Prof. Wright's office hours: Mon. 1–2, Tues. 10–11, Wed. 2–3, Thurs 10–11, Fri. 1–2, whenever the door is open, or by appointment in RMS 405
Help sessions: Tuesdays 7–8pm in Tomson 186
- Read §2.1 and §2.2. Note the definition of a linear operator and the principle of superposition.
- Finish Homework 2 (due 4pm Thursday).
- Read the §2.3 Appendix (pages 54–55). Also read §2.4, and make sure you understand the two examples in this section.
- Finish Homework 3 (due 4pm Thursday).
Time-dependent solutions to the heat equation
- Read §3.1 and §3.2. Note the convergence theorem for Fourier series.
- Finish Homework 4 (due 4pm Thursday).
Take-home exam assigned
- Read §3.3. Pay close attention to the definitions, examples, and convergence properties of Fourier sine and cosine series.
- Read §3.4. Note the conditions under which a Fourier (cosine/sine) series can be differentiated term by term.
- Take a look at Homework 5.
- Re-read §3.4. Make sure you understand the conditions under which a Fourier (cosine/sine) series can be differentiated term by term. Also note the method of eigenfunction expansion.
- Read §3.5 (it's short!). Note what happens when you integrate Fourier series.
- Finish Homework 5.
- Finish Homework 6 (due 4pm Thursday).
- Work on Problem 3 on the Wave Equation Worksheet from class. Try to finish the derivation of D'Alembert's solution of the wave equation.
- Begin Homework 7.
Intro to Sturm-Liouville problems
Operators, orthogonality, and self-adjointness
- Re-read §5.5. Note the role of Lagrange's identity and Green's formula in the proofs presented in this section.
- Read §5.6. Observe how the Rayleigh quotient can provide a bound on the lowest eigenvalue.
- Finish Homework 8 (due 4pm Thursday).
- Continue thinking about what you might want to work on for the Final Project.
Rayleigh quotient and eigenvalue bounds
- Read §5.7. This example should look familiar now!
- Read §6.1 and §6.2. Observe how Taylor series can be used to approximate the value of a derivative of a function using values of the function at nearby points.
- Complete the Final Project Planning Survey on Moodle. See also the Final Project Information.
- Begin Homework 9.
- Re-read §6.2. Note how the finite difference approximations can be applied to second derivatives.
- Read §6.3.1–§6.3.3. Observe how finite difference approximations for derivatives can be used to approximate solutions to the heat equation.
- Finish Homework 9 (due 4pm Thursday).
Take-home exam assigned
For two extra-credit points, attend the Research Seminar by Jasper Weinburd (Nov. 16, 3:40pm, RNS 204), and complete these two questions on Moodle.
- Re-read §6.3. Focus on §6.3.4, which expands on what we said in class about stability analysis. Read §6.3.6, about matrix notation, noting connections to linear algebra. Also take a look at the short subsections §6.3.7 and §6.3.8.
- Begin Homework 10.
- Read §6.5. (It's short!) Observe how finite differences can be used to approximate the wave equation.
- Finish Homework 10 (due 4pm Thursday).
2:00 – 4:00pm