SES #  TOPICS  KEY DATES 

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 