Week 
Topics and Sections 
Homework 
DUE 
Aug 31, Sep 1 
Introduction §1.1 Mathematical Models and Slope Fields §1.2 Solutions to Some Differential Equations §1.3 Classification of Differential Equations
Aug 31 Sep 1 
Please become familiar with the organization of this course by carefully reading the syllabus on this webpage.
Do the following exercises from the textbook: §1.1: 2, 4, 1520 §1.2: 3, 7, 13, 15 §1.3: 1, 2, 4, 9, 17 (Use a computer to draw direction fields and print them out)
Selected Solutions 
Sep 8 
Sep 6, 8 
§2.1 Linear Equations and Integrating Factors §2.2 Separable Equations §2.3 Modeling with First Order Equations
Sep 6 Sep 8 
Do the following exercises: §2.1: 10, 20, 22, 28, 30, 35 §2.2: 2, 5, 14, 22, 24, 29
Read section §2.3 from the textbook
Selected Solutions 
Sep 15 
Sep 11, 13, 15 
§2.4 Linear vs. Nonlinear Equations §2.5 Autonomous Equations and Population Dynamics §2.5 Exercises: Bifurcation Theory and Diagrams
Sep 11 Sep 13 Sep 15 
Do the following exercises: §2.4: 4, 5, 13, 15, 26, 27 §2.5: 2, 4, 7, 9, 14, 16, 17, 26, 27
Selected Solutions 
Sep 22 
Sep 18, 20, 22 
§2.6 Exact Equations and Integrating Factors §2.8 Existence and Uniqueness Theorem §3.1 Homogeneous Equations
Sep 18 Sep 20 Sep 22 
Do the following exercises: §2.6: 4, 5, 8, 12, 14, 16 §3.1: 5, 7, 14, 18, 20, 21, 24, 25
Selected Solutions 
Sep 29 
Sep 25, 27, 29 
§3.2 The Wronskian §3.3 Char. Eqn. Roots: Complex
Sep 25 Sep 27 Sep 29 
Do the following exercises: §3.2: 1, 4, 8, 11, 14, 18, 26, 28, 31, 33, 37 §3.3: 3, 10, 14, 19, 25, 27
Selected Solutions 
Oct 06 
Oct 2, 4, 6 
§3.4 Char. Eqn. Roots: Repeated §3.5 Nonhomogeneous Equations §3.6 Variations of Parameters §3.7 Mech. and Electr. Vibrations
Oct 2 Oct 4 Oct 6 
Do the following exercises: §3.4: 4, 8, 18, 24, 27 §3.5: 3, 10, 12, 14, 17, 30
Selected Solutions 
Oct 13 
Oct 9, 11, 13 
1st midterm on Monday in class
§4.1 Higher Order Linear Equations §4.2 Homogeneous Equations §4.3 Undetermined Coefficients
Oct 11 Oct 13 
Do the following exercises: §3.6: 3, 7, 10, 15, 18, 28, 29
Read Section 3.7.
Note: This homework is already due on Wednesday, October 18, due to fall break!
Selected Solutions 
Oct 18 
Oct 16, 18 
§7.1 Introduction to Systems §7.2 Review of Matrices §7.3 Linear Algebraic Equations
Oct 16 Oct 18 Note: Fall break on Friday, October 20 
Do the following exercises: §4.1: 6, 8, 18, 19 §4.2: 11, 12, 18, 31 §4.3: 1, 2 §7.1: 4, 6, 15 §7.2: 2, 11, 23, 24 §7.3: 1, 8, 19, 20
Selected Solutions 
Oct 27 
Oct 23, 25, 27 
§7.4 First Order Linear Systems §7.5 Homogeneous Linear Systems
Oct 23 Oct 25 Oct 27 
Do the following exercises: §7.4: 4, 6 §7.5: 4, 5, 8, 15, 16, 24, 25, 27, 29, 31 (Use a computer to draw the direction fields and print them out)
Selected Solutions 
Nov 3 
Oct 30, Nov 1, 3 
§7.6 Complex Eigenvalues §7.7 Fundamental Matrices §7.8 Repeated Eigenvalues
Oct 30 Nov 1 Nov 3 
Do the following exercises: §7.6: 1, 3, 9, 13, 15, 28 §7.7: 3, 5, 8, 11 §7.8: 4, 8, 15
Selected Solutions Correction for §7.6 3(b): The solutions are periodic Corrected Solution for §7.7: 8(b) 
Nov 10 
Nov 6, 8, 10 
§9.1 The Phase Plane §9.2 Autonomous Systems and Stability §9.3 Locally Linear Systems
Nov 6 Nov 8 Nov 10 

Nov 17 
Nov 13, 15, 17 
2nd midterm on Monday in class
§9.3 Locally Linear Systems §9.4 Competing Species Nov 15 Nov 17 
Do the following exercises: §9.3: 5, 6, 16, 20, 27 §9.4: 2, 17 §9.5: 1, 12 (We will cover Section 9.5 on Monday after the break) 
Dec 1 
Nov 2026 
Thanksgiving vacation 
No homework 

Nov 27, 29 Dec 1 
§9.5 PredatorPrey Equations §9.7 Periodic Solutions and Limit Cycles §6.1 Definition of the Laplace Transform 


Dec 4, 6, 8 
§6.2 Solution of Initial Value Problems §8.1 The Euler or Tangent Line Method 

