Math 23
Differential Equations
Last updated May 24, 2016

## Syllabus

The following is a tentative syllabus for the course. The textbook section listed for each day is the one that we intend to cover for that day, and it should be read before coming to class. Please separate your turn-in homework in an A pile and a B pile, staple each pile separately and turn them in in the appropriate box outside Kemeny 008 on Wednesday by 11AM.

Here is a practice first midterm and its solutions. You can find multiple old final exams here. Please keep in mind that questions in the practice exams may use material we haven't covered or emphasized in the class. The exam will be loosely based on the turn-in homework.

Lectures Sections in Text Brief Description Turn-in Homework Extra Practice Homework
M 3/28 1.1, 1.2 What are differential equations? A: 1.1: problems 4,9,23
A: 1.2: problems 7
1.1: problems 1-3, 5-8, 10-20
1.2: problems 8,9,12,13
W 3/30 1.3, 2.1 Classification and linear first-order ODEs. A: 1.3: problems 5,6
B: 2.1: problems 16,19,30
1.3: problems 21-24
2.1: problems 1-15, 27-29, 31-33
F 4/01 2.2,2.4 Separable equations and existence-uniqueness theorems B: 2.2: problems 3,6,23 2.2: problems 7-27 (only part a)
M 4/04 2.3 Modeling with differential equations A: 2.4: problems 4,15,25
A: 2.3: problems 2,8
2.4: problems 1-6, 13-16, 27, 28
2.3: problems 1, 3-7, 9-12
W 4/06 2.5 Autonomous equations and population dynamics B: 2.5: problems 3 (also implicitly solve the equation), 7 2.5: problems 1-2, 4-6, 8-13
F 4/08 2.6 Exact equations B: 2.6: problems 8,10,14 2.6: problems 1-7, 9, 11-13, 18-22
M 4/11 3.1, 3.2 Second order constant coefficient with distinct real roots; the Wronskian A: 3.1: problems 5, 11 (do not sketch)
A: 3.2: problems 6, 10, 12, 25
3.1: problems 1-4, 6-10, 12-18
3.2: problems 1-5, 7-9, 11, 13-27
Tu 4/12 Section 1 (Tanabe) meets instead of 4/11. Covers the same topics.
W 4/13 3.3 Complex conjugate roots B: 3.3: problems 11, 22 (do not sketch) 3.3: problems 1-10, 12-21
F 4/15 3.4 Repeated roots and reduction of order B: 3.4: problems 6, 12 (do not sketch), 28 3.4: problems 1-5, 7-11, 13-14, 23-27, 29-30
M 4/18 3.5 Method of undetermined coefficients A: 3.5: problems 6, 18 3.5: problems 1-5, 7-17, 18-20
Tu 4/19 Review for midterm
W 4/20 3.6 Variation of parameters A: 3.6: problems 4, 13 3.6: problem 1-3, 5-12, 14-20
F 4/22 3.7, 3.8 Modeling of vibrations B: This problem set
M 4/25 7.2 Review of matrices, part 1 No HW today. Do extra problems until you're confortable with matrix multiplication and determinants 7.2: problems 1-9
W 4/27 4.1, 4.2 Order n homogeneous linear equations with constant coefficients A: 4.1: problems 3, 15
A: 4.2: problem 12, 15, 32 (do not graph)
4.1: problems 1-2, 4-6, 11-14
4.2: problems 1-11, 13-14, 16-31, 33-36
F 4/29 4.3, 4.4 Undetermined coefficients and variation of parameters for order n equations B: 4.3: problems 5,11 (do not graph)
B: 4.4: problems 3
4.3: problems 1-4, 6-10, 12-18, 20-22
4.4: problems 1-2, 4-6, 9-12
M 5/02 7.1, 7.3 Review of matrices, part 2. Introduction to systems of ODEs. A: 7.1: problems 5, 7(a), 22(a)
No HW for 7.3, do extra problems until you're confortable with finding eigenvalues and eigenvectors.
7.1: problems 1-4, 6, 8-12, 17-21
7.2: problems 10-19
7.3: problems1-25
W 5/04 7.4 Existence and uniqueness of solutions of systems of ODEs A: 7.4: problem 6 7.4: problems 4, 7
F 5/06 7.5 Constant coefficients systems with distinct real eigenvalues B: 7.5: problems 9,11,15 7.5: problems 1-8, 10, 12-14, 16-18
M 5/09 7.6 Constant coefficient systems with complex conjugate eigenvalues A: 7.6: problems 7, 9 7.6: problems 1-6, 8, 10
Tu 5/10 Review for midterm
W 5/11 7.8 Repeated eigenvalues A: 7.8: problems 7 and 11, part (a) 7.8: problem 1-6,8-10,12,17-21
F 5/13 5.1, 5.2 Power series review and solution near an ordinary point No turn-in HW for 5.1; do as much practice as required.
B: 5.2: problems 5 and 7, parts (a)-(c)
5.1: problems 1-8, 19-26
5.2: problems 1-4,6,8-14
M 5/16 5.3, 5.4 Convergence of power series solutions; the Euler equation A: 5.3: problems 6
A: 5.4: problems 9, 14
5.3: problems 5,7,8
5.4: problems 1-8, 10-13, 15-16
W 5/18 10.1 Boundary value problems; eigenfunctions B: 10.1: problems 3, 8, 15 10.1: problems 1-2, 4-7, 9-14, 16-19, 23
F 5/20 10.2 Fourier series B: 10.2: problem 13 10.2: problems 1-12, 14-24, 29
M 5/23 10.3, 10.4 Fourier convergence theorem. Even and Odd Functions. Note: the turn-in HW for this week will not be collected or graded. It is only meant as an indication of exam-type problems.
10.3: problem 2(a)
10.4: problems 7, 9, 15
10:3: problems 1, 3-12, 17
10.4: problems 1-6,8,9-12, 13, 16-21, 35-40
W 5/25 10.5 The heat equation 10.5: problems 8, 10 10.5: problems 9, 11, 12
F 5/27 10.6 Other heat conduction problems 10.6: problems 11 (a), 14 (a) 10.6: problems 1-8, 9-10 (a), 12 (a)-(b), 13 (a)
Tu 05/31 Review

Nicolas Petit
Last updated May 24, 2016