18.034 | Spring 2004 | Undergraduate

# Honors Differential Equations

The readings referred to in the table are from the text: Borrelli, R. and C. Coleman. Differential Equations: A Modeling Perspective. Wiley Text Books, 2nd ed., New York, 2003. ISBN: 0471433322.

Unit I : First-order ODE’s
1 Modeling and Terminology Chapter 1
2 Linear Differential Equations Chapter 2: Sections 2.1 and 2.2
3 Existence and Uniqueness of Solutions: Uniqueness Chapter 2: Sections 2.3 and A.1
4 Existence and Uniqueness of Solutions: Picard Iterates Chapter 2: Section A.2
5 Extension of Solutions Chapter 2: Section A.3
6 Slope Fields

Separable Equations

Chapter 2: Sections 2.4 and 2.5
7 Qualitative Analysis Chapter 2: Section 2.8
8 Approximate Numerical Solutions Chapter 2: Page 122
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 Chapter 3: Sections 3.1 and 3.2
12 Direction Fields

Brief Review of Complex Numbers

Chapter 3: Section 3.3
13 Inhomogeneous 2nd Order Linear ODE’s Chapter 3: Sections 3.5 and 3.6
14 Theory of 2nd Order Linear and Nonlinear ODE’s Chapter 3: Sections 3.7 and 3.8
15 Beats, Resonance, and Frequency Response Modeling Chapter 4: Sections 4.1 and 4.3
16 Extra Topics

Unit III: Fourier Series
17 Fourier Trigonometric Series Chapter 10: Sections 10.1 and 10.2
18 Half-range and Exponential Fourier Series Chapter 10: Section 10.3
19 In-class Exam 2

20 The Dirac Delta Function Chapter 10: Page 328
Unit IV: The Laplace Transform
21 The Laplace Transform: Solving IVP’s Chapter 5: Section 5.1
22 Properties of the Transform Chapter 5: Sections 5.2 and 5.3
23 Convolution Chapter 5: Section 5.4
24 Extra Topics

Unit V: Linear Systems of ODE’s
25 Compartment Models

Introduction to Linear Algebra

Chapter 6: Section 6.1 and page 421
26 Eigenvalues, Eigenvectors and Eigenspaces Chapter 6: Section 6.2
27 Homogeneous Linear Systems: Real Eigenvalues Case Chapter 6: Section 6.3
28 Homogeneous Linear Systems: Complex Eigenvalues Case Chapter 6: Section 6.4
29 Inhomogeneous Linear Systems: Exponentials of Matrices Chapter 6: Section 6.6
30 Theory of General Linear Systems of ODE’s Chapter 6: Section 6.8
31 Extra Topics and/or Review

32 In-class Exam 3

Unit VI: Nonlinear Systems of ODE’s
33 The Fundamental Theorem Chapter 7: Section 7.1
34 Autonomous Systems

Interacting Species Models

Chapter 7: Sections 7.2 and 7.3
35 Stability of Linear and Nonlinear Autonomous Systems Chapter 8: Sections 8.1 and 8.2
36 Conservative Systems

Lyapunov Functions

Chapter 8: Sections 8.3 and page 508
37 Limit Cycles and Planar Autonomous Systems Chapter 9: Sections 9.1 and 9.2
38 Extra Topics

39 Review

40 Final Exam

## Course Info

Spring 2004
##### Learning Resource Types
Exams with Solutions
Lecture Notes
Problem Sets with Solutions