Courses:

Honors Differential Equations >> Content Detail



Study Materials



Readings

Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.
The readings referred to in the table are from the text: Amazon logo Borrelli, R. and C. Coleman. Differential Equations: A Modeling Perspective. Wiley Text Books, 2nd ed., New York, 2003. ISBN: 0471433322.

SES #TOPICSREADINGS
Unit I : First-order ODE's
1Modeling and TerminologyChapter 1
2Linear Differential EquationsChapter 2: Sections 2.1 and 2.2
3Existence and Uniqueness of Solutions: UniquenessChapter 2: Sections 2.3 and A.1
4Existence and Uniqueness of Solutions: Picard IteratesChapter 2: Section A.2
5Extension of SolutionsChapter 2: Section A.3
6Slope Fields

Separable Equations
Chapter 2: Sections 2.4 and 2.5
7Qualitative AnalysisChapter 2: Section 2.8
8Approximate Numerical SolutionsChapter 2: Page 122
9Extra Topics and/or Review
10In-class Exam 1
Unit II: Second-order ODE's
11Homogeneous 2nd Order Linear ODE's with Constant CoefficientsChapter 3: Sections 3.1 and 3.2
12Direction Fields

Brief Review of Complex Numbers
Chapter 3: Section 3.3
13Inhomogeneous 2nd Order Linear ODE'sChapter 3: Sections 3.5 and 3.6
14Theory of 2nd Order Linear and Nonlinear ODE'sChapter 3: Sections 3.7 and 3.8
15Beats, Resonance, and Frequency Response ModelingChapter 4: Sections 4.1 and 4.3
16Extra Topics
Unit III: Fourier Series
17Fourier Trigonometric SeriesChapter 10: Sections 10.1 and 10.2
18Half-range and Exponential Fourier SeriesChapter 10: Section 10.3
19In-class Exam 2
20The Dirac Delta FunctionChapter 10: Page 328
Unit IV: The Laplace Transform
21The Laplace Transform: Solving IVP’sChapter 5: Section 5.1
22Properties of the TransformChapter 5: Sections 5.2 and 5.3
23ConvolutionChapter 5: Section 5.4
24Extra Topics
Unit V: Linear Systems of ODE's
25Compartment Models

Introduction to Linear Algebra
Chapter 6: Section 6.1 and page 421
26Eigenvalues, Eigenvectors and EigenspacesChapter 6: Section 6.2
27Homogeneous Linear Systems: Real Eigenvalues CaseChapter 6: Section 6.3
28Homogeneous Linear Systems: Complex Eigenvalues CaseChapter 6: Section 6.4
29Inhomogeneous Linear Systems: Exponentials of MatricesChapter 6: Section 6.6
30Theory of General Linear Systems of ODE'sChapter 6: Section 6.8
31Extra Topics and/or Review
32In-class Exam 3
Unit VI: Nonlinear Systems of ODE's
33The Fundamental TheoremChapter 7: Section 7.1
34Autonomous Systems

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

Lyapunov Functions
Chapter 8: Sections 8.3 and page 508
37Limit Cycles and Planar Autonomous SystemsChapter 9: Sections 9.1 and 9.2
38Extra Topics
39Review
40Final Exam

 








© 2009-2020 HigherEdSpace.com, All Rights Reserved.
Higher Ed Space ® is a registered trademark of AmeriCareers LLC.