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Lecture Notes



Lecture Notes

The lecture notes below represent a summary of the topics discussed and analyzed in class.

SES #TOPICS
Unit I: First-order ODE's
1Modeling and Terminology (PDF)
2Linear Differential Equations (PDF)
3Existence and Uniqueness of Solutions: Uniqueness (PDF)
4Existence and Uniqueness of Solutions: Picard Iterates (PDF)
5Extension of Solutions (PDF)
6Slope Fields

Separable Equations
7Qualitative Analysis (PDF)
8Approximate Numerical Solutions (PDF)
9Extra Topics and/or Review
10In-class Exam 1
Unit II: Second-order ODE's
11

Homogeneous 2nd Order Linear ODE's with Constant Coefficients (PDF)

Some Instructions on Plotting Functions in MATLAB® (PDF)

12Direction Fields

Brief Review of Complex Numbers
13Inhomogeneous 2nd Order Linear ODE's (PDF)
14Theory of 2nd Order Linear and Nonlinear ODE's (PDF)
15Beats, Resonance, and Frequency Response Modeling
16Extra Topics (PDF)
Unit III: Fourier Series
17Fourier Trigonometric Series (PDF)
18Half-range and Exponential Fourier Series
19In-class Exam 2
20The Dirac Delta Function (PDF)
Unit IV: The Laplace Transform
21The Laplace Transform: Solving IVP’s (PDF)
22Properties of the Transform (PDF)
23Convolution (PDF)
24Extra Topics (PDF)
Unit V: Linear Systems of ODE's
25Compartment Models and Introduction to Linear Algebra (PDF)
26Eigenvalues, Eigenvectors and Eigenspaces (PDF)
27Homogeneous Linear Systems: Real Eigenvalues Case (PDF)
28Homogeneous Linear Systems: Complex Eigenvalues Case
29Inhomogeneous Linear Systems: Exponentials of Matrices
30Theory of General Linear Systems of ODE's (PDF)
31

Extra Topics and/or Review

Supplementary Notes on Jordan Normal Form (PDF)

32In-class Exam 3
Unit VI: Nonlinear Systems of ODE's
33The Fundamental Theorem (PDF)
34Autonomous Systems and Interacting Species Models (PDF)
35Stability of Linear and Nonlinear Autonomous Systems (PDF)
36Conservative Systems and Lyapunov Functions (PDF)
37Limit Cycles and Planar Autonomous Systems
38Extra Topics
39Review
40Final Exam

 


 








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