Honors Differential Equations

Calendar

SES #	TOPICS	KEY DATES
Unit I : First-order 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	In-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®
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	Half-range and Exponential Fourier Series
19	In-class 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	In-class 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