 Math 3430, Spring 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, Ls. 3); general/particular solutions (Ls. 4)

01/22    1st-order ODEs, Direction field (Ls. 5); 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, 17)
Higher-order ODEs and complex numbers (Ls. 18)

02/10    2nd-order Constant-coefficient Linear ODE, method of characteristic polynomial (Ls. 20, 21);
Existence theorem of linear ODEs (Ls. 19); reduction of order (Ls. 23)

02/17 (Midterm I on Wednesday)    Variation of parameters (Ls. 22); Laplace transform (Ls. 27A)

02/24    Laplace transform, properties (Ls. 27B,D); the Laplace method (Ls. 27C);
step functions and delta functions (additional notes)

03/02    Undamped Motion (Ls. 28); damped Motion (Ls. 29); other 2nd-order problems (selection from Ls. 30M)

03/09

03/16

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]

## Exams

Midterm I: 2/19 Wednesday

Midterm II: 4/8 Wednesday

Final: TBD