## Mathematics 302-010Ordinary Differential Equations Fall 2024Department of Mathematical Sciences University of Delaware

• Course Syllabus (size: not yet posted)
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• Online Resources
•  I don’t officially endorse any of these links, but they are a place to get started. Integrating Factors (do NOT use Khan Academy) Bridge collapse under forcing at resonance Separable Equations Variation of Parameters Second-Order Constant Coefficient Equations
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• Mathematica Notebooks
•  Basic ODE Commands (size: not yet posted) Advanced Systems, Intro to Laplace Transforms (size: not yet posted) Homogeneous Equations I (size: not yet posted) Laplace Transforms and ODEs (size: not yet posted) Homogeneous Equations II (size: not yet posted) Euler Equations (size: not yet posted) Homogeneous Equations III (size: not yet posted) Fourier Series (size: not yet posted) Forced Equations (size: not yet posted) Fourier Sine and Cosine Series (size: not yet posted) Linear Algebra and Systems (size: not yet posted)
• Exam Template (size: not yet posted)
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• Handouts
•  Calculus Review (size: not yet posted) Phase Plane: Real Eigenvalues (size: not yet posted) Direction Fields (size: not yet posted) Phase Plane: Imaginary Eigenvalues (size: not yet posted) Integral Curves (size: not yet posted) Phase Plane: Complex Eigenvalues (size: not yet posted) Nonlinear Equations (size: not yet posted) Phase Plane: Generalized Eigenvectors (size: not yet posted) Logistic Growth (size: not yet posted) Nonlinear Systems (size: not yet posted) Amplitude-Phase Form (size: not yet posted) The Hopf Bifurcation (size: not yet posted) Unforced Spring (size: not yet posted) Step Function Forcing (size: not yet posted) Inhomogeneous Equations (size: not yet posted) Dirac Forcing (size: not yet posted) Beats (size: not yet posted) Fourier Series (size: not yet posted) First-Order Systems (size: not yet posted) Sine and Cosine Series (size: not yet posted)
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• Homework Sets
Homework Set 1 (size: not yet posted), Solution Set (size: not yet posted)
First order ODEs (sections 1.1, 2.1, 2.2, 2.4).
Homework Set 2 (size: not yet posted), Solution Set (size: not yet posted)
First- and second-order ODEs (sections 2.5, 2.7, 2.8, 3.1).
Homework Set 3 (size: not yet posted), Solution Set (size: not yet posted)
Homogeneous multiple-order ODEs with real roots (sections 3.2. 4.1, 4.2).
Homework Set 4 (size: not yet posted), Solution Set (size: not yet posted)
Second-order ODEs (sections 3.3-3.6, 4.2).
Homework Set 5 (size: not yet posted), Solution Set (size: not yet posted)
Modeling with ODEs (sections 3.7, 3.8, 7.1).
Homework Set 6 (size: not yet posted), Solution Set (size: not yet posted)
Matrices, homogeneous first-order systems with real eigenvalues (sections 7.1-7.5, 9.1).
Homework Set 7 (size: not yet posted), Solution Set (size: not yet posted)
Linear and nonlinear first-order systems, the Laplace transform (sections 7.6, 7.8, 7.9, 9.1, 9.3, 9.7, 6.1).
Homework Set 8 (size: not yet posted), Solution Set (size: not yet posted)
Laplace transforms for ODEs (sections 6.2-6.4).
Homework Set 9 (size: not yet posted), Solution Set (size: not yet posted)
Laplace transforms, Euler equations, separation of variables, Fourier series (sections 5.4, 6.5, 6.6, 10.2, 10.3).
Supplemental Study Material (size: not yet posted), Solution Set (size: not yet posted)
Fourier sine and cosine series for PDEs, solving the heat equation (sections 10.4, 10.5).