- Course calendar
- Course syllabus
- Canvas, where you access the WileyPlus online homework
- Remote Proctor software for taking online exams.
- Phase plane applet (for Section 4)
- Fourier Series applet (for Section 6)
- Wave equation applet (for Section 7)
- 2D wave equation applet (for Section 7)
- Online textbook by Trefor Bazett and Jiri Lebl.
- Online problem bank by Steven Clontz, ideal for self-study.
- Want to learn more? Check out my Math 4340 course (Advanced Engineering Mathematics), which I've designed to be a natural follow-up to Math 2080.

**Section 1: Introduction to Ordinary Differential Equations**. (3
lectures: 1 hr 23 min).

__Lecture notes__. 9 pages, last updated 1/21/11. Brannan/Boyce: Sections 1.1--1.3, 2.3, 8.1, supplemental material.

- Lecture 1.1: What is a differential equation?
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- Lecture 1.2: Plotting solutions to differential equations.
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- Lecture 1.3: Approximating solutions to differential equations.
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- Lecture 2.1: Separation of variables.
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- Lecture 2.2: Initial value problems.
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- Lecture 2.3: Falling objects with air resistance.
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- Lecture 2.4: Solving 1st order inhomogeneous ODEs.
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- Lecture 2.5: Linear differential equations.
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- Lecture 2.6: Basic mixing problems.
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- Lecture 2.7: Advanced mixing problems.
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- Lecture 2.8: The logistic equation.
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- Lecture 3.1: Second order linear ODEs.
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- Lecture 3.2: Equations with constant coefficients.
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- Lecture 3.3: The method of undetermined coefficients.
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- Lecture 3.4: Simple harmonic motion.
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- Lecture 3.5: Damped and driven harmonic motion.
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- Lecture 3.6: Variation of parameters.
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- Lecture 3.7: Cauchy-Euler equations.
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- Lecture 3.8: Power series solutions.
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- Lecture 3.9: The method of Frobenius.
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- Lecture 4.1: Basic matrix algebra.
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- Lecture 4.2: Eigenvalues and eigenvectors.
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- Lecture 4.3: Mixing with two tanks.
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- Lecture 4.4: Solving a 2x2 system of ODEs.
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- Lecture 4.5: Phase portraits with real eigenvalues.
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- Lecture 4.6: Phase portraits with complex eigenvalues.
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- Lecture 4.7: Phase portraits with repeated eigenvalues.
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- Lecture 4.8: Stability of phase portraits.
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- Lecture 4.9: Variation of parameters for systems.
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- Lecture 5.1: What is a Laplace transform?
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- Lecture 5.2: Properties & applications of Laplace transforms.
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- Lecture 5.3: Discontinuous forcing terms.
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- Lecture 5.4: Periodic forcing terms.
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- Lecture 5.5: Impulse functions.
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- Lecture 5.6: Convolution.
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- Lecture 6.1: Introduction to Fourier series.
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- Lecture 6.2: Computing Fourier series.
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- Lecture 6.3: Fourier sine and cosine series.
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- Lecture 6.4: Complex Fourier series.
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- Lecture 6.5: Applications of Fourier series.
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- Lecture 6.6: Boundary value problems.
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- Lecture 7.1: The heat equation.
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- Lecture 7.2: Different boundary conditions.
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- Lecture 7.3: The transport equation.
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- Lecture 7.4: The wave equation.
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- Lecture 7.5: Harmonic functions.
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- Lecture 7.6: Laplace's equation.
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- Lecture 7.7: The 2D heat equation.
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- Lecture 7.8: The 2D wave equation.
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- Lecture 8.1: Modeling with nonlinear systems.
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- Lecture 8.2: Linearization and steady-state analysis
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- Lecture 8.3: Predator-prey models
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