www.math.buffalo.edu/306/index.php

Shared Resources for Math 306
Ordinary Differential Equations

This page www.math.buffalo.edu/306/index.php provides access to materials shared by different sections of the course. Your instructor may choose to employ part of this material, and there may be additional materials posted elsewhere. See the handout from the first week of class for your course section.
Note to instructors: please see Information for instructors about obtaining ETEC combination
Note to students and to TAs: please see Hochstetter 139 Usernames
Note to TAs: please see Information for TAs about Hochstetter 139 lock

For help on downloading, please scroll down to the bottom of this page.

Syllabus (1ed,J.R.), Syllabus for 306DL (J.R., B.H.)

Ch. 1 One First-Order Equation

Maple Guide: Introduction (J.R., B.H.)
306ch0.html (view in browser), 306ch0m9.mws (Maple 9,10), 306ch0m8.mws (Maple 8), 306ch0m6.mws (Maple 6), 306ch0m5.mws (Maple 5)
Maple basics: What can Maple do for you?, Giving instructions to Maple, ..

If the Maple workspace versions appears in your browser window as strange looking text, or if your browser offers to download this file, then your browser is not equipped with Maple as a helper application: please scroll to the bottom of this page for help on downloading Maple workspace files.

Maple Guide for Ch. 1 (J.R., B.H)
306ch1.html (view in browser), 306ch1m9.mws (Maple 9,10), 306ch1m8.mws (Maple 8), 306ch1m6.mws (Maple 6), 306ch1m5.mws (Maple 5)
Slope fields, A numerical method: Euler's, Plotting a function (such as an analytical solution), Combining plots

Section 1.1 (J.J.F.)
mth3060101m9.html (view in browser), mth3060101m9.mws (Maple 9,10), mth3060101m6.mws (Maple 6), mth3060101m5.mws (Maple 5)
Modeling via Differential Equations: Models, Radioactive Decay, Logistic Growth of a Population, A Predator-Prey System
Section 1.2 (J.J.F.)
mth3060102m9.html (view in browser), mth3060102m9.mws (Maple 9,10), mth3060102m6.mws (Maple 6), mth3060102m5.mws (Maple 5)
Analytic Technique: A Mixing Problem, The Problem, Translation, Solution, A Better Translation and Solution
Section 1.3 (J.J.F.)
mth3060103m9.html (view in browser), mth3060103m9.mws (Maple 9,10), mth3060103m6.mws (Maple 6), mth3060103m5.mws (Maple 5)
Qualitative Technique: Slope Fields, Sample Slope Field, The On-Off RC Circuit
Section 1.4 (J.J.F.)
mth3060104m9.html (view in browser), mth3060104m9.mws (Maple 9,10), mth3060104m6.mws (Maple 6), mth3060104m5.mws (Maple 5)
Numerical Techniques: four example applications of Euler's method
Section 1.7 (J.J.F.)
mth3060107m9.html (view in browser), mth3060107m9.mws (Maple 9,10), mth3060107m6.mws (Maple 6), mth3060107m5.mws (Maple 5)
How to draw the bifurcation diagram for dy/dt = y⁶-2 y⁴+alpha
Section 1.8 (J.J.F.)
mth3060108m9.html (view in browser), mth3060108m9.mws (Maple 9,10), mth3060108m6.mws (Maple 6), mth3060108m5.mws (Maple 5)
Linear Differential Equations: A Finance Problem, A student has saved .., Setup, Solving the DE, Solving the problem Inaccuracy and Instability of Euler's method (Euler3a.html->Euler3a.class, J.R.)
How varying step-size changes the approximate solution

Ch.2 Systems of First-Order Equations

Maple Guide for Ch. 2 (J.R., B.H)
306ch2.html (view in browser), 306ch2m9.mws (Maple 9,10), 306ch2m8.mws (Maple 8), 306ch2m6.mws (Maple 6), 306ch2m5.mws (Maple 5)
Systems of two first-order equations: Direction fields and vector fields for 2D systems, Euler's method for 2D systems, combining plots. Section 2.1 (J.J.F.)
mth3060201m9.html (view in browser), mth3060201m9.mws (Maple 9,10), mth3060201m6.mws (Maple 6), mth3060201m5.mws (Maple 5)
Modeling via Systems: Predator-Prey (Foxes and Rabbits), Modified Predator Prey - Logistic Growth for Rabbits
Section 2.1 (J.J.F.)
mth3060201am9.html (view in browser), mth3060201am9.mws (Maple 9,10), mth3060201am6.mws (Maple 6), mth3060201am5.mws (Maple 5)
Bluegills and Redears: Modeling Competitive Species This worksheet provides examples of the phase portrait of the system dx/dt = b*x*(1-x/B-beta*y/R), dy/dt = r*y*(1-y/R-rho*x/B) for various values of the parameters b,r,B,R,beta,rho
Section 2.2 (J.J.F.)
mth3060202m9.html (view in browser), mth3060202m9.mws (Maple 9,10), mth3060202m6.mws (Maple 6), mth3060202m5.mws (Maple 5)
The Geometry of Systems: The difference between vector fields and direction fields, Some Important Examples, The Radial Vector Field (out), The Radial Vector Field (in), A Different Inward Vector Field, The Standard Circular Field, The Standard Hyperbolic Field
Section 2.3 (J.J.F.)
mth3060203m9.html (view in browser), mth3060203m9.mws (Maple 9,10), mth3060203m6.mws (Maple 6), mth3060203m5.mws (Maple 5)
Guess and Test: An example with real exponential solutions, An example without real exponential solutions
Section 2.4 (J.J.F.)
mth3060204m9.html (view in browser), mth3060204m9.mws (Maple 9,10), mth3060204m6.mws (Maple 6), mth3060204m5.mws (Maple 5)
Euler's method for a 2D system, the Van der Pol initial value problem: dx/dt(t) = y, dy/dt = -x + (1-x²) y, x(0) = 1, y(0) = 1.

Ch.3 Linear Systems

Maple Guide for Ch. 3 (J.R., B.H)
306ch3.html (view in browser), 306ch3m9.mws (Maple 9,10), 306ch3m8.mws (Maple 8), 306ch3m6.mws (Maple 6), 306ch3m5.mws (Maple 5)
2D linear systems (including the harmonic oscillator): Constant coefficient systems, Homogeneous systems, Constant coefficient homogeneous systems part 1: componentwise derivation of the characteristic equation, Constant coefficient homogeneous systems part 2: the eigenproblem, Eigenvalues and eigenvectors, Solution of a constant coefficient homogenous system with coefficient matrix having real unequal eigenvalues, Computing eigenvalues and eigenvectors with Maple, Solutions of a linear constant coefficient homogenous system with complex eigenvalues: the harmonic oscillator, Solutions of a linear constant coefficient homogenous system with complex eigenvalues, in which the solutions decay exponentially Section 3.3 (J.J.F.)
mth3060303m9.html (view in browser), mth3060303m9.mws (Maple 9,10), mth3060303m6.mws (Maple 6), mth3060303m5.mws (Maple 5)
Phase Planes for Linear Systems with Real Eigenvalues: Saddles, Sinks, Sources, Stability
Section 3.4 (J.J.F.)
mth3060304m9.html (view in browser), mth3060304m9.mws (Maple 9,10), mth3060304m6.mws (Maple 6), mth3060304m5.mws (Maple 5)
Phase Planes for Systems with Complex Eigenvalues: How to get Maple to do such an example, A Linear Second Order Equation Example
Section 3.5 (J.J.F.)
mth3060305m9.html (view in browser), mth3060305m9.mws (Maple 9,10), mth3060305m6.mws (Maple 6), mth3060305m5.mws (Maple 5)
Phase Planes for Systems with Repeated or Zero Eigenvalues
Section 3.7 (J.J.F.)
mth3060307m9.html (view in browser), mth3060307m9.mws (Maple 9,10), mth3060307m6.mws (Maple 6), mth3060307m5.mws (Maple 5)
The Trace Determinant Plane (Warning: 4 Mb)

Ch.4 Forcing and Resonance

Maple Guide for Ch. 4 (J.R., B.H)
306ch4.html (view in browser), 306ch4m9.mws (Maple 9,10), 306ch4m8.mws (Maple 8), 306ch4m6.mws (Maple 6), 306ch4m5.mws (Maple 5)
Forced Oscillators, Undetermined coefficients, Resonance peaks dependence on damping Section 4.2, 4.3 (J.J.F.)
mth3060402m9.html (view in browser), mth3060402m9.mws (Maple 9,10), mth3060402m6.mws (Maple 6), mth3060402m5.mws (Maple 5)
Sinusoidal Forcing and Undamped Forcing
Section 4.3, 4.4 (J.J.F.)
mth3060404m9.html (view in browser), mth3060404m9.mws (Maple 9,10), mth3060404m6.mws (Maple 6), mth3060404m5.mws (Maple 5)
Forcing and Resonance

Ch.5 Nonlinear Systems

Maple Guide for Ch. 5 (J.R., B.H)
306ch5.html (view in browser), 306ch5m9.mws (Maple 9,10), 306ch5m8.mws (Maple 8), 306ch5m6.mws (Maple 6), 306ch5m5.mws (Maple 5)
Linear and non-linear, Autonomous and non-autonomous, Phase plane plots, Implicitplot for tricky nullclines, Contourplot

Section 5.1 (J.J.F.)
mth3060501m9.html (view in browser), mth3060501m9.mws (Maple 9,10), mth3060501m6.mws (Maple 6), mth3060501m5.mws (Maple 5)
Equilibrium Point Analysis: Van der Pol's Equation, Competing Species, A Bifurcation Example
Section 5.2 (J.J.F.)
mth3060502m9.html (view in browser), mth3060502m9.mws (Maple 9,10), mth3060502m6.mws (Maple 6), mth3060502m5.mws (Maple 5)
Qualitative Techniques: Nullclines, two (colorful) examples of
Section 5.3 (J.J.F.)
mth3060503m9.html (view in browser), mth3060503m9.mws (Maple 9,10), mth3060503m6.mws (Maple 6), mth3060503m5.mws (Maple 5)
Hamiltonian Systems: Pictures of the Ideal Pendulum's Hamiltonian H = v²/2-cos(theta), Contour Lines -- the "undirected" phase plane, Three dimensional plots -- the graph of the function, (>1Mb)

Ch.X Power Series Solutions

Maple Guide for Ch. X (B.H.)
306chX.html (view in browser), 306chXm9.mws (Maple 9,10), 306chXm8.mws (Maple 8), 306chXm6.mws (Maple 6), 306chXm5.mws (Maple 5)
Chapter X (J.J.F.)
mth306chXm9.html (view in browser), mth306chXm9.mws (Maple 9,10), mth306chXm6.mws (Maple 6), mth306chXm5.mws (Maple 5)
Power Series Solutions

Note: As of Sept. 2006, an updated version of Chapter X is incorporated in the U.B. edition of the text.

Ch.6 The Laplace Transform Method

Maple Guide for Ch. 6 (J.R.)
306ch6.html (view in browser), 306ch6m9.mws (Maple 9,10), 306ch6m8.mws (Maple 8), 306ch6m6.mws (Maple 6), 306ch6m5.mws (Maple 5)
A series RC circuit with a stepped applied voltage (1st order diff. eq.), Some more complicated inverse Laplace transforms, A second-order example

Section 6.2 (J.J.F.)
mth3060602m9.html (view in browser), mth3060602m9.mws (Maple 9,10), mth3060602m6.mws (Maple 6), mth3060602m5.mws (Maple 5)
Discontinuous Function
Section 6.4 (J.J.F.)
mth3060604m9.html (view in browser), mth3060604m9.mws (Maple 9,10), mth3060604m6.mws (Maple 6), mth3060604m5.mws (Maple 5)
Impulse Forcing

Sample Exams with Answers

Sample Exam 1 (J.J.F.)
Exam_One_Answersm9.html (view in browser), Exam_One_Answersm9.mws (Maple 9,10), Exam_One_Answersm6.mws (Maple 6), Exam_One_Answersm5.mws (Maple 5)
Sample Exam 2 (J.J.F.)
Exam_2_Answersm9.html (view in browser), Exam_2_Answersm9.mws (Maple 9,10), Exam_2_Answersm6.mws (Maple 6), Exam_2_Answersm5.mws (Maple 5)
Sample Final (J.J.F.)
SampleFinalm9.html (view in browser), SampleFinalm9.mws (Maple 9,10), SampleFinalm6.mws (Maple 6), SampleFinalm5.mws (Maple 5)
Sketch for #7 (J.J.F) Note: You should be able to do these problems by hand, since will not have access to Maple during exams.

MAPLE VERSIONS AND FLAVORS
Maplesoft periodically releases new versions of Maple. Each Maple workspace file is identified internally with the version of Maple used to created it, and later versions of Maple can generally update workspaces created with previous versions.

If you have Maple 9 or later, please choose the "*m9.mws" files.
If you have an earlier version of Maple, please choose the workspace files with version number closest to yours but not greater than yours. For example, if you have Maple 7, choose the "*m6.mws" files rather than "*m8.mws" files.

Maple now comes in distinct flavors, "classic interface Maple" and "java interface Maple". The "java interface Maple" writes workspace files that have an ".mw" extension that cannot be read by "classic interface" Maple.
Because of this incompatibility, the Maple workspace files on this site are of the classic ".mws" type which can be read both by "classic interface" and "java interface" Maple.

In case of difficulty, please contact B.H.

MAPLE WORKSPACE DOWNLOAD HELP
If your browser is configured with Maple as a helper application, then when you click on a Maple workspace file (.mws extension), Maple will open the file.
If this doesn't happen, and instead the browser offers to download the Maple workspace, then

save the file in a convenient folder,
start Maple and open the file that you saved, from within Maple.

With some browsers, the workspace may appear as strange looking text in a window. If this happens, save the text as a file with a ".mws" extensions, then start Maple and load the file.

AUTHORS: J.R. = John Ringland, B.H. = Brian Hassard, J.J.F = James J. Faran V

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This page maintained by webmaster@math.buffalo.edu Revised: July 24, 2006 [BH]