Math 333 Course Schedule

Homogeneous Differential Equations

1.3: Slope Fields

Graphical Simulations in Maple

This Maple worksheet is posted on the P:drive at P:/Class/Math/Paquin/DiffEq/SlopeFields.mw

Quiz 1

Numerical Simulations in Maple: read 1.4, 7.1, 7.2, and 7.3 in the textbook

1.5: Existence and Uniqueness of Solutions

This Maple worksheet is posted on the P:drive at P:/Class/Math/Paquin/DiffEq/Euler.mw

Numeric simulations of IVP's in Maple

This Maple worksheet is posted on the P:drive at P:/Class/Math/Paquin/DiffEq/Numeric.mw

Some practice with partial derivatives (for those of you that have not taken Calc C). Please let me know if you would like additional practice problems.

1.6: Equilibria and the Phase Line

1.7: Bifurcations

1.8: Intro to Linear Equations

This Maple worksheet is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/Bifurcation.mw

Introduction to Linear Equations

Quiz 2

1.9: Integrating Factors for Linear Equations

2.1: Modeling with Systems

2.2: The Geometry of Systems

Simulation of Systems

Maple file for graphical simulation of systems

This Maple worksheet is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/Systems.mw

Modeling second-order DE's using systems of first-order DE's

Begin Lab 1

This Maple worksheet is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/MassSpring.mw

Maple file for the damped harmonic oscillator

This Maple worksheet is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/DampedMassSpring.mw

Introduction to second order differential equations

Second order linear homogeneous differential equations with constant coefficients

Note: For the next few weeks, we will NOT be following the textbook. I will post lecture notes here on the Course Schedule page that should serve as your reference material. I will also post power point slides that you can use as an additional reference. The reference material will supplement the lecture discussions, though the lecture discussions will be self-contained.

Here is a power point file on second order DE's and solving second order linear homogeneous DE's with constant coefficients. When you click on the link, you will be able to open the power point presentation or save it as a file to view later.

Fundamental solutions of second order DE's

Power point file on fundamental solutions of second order linear DE's

Complex roots of the characteristic equation

Power point file on complex roots of the characteristic equation

Lab 1 due

Take-home midterm distributed

Repeated roots of the characteristic equation

Power point file on repeated roots of the characteristic equation

Summary of results for second-order linear homogeneous differential equations with constant coefficients

Take-home midterm due 5:00 pm

Forced second-order differential equations. This material corresponds (approximately) to Sections 4.1 and 4.2 in your textbook. You should use the posted lecture notes as reference material.

Forced second-order differential equations (continued). This material corresponds (approximately) to Sections 4.1 and 4.2 in your textbook. You should use the posted lecture notes as reference material.

Maple file for symbolic differentiation (Example 5 from the lecture notes). This Maple file is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/SymbolicDiff.mw.

Qualitative results: forced harmonic oscillators. See the posted lecture notes and Maple file for reference material.

Maple simulation file for forced harmonic oscillators. This Maple file is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/ForcedOscillator.mw.

Qualitative results: damped harmonic oscillators

Qualitative results: sinusoidal forcing. See the posted lecture notes and Maple file for reference material.

Begin Lab 2. Lab 2 is due at 5:00 pm on Friday, April 18.

Maple simulation file for sinusoidal forcing. This Maple file is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/Resonance.mw.

Lecture notes: Higher order differential equations, part 2 (nonhomogeneous higher order differential equations)

Review of power series

Intro. to series solutions of differential equations near an ordinary point

Some important power series

Series Solutions of differential equations near an ordinary point. See p. 1 and Example 1 of these lecture notes.

Homework 10 due.

Series solutions of differential equations near an ordinary point: Hermite polynomials

Outline for solving differential equations using series methods.

Series solutions of differential equations near an ordinary point: Airy's equation

Maple file for plotting series solutions. This Maple file is posted on the P: drive at P:/Class/Math/Paquin/SeriesPlots.mw.

Series Solutions of differential equations near an ordinary point. See Examples 3 and 4 (Airy's equation) of these lecture notes.

Here are some practice problems on series solutions. The answers are included so that you can check your work as you go. These problems will not be collected or graded. For each problem, you should find the general recurrence relation, and then use the recurrence relation to try to write down the general solution of the DE. If you can't observe the general formula for the a_n, it's ok to just write down the first several terms of the series solution. In the posted solutions, don't worry about the y_1(x) and y_2(x). Just make sure that you are able to obtain the recurrence relation.

Lab 2 is due at 5:00 pm on Friday, April 18.

Begin discussion of series solutions near a singular point

Regular singular points

Regular singular points

Begin discussion of Euler equations. Practice problems on Euler equations (that will not be collected or graded) are posted on the Homework page.

Continued discussion of Euler equations.

Series solutions near a regular singular point.

Series solutions near a regular singular point.

Course Evaluations