18.034 | Spring 2004 | Undergraduate

Honors Differential Equations


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

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


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

Course Info

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