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Honors Differential Equations >> Content Detail



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Calendar

SES #TOPICSKEY DATES
Unit I : First-order ODE's
1Modeling and Terminology
2Linear Differential Equations
3Existence and Uniqueness of Solutions: Uniqueness
4Existence and Uniqueness of Solutions: Picard Iterates
5Extension of SolutionsProblem set 1 due
6Slope Fields

Separable Equations
7Qualitative Analysis
8Approximate Numerical SolutionsProblem set 2 due
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

Some Instructions on Plotting Functions in MATLAB® 

12Direction Fields

Brief Review of Complex Numbers
13Inhomogeneous 2nd Order Linear ODE's
14Theory of 2nd Order Linear and Nonlinear ODE'sProblem set 3 due
15Beats, Resonance, and Frequency Response Modeling
16Extra Topics
Unit III: Fourier Series
17Fourier Trigonometric SeriesProblem set 4 due
18Half-range and Exponential Fourier Series
19In-class Exam 2
20The Dirac Delta Function
Unit IV: The Laplace Transform
21The Laplace Transform: Solving IVP’s
22Properties of the Transform
23ConvolutionProblem set 5 due
24Extra Topics
Unit V: Linear Systems of ODE's
25Compartment Models

Introduction to Linear Algebra
26Eigenvalues, Eigenvectors and EigenspacesProblem set 6 due
27Homogeneous Linear Systems: Real Eigenvalues Case
28Homogeneous Linear Systems: Complex Eigenvalues Case
29Inhomogeneous Linear Systems: Exponentials of MatricesProblem set 7 due
30Theory of General Linear Systems of ODE's
31

Extra Topics and/or Review

Supplementary Notes on Jordan Normal Form

Problem set 8 due
32In-class Exam 3
Unit VI: Nonlinear Systems of ODE's
33The Fundamental Theorem
34Autonomous Systems

Interacting Species Models
Problem set 9 due
35Stability of Linear and Nonlinear Autonomous Systems
36Conservative Systems

Lyapunov Functions
37Limit Cycles and Planar Autonomous SystemsProblem set 10 due
38Extra Topics
39Review
40Final Exam

 








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