Math 2280
Introduction to
Differential Equations
Spring term, 2001

Maple Projects

Send e-mail to : Professor Korevaar

Links:
Math 2280-2 home page
Professor Korevaar's home page
Department of Mathematics


Most recent listings are first.


Last Maple Project: You are to do the Section 9.5 and 9.6 computing projects. You may make your own solution templates. The notes from Tuesday April 17 contain useful commands for the section 9.5. The notes from Friday April 20 are about wave motion.

April 20 notes on traveling waves:
   waves.pdf
   waves.mws
April 17 notes in which examples 2 and 3 of section 9.5 are worked out in Maple:
   heateqtn.pdf
   heateqtn.mws


Even and odd extensions of Fourier series; differentiation and integration of Fourier series:
2280april10.pdf
2280april10.mws


Fourier series of 2L-periodic functions:
2280april9.pdf
2280april9.mws


Hey! I thought I understood resonance; and an introduction to Fourier series:
2280april6.pdf
2280april6.mws


Linearization and stability for non-linear systems of first order differential equations, using %6.1 hw #8 as an example:
2280march27.pdf
2280march27.mws


Illustrations of the zero equilibrium solution for homogeneous systems of two linear first order differential equations, classified according to the table on page 396.
2280march26.pdf
2280march26.mws


Solving non-homogeneous systems of differential equations via the method of undetermined coefficients and via variation of parameters; example 2 page 368 and example 4 page 372, worked out in maple.
2280march23.pdf
2280march23.mws


Generalized eigenvectors, Jordan Canonical form, fundamental matrix solutions and matrix exponentials - some medium-sized examples worked out in Maple, illustrating the connection between the power series definition of matrix exponential and the formula for computing it from an FMS.
2280march20.pdf
2280march20.mws


Maple Project 2: Earthquakes shaking tall buildings.
This is the project from section 5.3 of the text. There is a handout, as well as a solution template. both documents can be downloaded as .mws files (to be opened from Maple), or as .pdf documents (to be viewed or printed out). The solution template is to be used to organize your answers to the project. The handout contains example commands which you may find useful.
Handout:
   2280quake.mws
   2280quake.pdf
Solution template:
   2280quaketemplate.mws
   2280quaketemplate.pdf

  Grading: total points = 15: 2 points for #2, 3, 7; 3 points for #4, 5 ,6.


Notes on Ziggy's 2-mass 3-spring system and washboarding cars:
   2280march6.mws   
   2280march6.pdf


Example 7 page 249 - the geometric meaning of a first order system of differential equations, in terms of velocity fields.
   2280feb26.mws
   2280feb26.pdf


2280feb20.mws Notes on forced harmonic oscillators, maple worksheet version.
2280feb20.pdf pdf format, for printing.



Maple Project 1 This project has two parts. There are class handouts and solution templates for each part. Both parts of this project will be due on Monday February 5. The first part of the project is to do Investigation C on page 88 of the text, which is a logistic model of World population. The second part of the project has to do with numerical solutions to differential equations, sections 2.4-2.6 of the text.

2280proj1a.mws Maple worksheet on logistic equation for U.S. popluations, discussed in class on Tuesday January 23. This file contains commands which will be useful for Investigation C on page 88.
2280template1a.mws The template for your solutions to part 1. Download this, open it from Maple, and answer the questions as indicated.

2280proj1b.mws Maple worksheet of class handout on numerical methods for solving first order differential equations, with commands helpful for the second part of the first Maple project.
2280template1b.mws Maple worksheet of solutions template for part 2.

2280proj1a.pdf pdf format of proj1a above, for viewing or printing out, but NOT for opening from Maple
2280template1a.pdf The pdf version of template1a.
2280proj1b.pdf pdf format of proj1b.
2280template1b.pdf pdf format of template1b.

   Grading:
   Part 1: A total of 9 points, distributed as follows:
     2 = 1 point, 3-7 = 2 points each, 8, 9 = 1 point each.
   Part 2: A total of 26 points, distributed as follows:
     2, 3 = 2 points each, 4a = 1 point, 4b = 2 points, 4c = 2 points, 5(2.4#5)a = 2 points, b = 3 points, 5(2.5#5) = 2 points, 5(2.5#6) = 2 points, 6a = 3 points (n=50, 100), 6b = 3 points (time of zero velocity, velocity at landing), 7 = 2 points.




2280jan26.mws mws file of Jan 26 notes for section 2.3, in which we studied linear drag and a text example about a crossbow bolt.
2280jan26.pdf pdf version

Maple and Computer Lab Introduction:
   If you did not use Maple in your linear algebra class, and/or if you want to find out about using your account in the Math Computer lab, there is a tutorial introduction. It's on the Math 2250 Maple page, along with some other useful information and links.


2280jan9.pdf Pictures of slope fields for class on Tuesday January 9, pdf format.
2280jan9.html html format
2280jan9.mws Maple Worksheet format, if you want to download, open from Maple, and play.