Honors Differential Equations

Recitations

The recitation notes below provide suggestions from the professor to the teaching assistant.

SES #	TOPICS
Unit I: First-order ODE’s
1	Modeling and Terminology (PDF)
2	Linear Differential Equations (PDF)
3	Existence and Uniqueness of Solutions: Uniqueness
4	Existence and Uniqueness of Solutions: Picard Iterates
5	Extension of Solutions (PDF)
6	Slope Fields Separable Equations
7	Qualitative Analysis (PDF)
8	Approximate Numerical Solutions (PDF)
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 (PDF)
12	Direction Fields Brief Review of Complex Numbers
13	Inhomogeneous 2nd Order Linear ODE’s (PDF)
14	Theory of 2nd Order Linear and Nonlinear ODE’s (PDF)
15	Beats, Resonance, and Frequency Response Modeling
16	Extra Topics (PDF)
Unit III: Fourier Series
17	Fourier Trigonometric Series (PDF)
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 (PDF)
23	Convolution (PDF)
24	Extra Topics (PDF)
Unit V: Linear Systems of ODE’s
25	Compartment Models Introduction to Linear Algebra
26	Eigenvalues, Eigenvectors and Eigenspaces
27	Homogeneous Linear Systems: Real Eigenvalues Case (PDF)
28	Homogeneous Linear Systems: Complex Eigenvalues Case
29	Inhomogeneous Linear Systems: Exponentials of Matrices
30	Theory of General Linear Systems of ODE’s
31	Extra Topics and/or Review
32	In-class Exam 3
Unit VI: Nonlinear Systems of ODE’s
33	The Fundamental Theorem (PDF)
34	Autonomous Systems Interacting Species Models (PDF)
35	Stability of Linear and Nonlinear Autonomous Systems (PDF)
36	Conservative Systems Lyapunov Functions
37	Limit Cycles and Planar Autonomous Systems
38	Extra Topics
39	Review
40	Final Exam