## Course information

Department of Mathematics

University of California

Davis, CA 95616, USA

e-mail: `jkhunter@ucdavis.edu`

Office Phone: (530) 601-4444 x4016

Office: MSB 3230

Office hours: MW 4:15–5:30 p.m.

Classroom: Geidt 1001

Matthew Cha: MSB 3139

Office hours:
T 3:00–4:30 p.m.

Ji Chen: MSB 3131

Office hours:
M 11:00 a.m.–12:15 p.m.

Dmitry Shemetov: MSB 2127

Office hours:
R 1:45–3:00 p.m.

Yue Zhao: MSB 2202

Office hours:
R 3:00–5:00 p.m.

T=Tuesday, R = Thursday

## Announcements

Here are solutions to the final exam.

Scores should be posted to Canvas by the end of the week.

## Text

Elementary Differential Equations, William F. Trench, Free Edition 1.01 (December 2013)

The text is free to download and use under the American Institute of Mathematics' Open Textbook Initiative, subject to the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Click on the title above to download a copy.

## Solution Manual

Student Solutions Manual for Elementary Differential Equations, William F. Trench. (Has solutions to even-numbered problems.)

## Syllabus

The course will cover material from Chapters 1 – 6, 10 of the text

- Chapter 1 Introduction
- 1.1 Examples
- 1.2 Concepts
- 1.3 Direction fields

- Chapter 2 First order ODEs
- 2.1 Linear ODEs
- 2.2 Separable ODEs
- 2.3 Existence and uniqueness of solutions

- Chapter 3 Numerical methods
- 3.1 Euler's method (will not be on the final exam)

- Chapter 4 Applications of first order ODEs
- 4.1 – 4.2 Growth and decay
- 4.3 Mechanics

- Chapter 5 Linear second order ODEs
- 5.1 Homogeneous ODEs
- 5.2 Constant coefficient ODEs
- 5.3 – 5.5 Nonhomogeneous ODEs
- 5.6 Reduction of order

- Chapter 6 Applications of second order ODEs
- 6.1 – 6.2 Linear oscillators

- Chapter 10 Linear systems of ODEs
- 10.2 – 10.3 Systems of ODEs
- 10.4, 10.6 Constant coefficient homogeneous systems (we didn't cover 10.5 and it won't be on the final exam)

~~If time permits, the course will also cover
~~

~~Chapter 8 Laplace transforms~~Time did not permit.- 8.1 – 8.3 Solution of initial value problems

The department syllabus (using a different text) can be found here.

## Important Dates

- First class: Mon, Apr 3
- Last day to add: Tue, Apr 18
- Last day to drop: Fri, Apr 28
- Last class: Wed, Jun 7
- Academic holidays: Mon , May 29

## Exams

There will be two Midterms and a Final

- Midterm 1: Wed, Apr 26 (in class)
- Midterm 2: Wed, May 24 (in class)
- Final: Mon, June 12, 6:00 – 8:00 p.m. (Exam Code J)

**
There will be no makeup exams.
**

## Midterm 1

Here are solutions to Midterm 1. Scores will be posted to Canvas on Tue, May 4.

Midterm 1 will be in class 3:10-4:00 p.m. on Wed, Apr 26. The exam will cover introductory ideas on ODEs, first-order ODEs, and applications of first-order ODEs:

- Chapter 1 Introduction
- 1.1 Examples
- 1.2 Concepts
- 1.3 Direction fields

- Chapter 2 First order ODEs
- 2.1 Linear ODEs
- 2.2 Separable ODEs
- 2.3 Existence and uniqueness of solutions
- Chapter 4 Applications of first order ODEs
- 4.1 Growth and decay
- 4.2 Cooling and Mixing
- 4.3 Mechanics

Here are some sample midterm questions.

Here are solutions to the sample midterm questions.

## Midterm 2

Midterm 2 will be in class on Wed, May 24. It will cover second order linear ODEs

- 5.1 Homogeneous ODEs
- 5.2 Constant coefficient ODEs
- 5.3 – 5.4 Nonhomogeneous ODEs
- 5.6 Reduction of order

- 6.1 – 6.2 Linear oscillators

Here are some sample midterm questions. Here are solutions to the sample midterm questions.

## Final

Here are some sample final exam questions. Here are solutions to the sample final exam questions.

## Homework

Homework problems will be assigned each week on this web page from the text, but homework will not be collected or graded. Be sure to do the problems yourself before consulting the solutions, and don't expect to pass this class unless you do the homework.

## Grade

The course grade will be based on (weights in parentheses):

- Midterms (30% each)
- Final (40%)

## Other resources

Additional lecture notes for Math 22B are in Craig Tracy's Lectures on Ordinary Differential Equations.

MATLAB is a useful platform for the numerical solution of ODEs (and many other things).
MATLAB for Students is available to UCD students at no charge for Spring Quarter. Go to the https://software.ucdavis.edu website and select *MatLab for Students* to access the software. This license will expire on June 30th.

## Math 22B Support Workshops at SASC

Casey Davis, a math/physics specialist at the Student Academic Success Center, will be offering Math 22B support workshops: MW 12:10–1:00 p.m. in 3218 Dutton Hall as well as drop-in tutoring MR 3:30–5:30 p.m. and F 10:00–11:50 a.m. in 26 South Hall.

## Homework Sets

Problem numbers refer to the exercises in the text.

**Set 1** (Friday, Apr 7)

- Read Section 1.1 (We didn't cover this section in class. But you should read the other sections as well!)
- Sec. 1.2, p.14: 1, 2(a)(e)(g), 4(a)(d)(h), 5(d), 8, 9
- Sec. 1.3, p.20: 1, 2, 6, 7, 10

**Set 2** (Friday, Apr 14):

- Sec 2.1, p. 41: 1, 2, 3, 6, 9, 16, 19, 20, 30, 33, 45, 46
- Sec 2.2, p. 52: 1, 2, 3, 4, 11, 12, 17, 18, 20, 27, 29

**Set 3** (Friday, Apr 21):

- Sec 2.3, p. 60: 1, 2, 4, 7, 10, 13, 14, 16, 20
- Sec. 2.4, p. 68: 1, 2, 8
- Sec. 4.1, p. 138: 2, 8, 15
- Sec. 4.2, p. 148: 2, 10
- Sec. 4.3, p. 160: 4, 18

**Set 4** (Friday, May 5):

- Sec. 5.1, p. 203: 1, 2, 4(a)(b), 5(a)(b)(c), 8, 24, 28, 30, 37, 44
- Sec. 5.2, p. 217: 1, 2, 4, 6, 8, 14, 17

**Set 5** (Friday, May 12):

- Sec. 5.2, p. 217: 22 (a)(b), 30, 33, 34
- Sec. 5.3, p. 227: 1, 2, 8, 30, 31, 34, 39
- Sec. 5.4: p. 235: 2, 16, 24, 27
- Sec. 5.5: p. 244: 1, 4, 8, 24, 28, 29, 40(a)(b)

**Set 6** (Wednesday, May 24):

- Sec. 5.6, p. 253: 2, 18, 20
- Sec. 6.1, p. 277: 2, 11, 14, 18
- Sec. 6.2, p. 288: 8, 24, 25

**Set 7** (Friday, June 9):

- Sec. 10.2, p. 519: 1(c), 2(d), 3(a), 6
- Sec. 10.3, p. 526: 7(a)(b), 16(a)
- Sec. 10.4, p. 540: 4, 8, 16, 28, 30, 32, 33
- Sec. 10.6, p. 566: 2, 18, 26, 30, 33, 34