MA-36600 Fall 2018

Ordinary Differential Equations

Instructor: Plamen Stefanov
Time and Place: section 021: TueThu 10:30 - 11:45 in REC 123
section 193: TueThu 12:00 - 1:15 in REC 123
Office Hours: Tue Thu 2:15-3:15
Grader: Qiurui Li, li2889 at purdue dot edu
Book: Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, 10th edition. We are not going to do the Boundary Value Problems this semester, so you can get the shortest version of the book without it. On the other hand, that part of the book will be useful if you take MA-303/304 in the future. You do not need the access code for this course!

Lecture Notes (incomplete!)  

Login here to run Matlab and Maple remotely. For Maple, go to Standard Software -> Computational Packages

Or, use the web applet version.   

Syllabus

Labs


EXAM 1: Feb. 1, Thu, 6:30-7:30 in WTHR 104        You can use one crib sheet, both sides        No calculators or electronic device        Will cover 1.1-1.3, 2.1-2.5

EXAM 2: Mar 5, Mon, 8:00-9:00 in WTHR 104        You can use one crib sheet, both sides        No calculators or electronic devices  

EXAM 3: Apr 12, Thu, 6:30-7:30 in WTHR 104       You can use one crib sheet, both sides        No calculators or electronic devices  

Typical phase portraits

OLD EXAMS

 Resonances:

More links:


Homework

Week Due Section Problems Remarks
1 1/18, Thu 1.1 11, 15-20 (easy), 22  
1.2 5, 7, 8, 9, 12; read 13 and 17 Do not turn in #13 and #17
1.3 1-6 (easy), 9,15, 19  
2 1/23, Tue 2.1 6, 15, 16, 30. Read #38. Do #41 using the method in #38.
2.2 1, 2, 14, 16  
3 1/30, Tue 2.3 4, 7, 8, 10, 11, 16, 20, 26  
2.4 1-5 (easy), 13, 22, 28  
2.5 3, 4, 10, 12, 18, 21 For some of the problems, the DE does not need to be solved to answer the question.
4 2/6, Tue 2.7 1  
2.8 3  
3.1 1, 5, 6, 9  
5 2/13, Tue 3.2 1, 2, 3, 9, 28  
3.3 4, 6, 11, 12, 18, 29, 38  
3.4 5, 11, 28  
3.5 4, 7, 9, 10, 17  
7 2/20, Tue 3.6 5, 10, 11, 23, 29 When doing #23, take #22 for granted (do not do #22 but try to understand it)

The solution of #23 is the response of a spring-mass system with no damping, to an external force g(t)

8 2/27, Tue 3.7 3, 4, 6, 11, 19 Read Example 3 and Electrical Circuits
3.8 15, 17, 19 3.8 slides
9  
7.1 3, 5, 7, 8a Read #22
7.2 Read it  
7.3 3, 16, 19, 22  
7.4 none  
10   7.5 1, 2, 7, 12, 15  
7.6 1, 2, 7, 11, 13  
11     No HW this week  
12   7.7 3, 11  
7.8 1, 5, 10, 11
7.9 1, 3, 5
13   9.1 Read 9.1. It is a summary of most of Chapter 7
9.2 1, 5, 6, 7 5, 6, 7 in 9.2 are MATLAB questions - compute the equilibrium solutions only but do not try to solve the systems analytically (with a formula)
9.3 5, 6, 7, 26  
14   9.4 1, 5, 7 will not be collected
9.5 3, 9 will not be collected

Course Outline

Chapter 1. Introduction

1.1. What is a differential equation? Why do we need to study them? Some Basic Models; Direction Fields

1.2. Solutions of Some Differential Equations (actually, those a linear equations with constant coefficients).

1.3. Classification of Differential Equations

Chapter 2. First Order ODEs

2.1. Linear Equations; Integrating Factors

2.2. Separable Equations, including homogeneous ones

2.3. Modeling with First Order Equations

2.4. Differences Between Linear and Nonlinear Equations

2.5. Autonomous Equations and Population Dynamics

2.6 Exact Equations

2.7. Numerical Approximations: Eulerís Method

2.8. The Existence and Uniqueness Theorem

Chapter 3. Second Order Linear Equations

3.1. Homogeneous Equations with Constant Coefficients; Real Roots of the Characteristic Equation

3.2. Solutions of Linear Homogeneous Equations (with variable coefficients) , the Wronskian.

3.3. Complex Roots of the Characteristic Equation

3.4. Repeated Roots; Reduction of Order

3.5. Non-homogeneous Equations; Method of Undetermined Coefficients

3.6. Variation of Parameters

3.7. Mechanical and Electrical Vibrations

3.8. Forced Vibrations

Chapter 4. Higher Order Linear Equations

4.1. General Theory of n-th Order Linear Equations

4.2. Homogeneous Equations with Constant Coefficients

Chapter 5.  Series Solutions

 5.4. Euler Equations

Chapter 7. Systems of First Order ODEs

7.1. Introduction; Why study systems?

7.2. Review of Matrices (I will be very brief here: you know, I hope, what a matrix is!)

7.3. Linear Independence, Eigenvalues, Eigenvectors

7.4. Basic Theory of Systems of First Order Linear Equations

7.5. Homogeneous Linear Systems with Constant Coefficients; distinct eigenvalues

7.6. Complex Eigenvalues; Real Valued Solutions

7.8. Repeated Eigenvalues

7.7. Fundamental Matrices

7.9. Non-homogeneous Linear Systems

Chapter 9. Nonlinear Differential Equations and Stability

9.1. The Phase Plane: Linear Systems

9.2. Autonomous Systems and Stability

9.3. "Locally Linear Systems" (they are actually nonlinear)

9.4. Competing Species

9.5. Predator-Prey Equations