- Course Syllabus
- Weekly Schedule
- Blackboard (for WileyPlus online homework)
- Phase plane applet
- Fourier Series applet
- Wave equation applet
- 2D wave equation applet

**Section 1: Introduction to Ordinary Differential
Equations**. Modeling physical situations that exhibit exponential
growth and exponential decay. Plotting slope fields using the isocline
method. Sketching slope fields of autonomous differential
equations. Approximating solutions using Euler's method.

__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?
[YouTube (26:03)
| Worksheet]

- Lecture 1.2: Plotting solutions to differential equations.
[YouTube (29:36)
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- Lecture 1.3: Approximating solutions to differential equations.
[YouTube (27:38)
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- Lecture 2.1: Separation of variables.
[YouTube (23:52)
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- Lecture 2.2: Initial value problems.
[YouTube (38:37)
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- Lecture 2.3: Falling objects with air resistance.
[YouTube (27:23)
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- Lecture 2.4: Solving 1st order inhomogeneous ODEs.
[YouTube (47:44)
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- Lecture 2.5: Linear differential equations.
[YouTube (44:46)
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- Lecture 2.6: Basic mixing problems.
[YouTube (20:35)
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- Lecture 2.7: Advanced mixing problems.
[YouTube (48:22)
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- Lecture 2.8: The logistic equation.
[YouTube (37:53)
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- Lecture 3.1: Second order linear ODEs.
[YouTube (17:43)
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- Lecture 3.2: Equations with constant coefficients.
[YouTube (1:00:43)
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- Lecture 3.3: The method of undetermined coefficients.
[YouTube (54:39)
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- Lecture 3.4: Simple harmonic motion.
[YouTube (39:32)
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- Lecture 3.5: Damped harmonic motion.
[YouTube (58:25)
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- Lecture 3.6: Variation of parameters.
[YouTube (41:41)
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- Lecture 3.7: Cauchy-Euler equations.
[YouTube (35:07)
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- Lecture 3.8: Power series solutions.
[YouTube (31:45)
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- Lecture 3.9: The method of Frobenius.
[YouTube (44:52)
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- Lecture 4.1: Basic matrix algebra.
[YouTube (57:55)
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- Lecture 4.2: Eigenvalues and eigenvectors.
[YouTube (38:28)
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- Lecture 4.3: Mixing with two tanks.
[YouTube (29:55)
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- Lecture 4.4: Solving a 2x2 system of ODEs.
[YouTube (39:27)
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- Lecture 4.5: Phase portraits with real eigenvalues.
[YouTube (27:30)
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- Lecture 4.6: Phase portraits with complex eigenvalues.
[YouTube (47:10)
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- Lecture 4.7: Phase portraits with repeated eigenvalues.
[YouTube (37:24)
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- Lecture 4.8: Stability of phase portraits.
[YouTube (51:07)
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- Lecture 4.9: Variation of parameters for systems.
[
__YouTube__(coming soon) | Worksheet]

- Lecture 5.1: What is a Laplace transform?
[YouTube (28:10)
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- Lecture 5.2: Properties & applications of Laplace transforms.
[YouTube (57:52)
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- Lecture 5.3: Discontinuous forcing terms.
[YouTube (49:59)
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- Lecture 5.4: Periodic forcing terms.
[YouTube (40:41)
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- Lecture 5.5: Impulse functions.
[YouTube (24:36)
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- Lecture 5.6: Convolution.
[YouTube (30:58)
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- Lecture 6.1: Introduction to Fourier series.
[YouTube (28:52)
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- Lecture 6.2: Computing Fourier series.
[YouTube (27:31)
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- Lecture 6.3: Fourier sine and cosine series.
[YouTube (47:49)
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- Lecture 6.4: Complex Fourier series.
[YouTube (38:58)
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- Lecture 6.5: Applications of Fourier series.
[YouTube (24:45)
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- Lecture 6.6: Boundary value problems.
[YouTube (39:55)
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- Lecture 7.1: The heat equation.
[YouTube (27:41)
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- Lecture 7.2: Different boundary conditions.
[YouTube (36:23)
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- Lecture 7.3: The transport equation.
[YouTube (24:17)
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- Lecture 7.4: The wave equation.
[YouTube (21:57)
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- Lecture 7.5: Harmonic functions.
[YouTube (24:35)
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- Lecture 7.6: Laplace's equation.
[YouTube (36:27)
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- Lecture 7.7: The 2D heat equation.
[YouTube (44:49)
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- Lecture 7.8: The 2D wave equation.
[YouTube (26:32)
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- Lecture 8.1: Modeling with nonlinear systems.
[YouTube (30:04)
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- Lecture 8.2: Linearization and steady-state analysis
[YouTube (55:13)
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- Lecture 8.3: Predator-prey models
[YouTube (41:43)
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