## MATH 3200, Elementary Differential Equations (SPRING 2021)

Class Web Page

Course Syllabus

Welcome to Math 3200, Elementary Differential Equations, Spring 2021. Take a look at the course syllabus, and make sure you havge access to the course textbook.

This web site will be where you find

- course lecture videos
- assignments
- announcements
- handouts and other course material

so check the site regularly.

Class will be over Zoom at 991-699-1928 at the specified times, starting January 19, 2021. The first videos and assignment will be posted soon.

Take a look at this quick video introduction.

### Chapter 1

Here is the first lecture video first lecture video on the difference between explicit and implicit
solutions for ODE's.
Here is lecture #2 on the Euler method. I noticed that I wrote the exact solution to the example I did
incorrectly on the white board, but correctly in the Matlab program. See if you can find my mistake!

Homework problems for Thursday 1/21 and Tuesday 1/26.
Section 1.1 #13-17

Section 1.2 #1-13, 20,21,22

Here is the solution for problem 17 from section 1.1.

And you can expect a quick quiz based on the homework first thing tomoorow (tuesday). This will help me guage how we're all doing.

Homework problems for Tuesday 2/2. (We will discuss some from section 1.3 on 1/28.)
Section 1.3 #3,4

Section 1.4 #1,2,12

If you want to use Matlab, you will find instructions here:
https://www.ucdenver.edu/offices/office-of-information-technology/software/how-do-i-use/matlab

### Chapter 2

Here is Lecture 3 on first order linear ODE's.
Here is Lecture 4 on exact equations.
Note: Everybody in this course has been through the Calculus sequence, so you have learned how to integrate,
i.e., find anti-derivatives of functions. We all know how unpleasant this can be, so in this course it is ok (in fact incouraged)
to use a table of integrals, or software like "derive" to calculate integrals. From now on, you can think of using calculus
to solve a problem the same way you think of using algebraic techniques.

Homework problems for February 2 and 4.
Section 2.2 # 1-6, 17-22, 27, 28

Section 2.3 # 1-6, 7-10, 17-20, 25, 28, 29

Homework problems for February 9 and 11.
Section 2.4 #1-5, 9-13, 21-24, 32

Homework problems for February 16
Section 2.5 #1-4, 13,14

Section 2.6 #9-12, 21-24

Here is a solution for Quiz #3.

### Chapter 3

Here is Lecture 5 on improved Euler's method
Homework problems for February 23 and 25
Section 3.2 #6,7

Section 3.3 #1,2,15

Homework problems for March 2 and 4
Section 3.4 #1, 25a,b,c,d

Section 3.6 #1,2,18

Here's an exercise for the numerical techniques: y' = 1-xy, y(1)=1. Approximate Y(2) using Euler, Improved Euler, and Runge-Kutta with step size h=1.

### Chapter 4

Read over section 4.1 to get an idea of what we will be getting to in this chapter.
Homework problems for March 9
Section 4.2 #1-4, 13-16, 21

Here's the midterm exam due March 12 before midnight.
And here are solutions for the exam.
Homework problems for March 18
Section 4.3 #21-24, 28,29

Homework problems for March 23 and 25
Section 4.4 # 1-8 (no work needed on these), 9-16

Section 4.5 #1,2,3-6, 17-20

Section 4.6 #3,4,7,9,10

I just noticed that our syllabus isn't quite right for what we are going to do in chapters 4 and 5, so I made a few little changes.
We will start sections 4.9 and 4.10 on spring dynamics next week.
Here is Lecture 6 on the reduction of order method.
Homework problems on spring-mass systems, due tuesday, April6
Section 4.9 #3,5,13

Section 4.10 #3,7

And here is Lecture 7 on spring-mass systems with external forces (including the phenomenon of resonance).

The rest of the semester will be devoted to systems of ode's, in particular, sections 5.2, 5.4, and 9.4-9.8. If there's time
we can go back and cover section 5.3 on numerical solutions for systems of ode's.
### Chapter 5

Homework problems for April 8 and 13.
section 5.2 #34

section 5.4 #1,2,3,4,7,8,10

### Chapter 9

Homework for April 27 and 29
Read section 9.1-9.4. This should be mostly a review of what you learned in your Linear Algebra course,
but the idea of a matric of functions might be new.

Section 9.5 #1-4, 11-14

Section 9.6 #1-4, 5-8

Homework for May 4
Section 9.7 #1-4

Look at section 9.8 on matrix exponentials.

### Final Exam

Here is the Final Exam due tomorrow night before midnight. Email me if you have questions. Good luck!
And here are Solutions. I hope everybody enjoyed the course and learned some useful mathematics!