18.034 | Spring 2004 | Undergraduate

Honors Differential Equations

Readings

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.

SES # TOPICS READINGS
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

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