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

Jump to today

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Do the following before next class:

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

Do the following before next class:

- Read §2.1 and §2.2. Note the definition of a
*linear operator*and the*principle of superposition*. - Finish Homework 2 (due 4pm Thursday).

Do the following before next class:

- 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.

Do the following before next class:

- 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).

Thursday

September 27

September 27

Orthogonality and initial conditions

Time-dependent solutions to the heat equation

Time-dependent solutions to the heat equation

Homework 3

due today

due today

Do the following before next class:

- 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.

Do the following before next class:

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

Do the following before next class:

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

Do the following before next class:

- 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.

Fall break! No class Tuesday, October 16.

Do the following before next class:

- 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.

Do the following before next class:

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

Do the following before next class:

- Finish Homework 6 (due 4pm Thursday).

Do the following before next class:

- 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.

Tuesday

October 30

October 30

Finish D'Alembert's solution to the wave equation

Intro to Sturm-Liouville problems

Intro to Sturm-Liouville problems

Do the following before next class:

- 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.

Do the following before next class:

- 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.

Tuesday

November 6

November 6

Sturm-Liouville problems

Operators, orthogonality, and self-adjointness

Operators, orthogonality, and self-adjointness

Do the following before next class:

- 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.

Thursday

November 8

November 8

Sturm-Liouville problems

Rayleigh quotient and eigenvalue bounds

Rayleigh quotient and eigenvalue bounds

Homework 8

due today

due today

Do the following before next class:

- 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.

Do the following before next class:

- 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).

Thursday

November 15

November 15

Homework 9

due today

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.

Thanksgiving break! No class Thursday, Nov. 22

Do the following before next class:

- 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.

Tuesday

November 27

November 27

Guest presentation

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

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

Do the following before next class:

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

Work on your final project. Meet with your group. Look for resources and refine your topic.

Tuesday

December 4

December 4

Work on your final project. Prepare an outline of what you intend to write in your paper. One person per group should upload the outline here.

Work on your final project. Prepare a rough draft of your paper to hand in on Tuesday. One person per group should upload the rough draft here.

Finish your final project.
One person per group should upload the paper here.
Each person must complete the Final Project Evaluation (on Moodle).

Wednesday

December 19

December 19

Project presentations

2:00 – 4:00pm

2:00 – 4:00pm