MATH-225 Differential Equations - Fall 2008
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==Exam II== | ==Exam II== | ||
− | EXAM II - | + | EXAM II - BB204A - 7:30pm-9:00pm. |
No Notecards | No Notecards | ||
No Calculators | No Calculators | ||
Exam II review problems. | 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 | |
+ | |||
+ | {{PDF Table Item|filename=Math225_Review2.fall2008.pdf|title=Exam II - Review Problem Solutions}} | ||
+ | {{PDF Table Item|filename=Math225.EIISoln.fall2008.pdf|title=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. | ||
+ | |||
+ | {{PDF Table Item|filename=Math225_Chapter5Review.fall2008.pdf|title=Chapter 5 Review Problem - Solutions}} | ||
==Handouts== | ==Handouts== | ||
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[http://www.mines.edu/~sstrong/DiffEQ_Materials/EulersMethod.xls Euler's Method for Excel] | [http://www.mines.edu/~sstrong/DiffEQ_Materials/EulersMethod.xls Euler's Method for Excel] | ||
{{PDF Table Item|filename=LaplaceTransforms.fall2008.pdf|title=Series and Laplace Handout}} | {{PDF Table Item|filename=LaplaceTransforms.fall2008.pdf|title=Series and Laplace Handout}} | ||
+ | |||
+ | ===Chapter 5 === | ||
+ | {{PDF Table Item|filename=5.1.all.pdf|title= Graphs from 5.1 example}} | ||
+ | {{PDF Table Item|filename=5.center.all.pdf|title= Graphs from linearized center example}} | ||
+ | {{PDF Table Item|filename=chaos.pdf|title= Fractal/Chaos Presentation}} | ||
+ | [http://www.mines.edu/~sstrong/DiffEQ_Materials/chaos.mp4 - Lorenz System and its Strange Attractor - 1] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/DiffEQ_Materials/lorenz(1).mp4 - Lorenz System and its Strange Attractor - 2] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/DiffEQ_Materials/lorenz(2).mp4 - Lorenz System and its Strange Attractor - 3] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/DiffEQ_Materials/lorenz(3).mp4 - Lorenz System and its Strange Attractor - 4] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/DiffEQ_Materials/lorenz(4).mp4 - Lorenz System and its Strange Attractor - 5] | ||
==Lecture Slides == | ==Lecture Slides == | ||
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{{PDF Table Item|filename=Math225_L07.Linearity.fall2008.pdf|title=Lecture07 - Theory of Linear Equations}} | {{PDF Table Item|filename=Math225_L07.Linearity.fall2008.pdf|title=Lecture07 - Theory of Linear Equations}} | ||
{{PDF Table Item|filename=Math225_L09.Tank.fall2008.pdf|title=Lecture09 - Ideal Mixing}} | {{PDF Table Item|filename=Math225_L09.Tank.fall2008.pdf|title=Lecture09 - Ideal Mixing}} | ||
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− | |||
==Syllabus == | ==Syllabus == | ||
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{{PDF Table Item|filename=Math225_hw6.soln.fall2008.pdf|title=Homework 6 - Solutions}} | {{PDF Table Item|filename=Math225_hw6.soln.fall2008.pdf|title=Homework 6 - Solutions}} | ||
{{PDF Table Item|filename=Math225_hw7.fall2008.pdf|title=Homework 7 - Due: Wednesday, October 29th by 5:00pm}} | {{PDF Table Item|filename=Math225_hw7.fall2008.pdf|title=Homework 7 - Due: Wednesday, October 29th by 5:00pm}} | ||
+ | {{PDF Table Item|filename=Math225_hw7.soln.fall2008.pdf|title=Homework 7 - Solutions}} | ||
{{PDF Table Item|filename=Math225_hw8.fall2008.pdf|title=Homework 8 - Due: Wednesday, November 5th by 5:00pm}} | {{PDF Table Item|filename=Math225_hw8.fall2008.pdf|title=Homework 8 - Due: Wednesday, November 5th by 5:00pm}} | ||
+ | {{PDF Table Item|filename=Math225_hw8.soln.fall2008.pdf|title=Homework 8 - Solutions}} | ||
{{PDF Table Item|filename=Math225_hw9.fall2008.pdf|title=Homework 9 - Due: Wednesday, November 12th by 5:00pm}} | {{PDF Table Item|filename=Math225_hw9.fall2008.pdf|title=Homework 9 - Due: Wednesday, November 12th by 5:00pm}} | ||
+ | {{PDF Table Item|filename=Math225_hw9.soln.fall2008.pdf|title=Homework 9 - Solutions}} | ||
+ | {{PDF Table Item|filename=Math225_hw10a.fall2008.pdf|title=Homework 10 - Due: Wednesday, December 3rd by 5:00pm}} | ||
+ | {{PDF Table Item|filename=Math225_hw10.soln.fall2008.pdf|title=Homework 10 - Solutions}} | ||
==Project One== | ==Project One== |
Latest revision as of 02:37, 4 December 2008
Main Page | > | Mathematical and Computer Sciences Course Wikis |
Contents |
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
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