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Welcome to Partial Differential Equations! For course info and policies, please see the syllabus. For grades, log into Moodle. If you need help or have questions, please contact Prof. Wright

**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

- Complete the Syllabus Quiz.
- Read §1.1 through §1.2 in the textbook. Answer the reading questions, and bring your answers to class on Tuesday.
- Begin Homework 1.

- Read §1.3 and §1.4. Note three possible boundary conditions discussed in §1.3. Then note how the heat equation, with certain boundary conditions, can be solved for equilibrium solutions in §1.4.
- Finish Homework 1 (due 4pm Thursday). You may want to use the LaTeX template on Overleaf.

- Read §1.5, answer the reading questions, and bring your answers to class on Tuesday.
- Begin Homework 2.

- 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 §2.3. This is a long section, but the the first half (or so) should be somewhat familiar from class. Answer the reading questions (TeX source), and bring your answer to class on Tuesday.
- Begin Homework 3.

- 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).

September 27

Time-dependent solutions to the heat equation

due today

- Re-read §2.4. Note how orthogonality of sine and cosine functions is used to find the coefficients of the series solutions in this section.
- Read §2.5.1 and §2.5.2. Answer the reading questions (TeX source), and bring your answer to class on Tuesday.
- Begin Homework 4.

- Read §3.1 and §3.2. Note the convergence theorem for Fourier series.
- Finish Homework 4 (due 4pm Thursday).

- Complete the take-home exam: PDF file, TeX source, Moodle link for file upload.

- 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.

- Read §4.1–4.4. Answer the reading questions (TeX source), and bring your answers to class on Tuesday.
- Begin Homework 6.

- 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.

For two extra-credit points, attend one of these two talks by Minah Oh on Monday or Tuesday, and complete these two questions on Moodle.

October 30

Intro to Sturm-Liouville problems

- Read §5.1–§5.3. Answer the reading questions (TeX source), and bring your answers to class on Thursday.
- Finish Homework 7 (due 4pm Thursday).
- Read the Final Project Information sheet and start thinking about what topic you might want to study.

- Read §5.4 and §5.5. To better understand connections between differential equations and linear algebra, read the Appendix to 5.5.
- Continue thinking about what you might want to work on for the Final Project.
- Begin Homework 8.

November 6

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.

November 8

Rayleigh quotient and eigenvalue bounds

due today

- 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).

November 15

due today

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.

November 27

Finite difference computational investigation: Richardson Scheme and Crank-Nicolson Scheme

- Read §6.5. (It's short!) Observe how finite differences can be used to approximate the wave equation.
- Finish Homework 10 (due 4pm Thursday).

December 4

December 19

2:00 – 4:00pm