Source: http://mlwright.org/teaching/math330f18/
Timestamp: 2019-04-22 14:19:05+00:00

Document:
Read §1.1 through §1.2 in the textbook. Answer the reading questions, and bring your answers to class on Tuesday.
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.
Read §2.1 and §2.2. Note the definition of a linear operator and the principle of superposition.
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.
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.
Read §3.1 and §3.2. Note the convergence theorem for Fourier series.
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.
Fall break! No class Tuesday, October 16.
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 §4.1–4.4. Answer the reading questions (TeX source), and bring your answers to class on Tuesday.
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.
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.
Read §5.1–§5.3. Answer the reading questions (TeX source), and bring your answers to class on Thursday.
Read §5.4 and §5.5. To better understand connections between differential equations and linear algebra, read the Appendix to 5.5.
Re-read §5.5. Note the role of Lagrange's identity and Green's formula in the proofs presented in this section.
Complete the Final Project Planning Survey on Moodle. See also the Final Project Information.
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.
Complete the take-home exam before next class: PDF file, TeX source, Moodle link for file upload.
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.
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.
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).

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