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
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
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Exam I - Spring 2008
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Exam I - Topic List
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Chapter 3 - Phase Plane Review
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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
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Exam II - Review Problem Solutions
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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.
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Chapter 5 Review Problem - Solutions
Handouts
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MATH225.Fall2008.Review
Euler's Method for Excel
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Series and Laplace Handout
Chapter 5
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Graphs from 5.1 example
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Graphs from linearized center example
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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
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Lecture02
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Lecture02 - Graph: Linear Friction
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Lecture02 - Graph: Nonlinear Friction
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Lecture04 - Graph: Slope Fields 1
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Lecture04 - Graph: Slope Fields 2
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Lecture04 - Graph: Slope Fields 3
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Lecture04 - Graph: Slope Fields 4
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Lecture04 - Graph: Slope Fields 5
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Lecture05 - Existence and Uniqueness
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Lecture07 - Theory of Linear Equations
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Lecture09 - Ideal Mixing
Syllabus
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MATH225.Fall2008.Syllabus
Assignments
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Homework 1 - Due: Wednesday, August 27th by 5:00pm
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Homework 1 - Solutions
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Homework 2 - Due: Wednesday, September 3rd by 5:00pm
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Homework 2 - Solutions
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Homework 3 - Due: Wednesday, September 10th by 5:00pm
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Homework 3 - Solutions
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Homework 4 - Due: Wednesday, September 17th by 5:00pm
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Homework 4 - Solutions
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Homework 5 - Due: Wednesday, October 1st by 5:00pm
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Homework 5 - Solutions
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Homework 6 - Due: Wednesday, October 8th by 5:00pm
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Homework 6 - Solutions
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Homework 7 - Due: Wednesday, October 29th by 5:00pm
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Homework 7 - Solutions
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Homework 8 - Due: Wednesday, November 5th by 5:00pm
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Homework 8 - Solutions
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Homework 9 - Due: Wednesday, November 12th by 5:00pm
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Homework 9 - Solutions
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Homework 10 - Due: Wednesday, December 3rd by 5:00pm
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Homework 10 - Solutions
Project One
Please choose only one project to do. Lab 1.3 has been done as an example.
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Project 1 - Lab 1.3 - Example
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Project 1 - Lab 1.3 - Example - Choice Three Calculations
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Project 1 - Lab 1.1 - Problem Sheet
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Project 1 - Lab 1.4 - Problem Sheet
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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