Lecture 
Section(s) 
Topics Covered 
1 
1.11.3 
Introduction: Mathematical modeling with ODE, Classification
of ODE and PDE 
2 
2.1 
Linear equations; Method of Integrating Factors 
3 
2.2 
Separable Equations 
4 
2.3,2.4 
Modeling with First Order Equations; Differences
Between Linear and Nonlinear Equations 
5 
2.5 
Autonomous Equations and Population Dynamics 
6 
2.6 
Exact Equations and Integrating Factors 
7 
3.1,3.2 
Second Order Linear Equations:
Fundamental Solutions of Linear Homogeneous Equations 
8 
3.3 
Linear Independence and the Wronskian 
9 
3.4 
Complex Roots of the Characteristic Equation 
10 
3.5 
Repeated Roots; Reduction of Order 
Week 4 
Midterm 1 
TOPICS COVERED: Boyce and DiPrima 1.13.4.

11 
3.6 
Nonhomogeneous Equations;
Method of Undetermined Coefficients 
12 
3.7 
Variation of Parameters 
13 
7.1,7.2 
Systems of First Order Linear Equations: Introduction,
Review of Matrices 
14 
7.3 
Linear Algebraic Equations; Linear Independence,
Eigenvalues, Eigenvectors 
15 
7.4 
Basic Theory of Systems of First Order Linear Equations 
16 
7.5 
Homogeneous Linear Systems with Constant Coefficients 
17 
7.6 
Complex Eigenvalues 
18 
7.7,7.8 
Fundamental Matrices, Repeated Eigenvalues 
19 
7.9 
Nonhomogeneous Linear Systems 
20 
5.1 
Review of Power Series;
Using Power Series to Solve ODEs 
Week 8 
Midterm 2 
TOPICS COVERED: Boyce and DiPrima 3.53.7,7.17.9.

21 
5.2,5.3 
Series Solutions Near an Ordinary Point 
22 
6.1 
The Laplace Transform: Definition of the Laplace Transform 
23 
6.2 
Solution of Initial Value Problems 
24 
6.3,6.4 
Step Functions; Differential Equations with
Discontinuous Forcing Functions 
25 
6.5 
Impulse Functions. 
Week 10 
Review 
REVIEW for Final Exam 
Week 11 
Final Exam 
TOPICS COVERED: Boyce and DiPrima 1.17.9.
