Math 3430, Spring 2020

Due to COVID-19, we have changed this course to an online format using Canvas, so I've stopped updating this page since 03/16/2020.

# Ordinary Differential Equations CU Boulder

Instructor: Yuhao Hu

Office: Math 225

Office Hours: WF 4:00-5:45pm

Lectures: MWF 12:00-12:50pm at KCEN N252

## Overview

The subject of this course is ordinary differential equations (ODEs). These are equations that involve the rate of change of certain unknown function(s) with respect to a single independent variable, which is often time. Though there is a theoretical side of ODEs, this course is rather concerned with solution techniques and applications; hence, our goal is quite straightforward: to be able to identify the type of an ODE/system and solve it using an appropriate method.

## Textbook

Ordinary Differential Equations by M. Tenenbaum and H. Pollard

## Schedule

(weekly, only the first meeting of the week is dated; "Ls." stands for "Lesson" in the textbook.)

01/13    ODEs and their solutions (Ls. 1, 3); general/particular solutions (Ls. 4)

01/22    1st-order ODEs, Direction field, phase line (Ls. 5A, additional reading); separable equations (Ls. 6C)

01/27    1st-order ODE with homogeneous coefficients (Ls. 7); exact equations (Ls. 9, 10A);
integrating factors (Ls. 10B)

02/03    Linear 1st-order ODE, integrating factors (Ls. 11A-C);
applications of 1st-order ODEs (a selection from Ls. 13, 14);
higher-order ODEs and complex numbers (Ls. 18)

02/10    2nd-order Constant-coefficient Linear ODE, method of characteristic equations (Ls. 20);
higher order constant-coefficient Linear ODE (Ls. 20);
Constant-coefficient Linear ODE, non-homogeneous case (Ls. 21)

02/17 (Midterm I on Wednesday)    Reduction of order (Ls. 23)

02/24    Variation of parameters (Ls. 22); differential operators (Ls. 24)

03/02    Laplace transform (Ls. 27A); Laplace transform, properties (Ls. 27B,D); the Laplace method (Ls. 27C)

03/09    Step functions and delta functions (additional notes);
ODEs with discontinuous forcing terms (additional notes); Undamped Motion (Ls. 28)

03/16    Damped Motion (Ls. 29); other 2nd-order problems (selection from Ls. 30M)

03/23-27 (Spring break; no class)

03/30

04/06 (Midterm II on Wednesday)

04/13

04/20

04/27

## Homework

(Due on each Friday, unless specified otherwise.)

Homework 1 (Lectures 1-2) due Jan. 24

[Lecture 1]
Exercises: [p. 27, Ex3: 1, 2, 3] (meaning: page 27, Exercise 3, questions 1, 2 and 3.)

[Lecture 2]
Exercises: [p. 27, Ex3: 4] and [p. 37, Ex4: 4, 6, 12, 14, 20, 28]

Homework 2 (Lectures 3-4) due Jan. 31

[Lecture 3]
Exercises: [p. 45, Ex5: 3, 5]

[Lecture 4]
Exercises: [pp. 55-56, Ex6: 3, 4, 6, 7, 15, 18, 20]

Homework 3 (Lectures 5-7) due Feb. 7

[Lecture 5]
Exercises: [p. 61, Ex7: 1, 5, 6, 8, 10, 13]

[Lecture 6]
Exercises: [p. 79, Ex9: 4, 7, 8, 13, 15]

[Lecture 7]
Exercises: [pp. 90-91, Ex10: 3, 7, 8, 10, 12]

Homework 4 (Lectures 8-10) due Feb. 14

[Lecture 8]
Exercises: [p. 97, Ex11: 5, 6, 11, 14, 15, 17]

[Lecture 9]
Exercises: [p. 112, Ex13: 2, 14] and [p. 120, Ex 14 11, 14, 15]

[Lecture 10]
Exercises: [p. 204, Ex18: 4(b,g), 5, 6, 8]

Homework 5 (Lectures 11-13) due Feb. 21

[Lecture 11]
Exercises: [p. 220, Ex20: 1, 2, 14, 26, 33]

[Lecture 12]
Exercises: [p. 220, Ex20: 9, 15, 35]

[Lecture 13]
Exercises: [pp. 231-232, Ex21: 3, 4, 6, 8, 10]

Homework 6 (Lectures 14-15) due Feb. 28

[Lecture 14]
Exercises: [p. 232, Ex21: 28, 30, 31]

[Lecture 15]
Reading:pp. 241-246 (Note: The book uses different notations than we did in class.)
Exercises: [p. 246, Ex23: 1, 3, 11, 12, 16]

Homework 7 (Lectures 16-18) due Mar. 06

[Lecture 16]
Exercises: [p. 240, Ex22: 7, 9, 12, 19]

[Lecture 17]
Exercises: [p. 240, Ex22: 14, 18]

[Lecture 18]
Exercises: [p. 266, Ex24: 5(a,c), 6(c), 9(a), 10(a,c), 12(a), 13(a), 14(a,c), 15(a)]

Homework 8 (Lectures 19-21) due Mar. 13

[Lecture 19]
Reading: pp. 263-265 and pp. 292-295
Exercises: [p. 267, Ex24: 19, 33] and [p.311, Ex27: 1, 2]

[Lecture 20]
Exercises: [p. 311, Ex27: 13, 14, 15, 16, 18, 19]

[Lecture 21]
Exercises: no new exercises

## Exams

Midterm I: 2/19 Wednesday

Topics covered: Lectures 1-12
(A formula sheet allowed, A4 size, front and back, created on your own.)

Sample Exam // Solutions

Exam // Solutions

Midterm II: 4/8 Wednesday

Final: TBD