335 Differential Equations with Maple

Instructor John Starrett Schedule

           Text: Ordinary Differential Equations,
   Authors: Tenenbaum and Pollard
  Publisher: Dover
        ISBN: 0-486-64940-7

Available in the book store or from internet book sellers

Text: Paul's Online Math Notes for Differential Equations
Authors: Paul Dawkins
Publisher: buy bound version for $25 from NMT Math department or download free or use online at http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

CRN	Course	Days	Times	Location	Credit Hours	Title	Instructor
22288	MATH 335-02	T Th	1100-1215	Weir 102	3	Ordinary Differential Equations with Maple	John Starrett Weir 240 835-5763

Catalog course description:

MATH 335, Differential Equations I, 3 cr, 3 cl hrs
Prerequisite: MATH 132 passed with grade C- or better
Ordinary differential equations, series solutions, transform calculus

Course Objectives: An ordinary differential equation is an equation involving functions of a single variable as well as derivatives of these functions.

When we solve algebraic equations, we try to find real or complex numbers that satisfy a relationship given by explicit or implicit functions of several variables and constants. When we solve ordinary differential equations, we try to find functions that satisfy a relationship between an unknown function and its derivatives.

Differential equations arise in science and engineering whenever we attempt to describe quantities that change in time or space. The goal of this course is for you to understand ordinary differential equations and to be able not only to use and solve them, but to construct them from a description of a physical, electrical or chemical phenomenon.

In this particular section of Differential Equations 335, the use of the computer algebra system Maple is required. The reason for this is that science and engineering problems in the real world are usually of sufficient complexity that we must solve them using computer assistance. Maple is an easy to use program that can assist us in solving differential equations and graphing the solutions. We will use this software as an integral part of the course, not only for homework but for exams. It is essential that you either use Maple in the computer lab or on your own computer to many of the assigned HW problems.

I highly recommend that you buy a copy of Maple for yourself through the Maple Adoption Program, a program whereby Maple, on cooperation with New Mexico Tech, allows you to buy Maple for a discounted price. To get your copy of Maple, you must be registered for this course. Go to Maplesoft and use the promotion code

One other resource that I highly recommend is Paul's online notes on differential equations.

Homework problems listed are the problems that go with that week's lessons, and they are due Thursday of the next week.

For the first few weeks, all of the HW problems I will have you do by hand. Later most will be done using Maple. For now you are allowed to use Maple to do integration, partial fractions, solve for constants using initial conditions, draw graphs and the like, but note on your paper which things Maple did, saying something like "according to Maple..."

I will provide instructions in the box where the HW problems are listed. Once we start doing HW problems in Maple, you must email me the worksheet with the Maple problems with only the input to save space. Remove the output by Edit, Remove Output, From Worksheet . I will execute the code myself to view your answers.

Grading: homework 25%, exams 75%

Sample HW using Maple in html format

Sample HW using Maple (actual worksheet) -- right click to download

Sample HW 2 using Maple in html format

Sample HW 2 using Maple (actual worksheet) -- right click to download

Sample Maple worksheet for second and higher order linear homogeneous DEs

Sample worksheet for second and higher order linear homogeneous DEs in HTML format

Week of	Section and Homework Problems REMEMBER:Problems are assigned in the listed week and are due the Thursday of the following week	Topics Covered
Aug 24	page 55, problems 2, 4, 7, 8, 16, 17, 19, 21	General, 1st order separable equations, modeling, using Maple Yeast Model
Aug 31	page 61, problems 3, 4 and 10 page 97 problems 1, 4, 9, 10, 14,15,21, 25	integrating factors, change of variables, homogeneous equations
Sept 7	page 79 problems, 4, 8, 11, 12, page 91, problems 3, 8 page 97, problems 3, 22 page 103, problems 1, 3, 6, 10, 13	exact equations, exact integrating factors, Bernoulli equations, misc techniques for first order equations
Sept 14	page 220 problems 1, 11, 19, 23, 24, 34, 35	Second order linear homogeneous ODEs Higher order linear differential equations HW example in html format HW example in Maple format
Sept 21	page 231 4, 7, 8, 15, 16, 17, 24, 30, 32	HW example in html format HW example in Maple format
Sept 28	Geometric view of solutions to DEs, systems of DEs from higher order DEs	Practice Exam 1a Practice Exam 1b Practice Exam 1c Practice Exam 1d Practice Exam 1e Actual practice exam Actual practice exam solution
Oct 5	Exam Tuesday Example worksheet 1	Laplace Transforms document in pdf Laplace Transforms worksheet in html format Laplace Transforms worksheet in Maple format
Oct 12	Example worksheet 2 Exam Solutions HW Read the section on Laplace transforms in the Tennenbaum (blue book) 292-306 and read pages 181 to 187 in the Dawkins (white book). Do problems page 311, probs # 12, 13, 15, 17, 18,20, 21	Laplace Transforms for systems worksheet in html format Laplace Transforms for systems worksheet in Maple format
Oct 19	Do this HW in Maple, and for each problem, plot your answer. 1. Page 311, prob 16 with rhs Heaviside(x-1)sin(x)+Heaviside(x-4)cos(x). 2. Problem 16 with rhs consisting of 10 triangle waves of amplitude 1, with period Pi beginning at t=0. These triangle waves should ramp downward, as opposed to the examples we did in class. 3. Using the Heaviside function as a switch, construct a single continuous function x(t) that has these characteristics: a. has value 1 from 0 to 1, b. connects the point (1,1) to (Pi,-1) with a straight line, c. connects (Pi,2 Pi with a cosine curve 4. Use the curve above for the right hand side of x''-3x'+4x =rhs with ICs x(0)=1, x'(0)=1	Maple worksheet for Heaviside Maple worksheet for systems using Laplace transform
Oct 26	page 546 # 3, 4, 5, 8, 9,11, 12 using only the first series method.	Series solutions to differential equations
Nov 2	page 546 # 3, 4, 5, 8, 9,11, 12 using the second series method.	Series worksheet in html format Series worksheet in Maple format
Nov 9	page 546 # 3, 4, 5, 8, 9,11, 12 using the Maple worksheets SeriesLab1 and SeriesLab2	Worksheet for offset and initial conditions.
Nov 16	Exam over Laplace Transforms Thursday Review Worksheet in html Review Worksheet in maple Additional Review Worksheet in maple	Maple worksheet for Frobenius method Maple worksheet for Frobenius method in html format Practice exam for Laplace and non-homogeneous DE
Nov 23	page 546 # 10 by Series Method (not Taylor series!) page 584 # 2, 8, 10, 12	Series Solutions HW 1 pg1 pg2 pg3 pg4 pg5 pg6 pg6 pg8 pg9 pg10
Nov 30	HW: #1 Suppose we were to take two rings one meter in radius and place them one meter apart so that they line in parallel planes that are perpendicular to the line of their common radii (see this picture ). Find the shape of the surface you would get if you dipped the rings in bubble liquid. #2	Systems of equations worksheet in Maple format Systems of equations worksheet in html format Hamiltonian Systems in Maple format Hamiltonian Systems in html format
Dec 7	Final solutions Pg. 1 Pg.2 Pg. 3 Pg. 4 Pg.5 Pg. 6 Pg.7 Pg. 8 Pg. 9 Pg. 10 Pg. 11 Maple worksheet Maple	Practice final 1 Practice final 2 Practice final 3
Dec 14	Finals

Resources:

Many Maple worksheets demonstrating differential equations

Maple newsgroup
Maple student help center

Laplace transform table

Academic Policies

Maple worksheets: right click to download

Class 1

Worksheet 2

Worksheet 3

Series 1

Series 1a