MATH-225 Differential Equations - Fall 2008

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Course Information

MATH225:Differential Equations - Classical techniques for first and higher order equations and systems of equations. Laplace transforms. Phase plane and stability analysis of non-linear equations and systems. Applications to physics, mechanics, electrical engineering, and environmental sciences.

Prerequisite: Instructor Consent. 3 hours lecture; 3 semester hours.

Instructor Information

Instructor : Scott Strong

Office : Chauvenet Hall 278

Office Phone : 303.384.2446

email : math225g.fall2008@gmail.com

Course Calander

Classes Begin : August 20th, 2008

Meeting Days : Monday, Wednesday, Friday

Meeting Time : 2:00pm-2:50pm

Meeting Location : Berthoud Hall 108

Important Dates :

    September 3rd, 2008 - Last day to add/drop without a W
    October 9th, 2008 - Exam I  
    October 13th to 14th, 2008 - Fall Break
    October 28th, 2008 - Last day to withdrawal 
    November 13th - Exam II
    November 26th to 28th - Thanksgiving Break

Classes End : December 4th, 2008

Office Hours

Fixed Office Hours :

    Tuesday and Thursday --- 1:00pm-3:00pm


If you cannot meet during the previous office hours then please contact me to schedule another meeting time.

Textbook Information

    Textbook : Differential Equations - P. Blanchard, R. Devaney, and G. Hall, (PWS, Boston: 1996) ISBN 0-534-95004-3
    Second edition errata.
    Google Books Third Edition
    Textbook Website : The Boston University  - Ordinary Differential Equations Project 
    Publishers Website : Blanchard, Devaney, Hall Companion Site 


Course Documents

Pdf.png These downloads require Adobe Acrobat Reader

Exam I

EXAM I - BB204A - 7:30pm-9:00pm. No Notecards No Calculators

    Exam I review problems.
    Chapter 1: pp. 138-143
    #21,23,25,27,29,31,33,35,37,39,43,49,53,56
    Chapter 2: pp.220-223
    #19-22,26(a)-(c),27(a)-(c),29
    Chapter 3: pp.370-374
    #19,21,27-32
Exam I - Review Problem Solutions
Exam I - Spring 2008
Exam I - Topic List
Chapter 3 - Phase Plane Review
Exam I Solutions

Exam II

EXAM II - BB204A - 7:30pm-9:00pm. No Notecards No Calculators

    Exam II review problems.
    Chap. 3: p.374 
    #23-25 
    Chap. 4: p.443-445 
    #2, 16, 18, 20, 21, 23, 24(a), 26(a) 
    Appendix B: p.742-743 
    #10 (a) Find the Recurrence Relation, (b) Find the power series solution and then use a known Taylor series to write y=f(t) 
    Chap. 6: p.621-623 
    #1, 8, 18, 19, 20, 21, 25, 29, 30
Exam II - Review Problem Solutions
Exam II Solutions

Final Exam

Final Exam - BB204A - Saturday, December 6th - 8:00am-10:00am

   Chapter 5 review: 1-5, 11, 15-18.
   on problems 15-18:
   (a) Find all equilibria.
   (b) Using the Jacobian matrix, classify all equilibria.
   (c) For each equilibrium point, sketch the phase portrait of the system near that point.  Sketch each of these graphs separately.
   (d) Sketch the x- and y-nullclines and indicate the direction of the vector field along each nullcline.
   
Chapter 5 Review Problem - Solutions

Handouts

MATH225.Fall2008.Review

Euler's Method for Excel

Series and Laplace Handout

Chapter 5

Graphs from 5.1 example
Graphs from linearized center example
Fractal/Chaos Presentation

- Lorenz System and its Strange Attractor - 1

- Lorenz System and its Strange Attractor - 2

- Lorenz System and its Strange Attractor - 3

- Lorenz System and its Strange Attractor - 4

- Lorenz System and its Strange Attractor - 5

Lecture Slides

Lecture02
Lecture02 - Graph: Linear Friction
Lecture02 - Graph: Nonlinear Friction
Lecture04 - Graph: Slope Fields 1
Lecture04 - Graph: Slope Fields 2
Lecture04 - Graph: Slope Fields 3
Lecture04 - Graph: Slope Fields 4
Lecture04 - Graph: Slope Fields 5
Lecture05 - Existence and Uniqueness
Lecture07 - Theory of Linear Equations
Lecture09 - Ideal Mixing

Syllabus

MATH225.Fall2008.Syllabus


Assignments

Homework 1 - Due: Wednesday, August 27th by 5:00pm
Homework 1 - Solutions
Homework 2 - Due: Wednesday, September 3rd by 5:00pm
Homework 2 - Solutions
Homework 3 - Due: Wednesday, September 10th by 5:00pm
Homework 3 - Solutions
Homework 4 - Due: Wednesday, September 17th by 5:00pm
Homework 4 - Solutions
Homework 5 - Due: Wednesday, October 1st by 5:00pm
Homework 5 - Solutions
Homework 6 - Due: Wednesday, October 8th by 5:00pm
Homework 6 - Solutions
Homework 7 - Due: Wednesday, October 29th by 5:00pm
Homework 7 - Solutions
Homework 8 - Due: Wednesday, November 5th by 5:00pm
Homework 8 - Solutions
Homework 9 - Due: Wednesday, November 12th by 5:00pm
Homework 9 - Solutions
Homework 10 - Due: Wednesday, December 3rd by 5:00pm
Homework 10 - Solutions

Project One

Please choose only one project to do. Lab 1.3 has been done as an example.

Project 1 - Lab 1.3 - Example
Project 1 - Lab 1.3 - Example - Choice Three Calculations
Project 1 - Lab 1.1 - Problem Sheet
Project 1 - Lab 1.4 - Problem Sheet

Material Ovierview

    Instructor's Online Manual Third Edition
    Instructor's Online Manual Second Edition


Course Links

    Dynamical System (overview)
    Dynamical System (mathematical formalism)
    Determinism
    Dynamical System
    Text Software : BDH
    BU DE Project : Animations
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