Math 3430, Spring 2020

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%