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 in RMS 405:** Mon. 9:00–10:00, Tues. 9:30–10:30, Wed. 2:00–3:00, Thurs 1:00–2:00, Fri. 9:00–10:00, whenever the door is open, or by appointment

**Help sessions:** Mondays 7:30–8:30 in RNS 204

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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.

Optionally, watch the following video: But what is a partial differential equation? (3Blue1Brown).

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.

Tuesday

September 17

September 17

Multidimensional heat equation

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). You may want to use the LaTeX template on Overleaf.

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, and bring your answer to class on Tuesday.
- Begin Homework 3.

Tuesday

September 24

September 24

Separation of variables, continued

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 26

September 26

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, and bring your answer to class on Tuesday.
- Begin Homework 4.

Tuesday

October 1

October 1

Laplace's equation and separation of variables

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).

Thursday

October 3

October 3

Fourier series

*Take-home exam assigned*Homework 4

due today

due today

Do the following before next class:

- Complete the take-home exam.

Tuesday

October 8

October 8

Fourier series

Take-home exam

due today

due today

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.

Thursday

October 10

October 10

Differentiation of Fourier series

Fall break! No class Tuesday, October 15.

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.

Thursday

October 17

October 17

Eigenfunction expansion

Homework 5

due today

due today

Do the following before next class:

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

Tuesday

October 22

October 22

Eigenfunction expansion

Wave equation

Wave equation

Do the following before next class:

- Finish Homework 6 (due 4pm Thursday).

Thursday

October 24

October 24

Wave equation

Homework 6

due today

due today

Do the following before next class:

- Begin Homework 7.

Tuesday

October 29

October 29

Intro to Sturm-Liouville problems

Do the following before next class:

- Read §5.1–§5.3. Answer the reading questions, 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.

Thursday

October 31

October 31

Sturm-Liouville problems

Homework 7

due today

due today

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 5

November 5

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 7

November 7

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!

Tuesday

November 12

November 12

Finite difference methods

Do the following before next class:

Thursday

November 14

November 14

Finite difference methods

Homework 9

due today

due today

Do the following before next class:

Tuesday

November 19

November 19

Finite difference methods

Do the following before next class:

Thursday

November 21

November 21

Finite difference methods

*Take-home exam assigned*Homework 10

due today

due today

Complete the take-home exam before next class.

Tuesday

November 26

November 26

To be determined

Thanksgiving break! No class Thursday, Nov. 22

Do the following before next class:

Tuesday

December 3

December 3

Final projects

Work on your final project.

Thursday

December 5

December 5

Final projects

Work on your final project.

Tuesday

December 10

December 10

Final projects

Work on your final project.

Wednesday

December 18

December 18

Project presentations

9:00 – 11:00am

9:00 – 11:00am