- Course calendar
- Course syllabus
- WileyPlus online homework
- Remote Proctor software for taking online exams.

**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)
| Worksheet]

__Lecture 1.3: Approximating solutions to differential equations__
[YouTube (27:38)
| Worksheet]

**Section 2: First Order Differential Equations**. Solving 1st
order ODEs using separation of variables, the integrating factor
method, and variation of parameters. Structure of solutions to 1st
order linear ODEs, and connections to parametrized lines. Models of
motion with air resistance. Mixing problems. The logistic equation as
a population model.

__Lecture notes__. 21 pages, last updated 2/17/11. Brannan/Boyce: Sections 2.1--2.6.

__Lecture 2.1: Separation of variables__
[YouTube (23:52)
| Worksheet]

__Lecture 2.2: Initial value problems__
[YouTube (38:37)
| Worksheet]

__Lecture 2.3: Falling objects with air resistance__
[YouTube (27:23)
| Worksheet]

__Lecture 2.4: Solving 1st order inhomogeneous ODEs__
[YouTube (47:44)
| Worksheet]

__Lecture 2.5: Linear differential equations__
[YouTube (44:46)
| Worksheet]

__Lecture 2.6: Basic mixing problems__
[YouTube (20:35)
| Worksheet]

__Lecture 2.7: Advanced mixing problems__
[YouTube (48:22)
| Worksheet]

__Lecture 2.8: The logistic equation__
[YouTube (37:53)
| Worksheet]

**Section 3: Second Order Differential Equations**. Models that use
2nd order ODEs. Solving homogeneous linear 2nd order ODEs. Solving
inhomogeneous ODEs using the method of undertermined
coefficients. Simple harmonic motion. Harmonic motion with damping and
with forcing terms. The variation of parameters method for 2nd order
ODEs. Solving 2nd order non-constant coefficient ODEs. Cauchy-Euler
equations. The power series method, and the theorem of
Frobenius.

__Lecture notes__. 29 pages, last updated 2/17/11. Brannan/Boyce: Sections 4.1--4.7, 9.1--9.6.

__Lecture 3.1: Second order linear ODEs__
[YouTube (17:43)
| Worksheet]

__Lecture 3.2: Equations with constant coefficients__
[YouTube (1:00:43)
| Worksheet]

__Lecture 3.3: The method of undetermined coefficients__
[YouTube (54:39)
| Worksheet]

__Lecture 3.4: Simple harmonic motion__
[YouTube (40:24)
| Worksheet]

__Lecture 3.5: Damped and driven harmonic motion__
[YouTube (58:25)
| Worksheet]

__Lecture 3.6: Variation of parameters__
[YouTube (41:41)
| Worksheet]

__Lecture 3.7: Cauchy-Euler equations__
[YouTube (35:07)
| Worksheet]

__Lecture 3.8: Power series solutions__
[YouTube (31:45)
| Worksheet]

__Lecture 3.9: The method of Frobenius__
[YouTube (44:52)
| Worksheet]

**Section 4: Systems of Differential Equations**. Intro to
linear algebra: Adding and multiplying matrices. Writing systems of
linear equations with matrices, inverses and determinants of 2x2
matrices, eigenvalues and eigenvectors of 2x2 matrices. Using linear
algebra to solve systems of two 1st order linear ODEs x'=Ax; 3 cases
(i) real distinct eigenvalues, (ii) repeated eigenvalues, (iii)
complex eigenvalues. The SIR model in epidemiology.

__Lecture notes__. 26 pages, last updated 10/20/10. Brannan/Boyce: Sections 3.1--3.6, A.1.

__Lecture 4.1: Basic matrix algebra__
[YouTube (57:55)
| Worksheet]

__Lecture 4.2: Eigenvalues and eigenvectors__
[YouTube (38:28)
| Worksheet]

__Lecture 4.3: Mixing with two tanks__
[YouTube (29:55)
| Worksheet]

__Lecture 4.4: Solving a 2x2 system of ODEs__
[YouTube (39:27)
| Worksheet]

__Lecture 4.5: Phase portraits with real eigenvalues__
[YouTube (27:30)
| Worksheet]

__Lecture 4.6: Phase portraits with complex eigenvalues__
[YouTube (47:10)
| Worksheet]

__Lecture 4.7: Phase portraits with repeated eigenvalues__
[YouTube (37:24)
| Worksheet]

__Lecture 4.8: Stability of phase portraits__
[YouTube (51:07)
| Worksheet]

__Lecture 4.9: Variation of parameters for systems__
[__YouTube__ (35:44)
| Worksheet]

**Section 5: Laplace Transforms**. Definition and properties of the
Laplace transform. Using Laplace transforms to solve ODEs. Using the
Heavyside function to express, and take the Laplace transform of,
piecewise continuous functions. Solving ODEs with discontinuous
forcing terms. Taking the Laplace transform of periodic
functions. Impulse functions and delta functions. Convolution.

__Lecture notes__. 21 pages, last updated 6/24/13. Brannan/Boyce: Sections 5.1--5.8.

__Lecture 5.1: What is a Laplace transform?__
[YouTube (28:10)
| Worksheet]

__Lecture 5.2: Properties & applications of Laplace transforms__
[YouTube (57:52)
| Worksheet]

__Lecture 5.3: Discontinuous forcing terms__
[YouTube (49:59)
| Worksheet]

__Lecture 5.4: Periodic forcing terms__
[YouTube (40:41)
| Worksheet]

__Lecture 5.5: Impulse functions__
[YouTube (24:36)
| Worksheet]

__Lecture 5.6: Convolution__
[YouTube (30:58)
| Worksheet]

**Section 6: Fourier Series & Boundary Value Problems**. Introduction to Fourier series -- derivation and computation. Even and odd functions, and Fourier cosine and sine series. Complex version of Fourier series. Parseval's
identity. Applications to summing series and to solving ODEs. Boundary values problems.

__Lecture notes__. 13 pages, last updated 12/9/11. Brannan/Boyce: Sections 10.1--10.3.

__Lecture 6.1: Introduction to Fourier series__
[YouTube (28:52)
| Worksheet]

__Lecture 6.2: Computing Fourier series__
[YouTube (27:31)
| Worksheet]

__Lecture 6.3: Fourier sine and cosine series__
[YouTube (47:49)
| Worksheet]

__Lecture 6.4: Complex Fourier series__
[YouTube (38:58)
| Worksheet]

__Lecture 6.5: Applications of Fourier series__
[YouTube (24:45)
| Worksheet]

__Lecture 6.6: Boundary value problems__
[YouTube (39:55)
| Worksheet]

**Section 7: Partial Differential Equations** The (1-dimensional)
heat, transport, and wave equations. Analysis of different boundary
conditions. Introduction to PDEs in higher dimensions. Harmonic
functions, Laplace's equation, and steady-state solutions to the heat
equation. Solving Laplace's equation, the heat equation, and the wave
equation in two dimensions.

__Lecture notes__. 23 pages, last updated 7/29/10. Brannan/Boyce: Sections 11.1--11.4, 11.6, 11.A, 11.B

__Lecture 7.1: The heat equation__
[YouTube (27:41)
| Worksheet]

__Lecture 7.2: Different boundary conditions__
[YouTube (36:23)
| Worksheet]

__Lecture 7.3: The transport equation__
[YouTube (24:17)
| Worksheet]

__Lecture 7.4: The wave equation__
[YouTube (21:57)
| Worksheet]

__Lecture 7.5: Harmonic functions__
[YouTube (24:35)
| Worksheet]

__Lecture 7.6: Laplace's equation__
[YouTube (36:27)
| Worksheet]

__Lecture 7.7: The 2D heat equation__
[YouTube (44:49)
| Worksheet]

__Lecture 7.8: The 2D wave equation__
[YouTube (26:32)
| Worksheet]