## Math 303 - Calculus IV: Ordinary Differential Equations (Fall 2017)

Instructor: Ben McMillan
Email: bmcmillan@math.stonybrook.edu
Locataion: MWF 12:00pm--12:53pm in Harriman Hall 137

### Announcements

• The final is in Harriman Hall 137, where lecture is.

### Course Information:

The course syllabus is here. Some critical points:
• The midterm will be in class on October 11.
• My office hours this term are Mondays 1-2pm and Fridays 3-4pm in the math tower, office 2-116. I will also be available in the MLC (S-235) on Wednesdays 1:30-2:30pm.

### Schedule and Homework:

The following is a tentative schedule for the course. As homework is assigned it will be posted here. You are encouraged to work with others, but please make sure to write up solutions in your own words (this will help you on the exams and quizzes!).

Unless stated otherwise, the homework is from the corresponding section of the book.

All of the problems assigned in week n are due to your TA (at the start of recitation) in week n+1.

Week Date Topic(s) Covered Reading Homework
1 8/28What's a differential equation, and why?Chapter 1.12, 3, 13, 27, 29, 34
8/30Integrals as solutions, initial value problems1.21, 2, 4, 12, 18, 31
9/1Separable equations1.43, 8, 11, 22
2 9/4Labor DayNoneNone
9/6Slope fields1.3[1, 8 do but don't turn in], 11, 13, 14, 27
9/8Linear first order equations1.51, 3, 16, 20, 29, 33
3
Quiz
Week
9/11Change of variables1.67, 12, 29, 57, 58
9/13More substitutions1.620, 24, 43, 45, 48, 53
9/15Population models2.19, 10, 12, 31
4 9/18Logistic Model of populations2.11, 21
9/20Equilibrium Solutions2.21, 3, 14, 19
9/22Second Order Linear Equations3.11, 9, 13, 15
5
Quiz
Week
9/25Superposition principle, existence and uniqueness of solutions3.117, 19, 29
9/27Solving constant coefficient 2nd order homogeneous equations. Linear independence3.133, 37, 51, 52
9/29The Wronskian3.121, 24, 26
6 10/2Inhomogeneous equations
Higher order linear equations
3.1
3.2
3.1 - 27
3.2 - 13, 17, 20, 21, 23, 25
10/4Variation of parameters3.53, 4, 13, 20, 30, 32
10/6Homogeneous constant coefficient equations3.33, 5, 12, 21, 27
10/11Midterm.Review
10/13Resonance phenomena3.6None
8 10/16Systems of differential equations4.11, 3, 5, 17 , 18, 24, 30
10/18The method of elimination4.21, 4, 7, 13, 39
10/20Linear Algebra5.1Read 5.1 and do problems 1, 3, 4, 6
9
Quiz
Week
10/23More Linear Algebra5.110, 11, 12, 13
10/25Linear algebra for systems of equations5.114, 19, 20
10/27Continued5.123, 24, 32, 33, 42
10 10/30Eigenvectors and solutions of homogeneous systems5.21, 2, 5, 9
11/1Eigenvectors and solutions of homogeneous systems5.217, use wolfram alpha to do 42, 45
11/3Solution Curves to linear systems5.31, 2, 9, 11
11
Quiz
Week
11/6Generalized Eigenvectors5.51, 3, 7, 13
11/8Generalized Eigenvectors5.520, 25, 33
11/10Matrix Exponentials5.61, 3, 21, 23, 25, 27
12 11/13Computing Matrix Exponentials5.67, 9, 12, 17, 29, 32
11/15Nonlinear Systems of Equations6.11, 4, 6, 13, 14
11/17Nonlinear Systems of Equations6.117, 18, 28, 29
13 11/20Linear Algebra Review.Here
11/22Thanksgiving BreakNoneNone
11/24Thanksgiving BreakNoneNone
14
Quiz
Week
11/27Almost Linear Systems6.21, 3, 7, 19, 21
11/29Jacobians, the space of 2x2 linear equations6.211, 14, 33, 34
12/1Ecological Models6.31, 2, 3, 11, 12, 13
15 12/4Ecological Models6.314, 15, 16, 17
12/6The non-linear pendulum6.49, 10, 11, 14, 15
12/8Review.Review Sheet
Solutions