18.034 | Spring 2004 | Undergraduate

Honors Differential Equations


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

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

Course Info

As Taught In
Spring 2004
Learning Resource Types
Exams with Solutions
Lecture Notes
Problem Sets with Solutions