Unit I : Firstorder ODE's 
1 
Modeling and Terminology 

2 
Linear Differential Equations 

3 
Existence and Uniqueness of Solutions: Uniqueness 

4 
Existence and Uniqueness of Solutions: Picard Iterates 

5 
Extension of Solutions 
Problem set 1 due 
6 
Slope Fields
Separable Equations 

7 
Qualitative Analysis 

8 
Approximate Numerical Solutions 
Problem set 2 due 
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
Some Instructions on Plotting Functions in MATLAB®


12 
Direction Fields
Brief Review of Complex Numbers 

13 
Inhomogeneous 2nd Order Linear ODE's 

14 
Theory of 2nd Order Linear and Nonlinear ODE's 
Problem set 3 due 
15 
Beats, Resonance, and Frequency Response Modeling 

16 
Extra Topics 

Unit III: Fourier Series 
17 
Fourier Trigonometric Series 
Problem set 4 due 
18 
Halfrange and Exponential Fourier Series 

19 
Inclass Exam 2 

20 
The Dirac Delta Function 

Unit IV: The Laplace Transform 
21 
The Laplace Transform: Solving IVP’s 

22 
Properties of the Transform 

23 
Convolution 
Problem set 5 due 
24 
Extra Topics 

Unit V: Linear Systems of ODE's 
25 
Compartment Models
Introduction to Linear Algebra 

26 
Eigenvalues, Eigenvectors and Eigenspaces 
Problem set 6 due 
27 
Homogeneous Linear Systems: Real Eigenvalues Case 

28 
Homogeneous Linear Systems: Complex Eigenvalues Case 

29 
Inhomogeneous Linear Systems: Exponentials of Matrices 
Problem set 7 due 
30 
Theory of General Linear Systems of ODE's 

31 
Extra Topics and/or Review
Supplementary Notes on Jordan Normal Form

Problem set 8 due 
32 
Inclass Exam 3 

Unit VI: Nonlinear Systems of ODE's 
33 
The Fundamental Theorem 

34 
Autonomous Systems
Interacting Species Models 
Problem set 9 due 
35 
Stability of Linear and Nonlinear Autonomous Systems 

36 
Conservative Systems
Lyapunov Functions 

37 
Limit Cycles and Planar Autonomous Systems 
Problem set 10 due 
38 
Extra Topics 

39 
Review 

40 
Final Exam 
