Unit I : Firstorder ODE's 
1 
Modeling and Terminology 
Chapter 1 
2 
Linear Differential Equations 
Chapter 2: Sections 2.1 and 2.2 
3 
Existence and Uniqueness of Solutions: Uniqueness 
Chapter 2: Sections 2.3 and A.1 
4 
Existence and Uniqueness of Solutions: Picard Iterates 
Chapter 2: Section A.2 
5 
Extension of Solutions 
Chapter 2: Section A.3 
6 
Slope Fields
Separable Equations 
Chapter 2: Sections 2.4 and 2.5 
7 
Qualitative Analysis 
Chapter 2: Section 2.8 
8 
Approximate Numerical Solutions 
Chapter 2: Page 122 
9 
Extra Topics and/or Review 

10 
Inclass Exam 1 

Unit II: Secondorder ODE's 
11 
Homogeneous 2nd Order Linear ODE's with Constant Coefficients 
Chapter 3: Sections 3.1 and 3.2 
12 
Direction Fields
Brief Review of Complex Numbers 
Chapter 3: Section 3.3 
13 
Inhomogeneous 2nd Order Linear ODE's 
Chapter 3: Sections 3.5 and 3.6 
14 
Theory of 2nd Order Linear and Nonlinear ODE's 
Chapter 3: Sections 3.7 and 3.8 
15 
Beats, Resonance, and Frequency Response Modeling 
Chapter 4: Sections 4.1 and 4.3 
16 
Extra Topics 

Unit III: Fourier Series 
17 
Fourier Trigonometric Series 
Chapter 10: Sections 10.1 and 10.2 
18 
Halfrange and Exponential Fourier Series 
Chapter 10: Section 10.3 
19 
Inclass Exam 2 

20 
The Dirac Delta Function 
Chapter 10: Page 328 
Unit IV: The Laplace Transform 
21 
The Laplace Transform: Solving IVP’s 
Chapter 5: Section 5.1 
22 
Properties of the Transform 
Chapter 5: Sections 5.2 and 5.3 
23 
Convolution 
Chapter 5: Section 5.4 
24 
Extra Topics 

Unit V: Linear Systems of ODE's 
25 
Compartment Models
Introduction to Linear Algebra 
Chapter 6: Section 6.1 and page 421 
26 
Eigenvalues, Eigenvectors and Eigenspaces 
Chapter 6: Section 6.2 
27 
Homogeneous Linear Systems: Real Eigenvalues Case 
Chapter 6: Section 6.3 
28 
Homogeneous Linear Systems: Complex Eigenvalues Case 
Chapter 6: Section 6.4 
29 
Inhomogeneous Linear Systems: Exponentials of Matrices 
Chapter 6: Section 6.6 
30 
Theory of General Linear Systems of ODE's 
Chapter 6: Section 6.8 
31 
Extra Topics and/or Review 

32 
Inclass Exam 3 

Unit VI: Nonlinear Systems of ODE's 
33 
The Fundamental Theorem 
Chapter 7: Section 7.1 
34 
Autonomous Systems
Interacting Species Models 
Chapter 7: Sections 7.2 and 7.3 
35 
Stability of Linear and Nonlinear Autonomous Systems 
Chapter 8: Sections 8.1 and 8.2 
36 
Conservative Systems
Lyapunov Functions 
Chapter 8: Sections 8.3 and page 508 
37 
Limit Cycles and Planar Autonomous Systems 
Chapter 9: Sections 9.1 and 9.2 
38 
Extra Topics 

39 
Review 

40 
Final Exam 
