| Unit I : First-order ODE's |
| 1 |
Modeling and Terminology |
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| 2 |
Linear Differential Equations |
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| 3 |
Existence and Uniqueness of Solutions: Uniqueness |
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| 4 |
Existence and Uniqueness of Solutions: Picard Iterates |
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| 5 |
Extension of Solutions |
Problem set 1 due |
| 6 |
Slope Fields
Separable Equations |
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| 7 |
Qualitative Analysis |
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| 8 |
Approximate Numerical Solutions |
Problem set 2 due |
| 9 |
Extra Topics and/or Review |
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| 10 |
In-class Exam 1 |
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| Unit II: Second-order ODE's |
| 11 |
Homogeneous 2nd Order Linear ODE's with Constant Coefficients
Some Instructions on Plotting Functions in MATLAB®
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| 12 |
Direction Fields
Brief Review of Complex Numbers |
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| 13 |
Inhomogeneous 2nd Order Linear ODE's |
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| 14 |
Theory of 2nd Order Linear and Nonlinear ODE's |
Problem set 3 due |
| 15 |
Beats, Resonance, and Frequency Response Modeling |
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| 16 |
Extra Topics |
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| Unit III: Fourier Series |
| 17 |
Fourier Trigonometric Series |
Problem set 4 due |
| 18 |
Half-range and Exponential Fourier Series |
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| 19 |
In-class Exam 2 |
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| 20 |
The Dirac Delta Function |
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| Unit IV: The Laplace Transform |
| 21 |
The Laplace Transform: Solving IVP’s |
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| 22 |
Properties of the Transform |
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| 23 |
Convolution |
Problem set 5 due |
| 24 |
Extra Topics |
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| Unit V: Linear Systems of ODE's |
| 25 |
Compartment Models
Introduction to Linear Algebra |
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| 26 |
Eigenvalues, Eigenvectors and Eigenspaces |
Problem set 6 due |
| 27 |
Homogeneous Linear Systems: Real Eigenvalues Case |
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| 28 |
Homogeneous Linear Systems: Complex Eigenvalues Case |
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| 29 |
Inhomogeneous Linear Systems: Exponentials of Matrices |
Problem set 7 due |
| 30 |
Theory of General Linear Systems of ODE's |
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| 31 |
Extra Topics and/or Review
Supplementary Notes on Jordan Normal Form
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Problem set 8 due |
| 32 |
In-class Exam 3 |
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| Unit VI: Nonlinear Systems of ODE's |
| 33 |
The Fundamental Theorem |
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| 34 |
Autonomous Systems
Interacting Species Models |
Problem set 9 due |
| 35 |
Stability of Linear and Nonlinear Autonomous Systems |
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| 36 |
Conservative Systems
Lyapunov Functions |
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| 37 |
Limit Cycles and Planar Autonomous Systems |
Problem set 10 due |
| 38 |
Extra Topics |
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| 39 |
Review |
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| 40 |
Final Exam |
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