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Honors Differential Equations >> Content Detail



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Readings

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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

 








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