# Ordinary Differential Equations

CU Boulder

Instructor: Yuhao Hu

Email: yuhao.hu@colorado.edu

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]

**Reading:**pp. 1-4, pp. 20-23

**Exercises:**[p. 27,

**Ex3**: 1, 2, 3] (meaning: page 27, Exercise 3, questions 1, 2 and 3.)

[Lecture 2]

**Reading:**pp. 24-27, pp. 28-36

**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

## Grading

Two lowest homework grades will be dropped.

**Homework:**30%**Midterm I:**20%**Midterm II:**20%**Final Exam:**30%