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

Sep. 27

Sep. 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.

Tuesday

Oct. 23

Oct. 23

Wave equation

Do the following before next class:

- Finish Homework 6 (due 4pm Thursday).

Do the following before next class:

Tuesday

Oct. 30

Oct. 30

Sturm-Liouville problems

Do the following before next class:

Thursday

Nov. 1

Nov. 1

Sturm-Liouville problems

Operators, orthogonality, and self-adjointness

Operators, orthogonality, and self-adjointness

Homework 7

due today

due today

Do the following before next class:

Tuesday

Nov. 6

Nov. 6

Sturm-Liouville problems

Rayleigh quotient and eigenvalue bounds

Rayleigh quotient and eigenvalue bounds

Do the following before next class:

Thursday

Nov. 8

Nov. 8

Finite difference methods

Homework 8

due today

due today

Do the following before next class:

Tuesday

Nov. 13

Nov. 13

Finite difference methods

Do the following before next class:

Thursday

Nov. 15

Nov. 15

Finite difference methods

*Take-home exam assigned*Homework 9

due today

due today

Do the following before next class:

Tuesday

Nov. 20

Nov. 20

Higher-dimensional PDEs

Take-home exam

due today

due today

Thanksgiving break! No class Thursday, Nov. 22

Begin working on your project.

Tuesday

Nov. 27

Nov. 27

Guest presentation

Work on your project. Identify sources, gather information, and make an outline for what you will include in your paper.

Thursday

Nov. 29

Nov. 29

To be determined

Work on your project.

Tuesday

Dec. 4

Dec. 4

Work on projects

Work on your project.

Thursday

Dec. 6

Dec. 6

Work on projects

Work on your project.

Tuesday

Dec. 11

Dec. 11

Work on projects

Finish your project.

Upload your paper here, and prepare your presentation for tomorrow.
Please complete the Final Project Evaluation (on Moodle).
Wednesday

Dec. 19

Dec. 19

Project presentations

2:00 – 4:00pm

2:00 – 4:00pm