| 20 | May 3 | Spectral theory of unbounded operators |
References on reserve at the Mathematics Library
Elliptic partial differential equations of second order / David Gilbarg, Neil S. Trudinger.
Elliptic partial differential equations of second order [electronic resource] / David Gilbarg, Neil S. Trudinger.
Extremum problems for eigenvalues of elliptic operators / Antoine Henrot.
Extremum problems for eigenvalues of elliptic operators [electronic resource] / Antoine Henrot.
Hilbert space methods for partial differential equations / R.E. Showalter (1 copy at Math, 1 copy at Grainger)
Isoperimetric inequalities and applications / Catherine Bandle. (1 copy at Math, 1 copy at Grainger)
Mathematical concepts of quantum mechanics / Stephen J. Gustafson, Israel Michael Sigal.
Mathematical concepts of quantum mechanics [electronic resource] / Stephen J. Gustafson, Israel Michael Sigal.
Mathematical methods of physics / Jon Mathews [and] R. L. Walker. (1 copy at Math, 1 copy at Grainger)
Methods of modern mathematical physics / Michael Reed [and] Barry Simon. (1 copy at Math, 1 copy at Grainger)
Partial differential equations / Lawrence C. Evans.
Partial differential equations : an introduction / Walter A. Strauss.
Partial differential equations for scientists and engineers / Stanley J. Farlow. (1 copy at Math, 1 copy at Grainger)
Partial differential equations for scientists and engineers [electronic resource] / Stanley J. Farlow.
Variational methods in mathematical physics : a unified approach / Philippe Blanchard, Erwin Brüning.
Variational Methods in Mathematical Physics [electronic resource] : a Unified Approach / by Philippe Blanchard, Erwin Brüning.