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, 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]
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]



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

[Lecture 3]
Reading: pp. 38-41, reading material 1 (link)
Exercises: [p. 45, Ex5: 3, 5]

[Lecture 4]
Reading: pp. 52-55
Exercises: [pp. 55-56, Ex6: 3, 4, 6, 7, 15, 18, 20]



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

[Lecture 5]
Reading: pp. 57-60
Exercises: [p. 61, Ex7: 1, 5, 6, 8, 10, 13]

[Lecture 6]
Reading: pp. 70-79
Exercises: [p. 79, Ex9: 4, 7, 8, 13, 15]

[Lecture 7]
Reading: pp. 83-87
Exercises: [pp. 90-91, Ex10: 3, 7, 8, 10, 12]



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

[Lecture 8]
Reading: pp. 92-95
Exercises: [p. 97, Ex11: 5, 6, 11, 14, 15, 17]

[Lecture 9]
Reading: pp. 107-110, pp. 117-118
Exercises: [p. 112, Ex13: 2, 14] and [p. 120, Ex 14 11, 14, 15]

[Lecture 10]
Reading: pp. 196-203
Exercises: [p. 204, Ex18: 4(b,g), 5, 6, 8]



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

[Lecture 11]
Reading: pp. 211-220
Exercises: [p. 220, Ex20: 1, 2, 14, 26, 33]

[Lecture 12]
Reading: no new readings
Exercises: [p. 220, Ex20: 9, 15, 35]

[Lecture 13]
Reading: pp. 221-230
Exercises: [pp. 231-232, Ex21: 3, 4, 6, 8, 10]



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

[Lecture 14]
Reading: no new readings
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]
Reading: pp. 233-240
Exercises: [p. 240, Ex22: 7, 9, 12, 19]

[Lecture 17]
Reading: no new readings
Exercises: [p. 240, Ex22: 14, 18]

[Lecture 18]
Reading: pp. 251-262
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]
Reading: pp. 295-303
Exercises: [p. 311, Ex27: 13, 14, 15, 16, 18, 19]

[Lecture 21]
Reading: Laplace Transform I
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



Grading

Two lowest homework grades will be dropped.

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