# Math 322 Applied Mathematical Analysis II: Fall 2018

 Lecture Room: 115 Van Hise Lecture Time: 11:00–12:15 TuTh Lecturer: Jean-Luc Thiffeault Office: 503 Van Vleck Email: Office Hours: Tue 12:15–13:00, Thu 8:30–9:15

## Final exam

The final is Wednesday December 19, 2018 at 12:25–14:25.

• No notes, books, calculators, cell phones, .... Just a pen/pencil and eraser.
• The exam consists of four questions.
• The exam material is cumulative, but it will be heavily skewed towards the post-midterm material.
• You should definitely know how to carry out separation of variables, both in Cartesian, cylindrical polar, and spherical polar coordinates.
• You do not need to know by heart the definition of Bessel functions, Legendre polynomials, or the equation they satisfy. If there is a question about them on the exam, this information will be provided. You do however need to carry out separation of variables in various coordinates systems, which will naturally lead to Bessel's equation and Legendre's equation.
• You do not need to know the derivation of Legendre polynomials themselves.
• The lectures on hagfish and cooking are not on the exam.
• Green's functions are not on the exam.

## Syllabus

See the official syllabus.

## Textbook

The textbook for the class is Applied Partial Differential Equations by Richard Haberman.

The current edition is the Fifth, but you can use earlier editions if you find them for cheaper. (Earlier edition might be missing a bit of material, so you can use the copy on reserve in the library for reference in those cases.)

## Prerequisites

Math 319 and 321.

## Homework

Every two weeks or so I will assign homework from the textbook (or other sources) and post it here. The homework will be due in class about two weeks later.

 homework due date problems 1 09/25 1.2: 3,5; 1.3: 1,2; 1.4: 1(bceg),2,5,10; 1.5: 1,3,5,12,18,19,22,23. 2 10/09 2.2: 2,3,4; 2.3: 1(bd),2(aceg),3(ab),4,5,7,11; 2.4: 1,2,3,4. 3 10/23 2.4: 6(b); 2.5: 1(bg),2,3(a),5(b),8(b),12; 3.3: 2(c),4,5(a),7,15. 3.4: 9,11; 3.5: 1; 3.6: 2; 4 5 4.2: 1; 4.4: 3,7,9,10. 5.3: 2,3,8,9; 5.4: 1; 5.5: 1(de),8; 5.8: 1,6,9,11. 7.2: 2; 7.3: 1(e),4(a),7(b); 7.7: 2(a),3,7. 7.8: 2; 7.9: 1(d),3(a),4(b); 7.10: 2(bd),9(d); 6 04/15 8.2: 1(bf),2(d),3,5,6(b); 8.3: 1(ae),6; 9.2: 4(ab); 9.3: 1,3,4,11,12(b),21,23.

There will be a midterm exam and a cumulative final exam. The final grade will be computed according to:

 Homework 35% Midterm exam 30% Final exam 35%

## Exam Dates

The midterm exam will be given in class on the date below.

 Midterm exam Tue Oct 30, 2018 at 11:00–12:15 (in class) Final exam Wed Dec 19, 2018 at 12:25–14:25 (room SOC SCI 6240)

## Canvas

We'll use Canvas discussions about the class and related topics. Feel free to post questions and answers there about homeworks and exams, logistics, or relevant interesting things you found on the web.

## Schedule of Topics

Note: there is not necessarily a one-to-one correspondence between lectures numbers and dates.

 lecture date(s) sections topic 1 09/06 1.1–1.2 Heat equation 2 09/11 1.3–1.4 Boundary conditions; Equilibrium distribution 3 09/13 1.5 Higher dimensions 4 09/18 2.1–2.3 Linearity; Separation of vatiables 5 09/20 2.3 Separation of variables (cont'd) 6 09/25 2.3.6; Appendix to 2.3 Separation of variables (cont'd) 7 09/27 2.4 Separation of variables (cont'd) 8 10/02 2.5 Laplace's equation 9 10/04 2.5.2 Laplace's equation in a disk 10 10/09 2.5.4 Mean value theorem; Maximum principle; Uniqueness 11 10/11 3.1–3.3 Fourier series; Sine and cosine series 12 10/16 3.4–3.6 Differentiation and integration of Fourier series; Complex form 13 10/18 4.1–4.5 Wave equation 14 10/23 5.1–5.4 Sturm–Liouville eigenvalue problems 15 10/25 5.5 Sturm–Liouville proofs – 10/30 – Midterm [mean 80.6%; solutions] 16 11/01 5.6–5.8 Rayleigh quotient; Sturm–Liouville example 17 11/06 7.1–7.5 Higher-dimensional PDEs 18 11/08 7.7–7.8 Vibrating circular membrane; Bessel functions 19 11/13 7.9 Laplace's equation in a cylinder 20 11/15 7.10 Spherical coordinates; Legendre polynomials 21 11/20 – Cooking by flipping 22 11/27 8.1–8.5 Nonhomogeneous problems; Resonance 23 11/29 9.1–9.3 Green's functions 24 12/04 9.4 Green's functions (cont'd) 25 12/06 9.5.5–9.5.6 Green's functions (cont'd) 26 12/11 – The heat equation and probability