# Math 322 Applied Mathematical Analysis II: Spring 2018

 Lecture Room: B123 Van Vleck Lecture Time: 11:00–12:15 TuTh Lecturer: Jean-Luc Thiffeault Office: 503 Van Vleck Email: Office Hours: Tue 10:00–11:00, Thu 12:30–13:15

## Final exam

The final is Monday May 7, 2018 at 14:45–16:45, room Van Vleck B239.

• 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 two lectures on reactive particles 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 02/08 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 02/22 2.2: 2,3,4; 2.3: 1(bd),2(aceg),3(ab),4,5,7,11; 2.4: 1,2,3,4. 3 03/08 2.4: 7(b); 2.5: 1(bg),2,3(a),5(b),8(b),12; 3.3: 2(c),4,5(a),7,15. 4 03/22 3.4: 9,11; 3.5: 1; 3.6: 2; 4.2: 1; 4.4: 3,7,9,10. 5 04/05 5.3: 2,3,8,9; 5.4: 1; 5.5: 1(de),8; 5.8: 1,6,9,11. 6 04/19 7.2: 2; 7.3: 1(e),4(a),7(b); 7.7: 2(a),3,7. 7 05/03 7.8: 2; 7.9: 1(d),3(a),4(b); 7.10: 2(bd),9(d); 8.2: 1(bf),2(d),3,5,6(b).

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 Tuesday March 13, 2018 at 11:00–12:15, room Van Vleck B123 (in class) [solutions] Final exam Monday May 7, 2018 at 14:45–16:45, room Van Vleck B239

## Piazza

We'll use Piazza Q&A for 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. Note that we will only use Piazza for the Q&A feature, not for posting the actual homeworks.

## Schedule of Topics

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

 lecture date(s) sections topic 1 01/23 1.1–1.2 Heat equation 2 01/25 1.2–1.3 Heat equation (cont'd); Boundary conditions 3 01/30 1.4–1.5 Equilibrium distribution; Higher dimensions 4 02/01 1.5; 2.1–2.2 Higher dimensions (cont'd); Linearity 5 02/06 2.3 Separation of variables 6 02/08 2.3 Separation of variables (cont'd) 7 02/13 2.4 Separation of variables (cont'd) 8 02/15 2.5 Laplace's equation 9 02/20 2.5.2 Laplace's equation in a disk 10 02/22 2.5.4 Mean value theorem; Maximum principle; Uniqueness 11 02/27 3.1–3.3 Fourier series; Sine and cosine series 12 03/01 3.4–3.6 Differentiation and integration of Fourier series; Complex form 13 03/06 4.1–4.4 Wave equation 14 03/08 4.5; 5.1–5.4 Vibrating membrane; Sturm–Liouville eigenvalue problems 15 03/13 – Midterm 16 03/15 5.5 Sturm–Liouville eigenvalue problems 17 03/20 5.8 Sturm–Liouville example 18 03/22 7.1–7.3 Higher-dimensional PDEs – 03/27,29 – Spring Break 19 04/03 7.7 Vibrating circular membrane; Bessel functions 20 04/05 7.7–7.8 More on Bessel functions 21 04/10 7.9 Laplace in a Cylinder; Modified Bessel functions 22 04/12 7.10 Spherical coordinates; Legendre polynomials 23 04/17 7.10.3–5 Legendre functions; Reactive particle 24 04/19 – Reactive particle (cont'd) 25 04/24 8.1–8.3 Nonhomogeneous problems 26 04/26 8.5 Resonance 27 05/01 – Discussion of final; Review