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Math 677 Fall '09 Prerequisites: MATH 214 or equivalent, knowledge of linear algebra and advanced calculus. Time and venue: TR 4:30-5:45pm Science & Tech I Room 242 Webpage: http://math.gmu.edu/memelian/teaching/Fall09 Instructor: Maria Emelianenko Email: memelian @ gmu.edu Office: 226A Science and Tech I Office hours: TR 2-3pm |
Site contents: Announcements Lecture notes Links Help info Anonymous Feedback Form
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This course provides an introduction to the dynamics of ordinary differential equations. Specific topics include existence theory, linear and nonlinear systems of ordinary differential equations, stability theory of equilibrium solutions, invariant manifolds, elementary bifurcation theory, strange attractors. It will also be demonstrated how these methods can be used in applications. [08/25/09] Welcome! Our first meeting is on Tuesday, Sept. 1 The textbook we are going to use is Lawrence Perko: Differential Equations and Dynamical Systems, third edition, Springer-Verlag, 2001. If you have time, please try to familiarize yourself with the material by reading the introduction and prepare for the fruitful work this semester. Hope it will be an enjoyable one! [09/03/09] Homework 1 has been posted, due on Thursday Sept. 10, in class. [09/15/09] Homework 2 has been posted, due on Thursday Sept. 24, in class. [09/25/09] Homework 3 has been posted, due on Thursday Oct. 8, in class. [10/09/09] There will be no class on Tuesday, Oct 13, due to Columbus day schedule change. [10/22/09] Homework 4 is due in class today. [10/22/09] Midterm I will be on Oct. 27 in class. You are allowed to bring one formula sheet. No calculators or books are permitted on the exam. [10/30/09] Homework 5 has been posted, due on Thursday Nov. 6, in class. [11/6/09] Homework 6 has been posted, due on Thursday Nov. 19, in class. [11/20/09] Homework 7 has been posted, due on Thursday Dec. 3, in class. [12/03/09] Final Exam will be held in the same room on Tue. 12/15, 4:30-7:15 pm. You are allowed to bring one formula sheet. No calculators or books are permitted on the exam. |
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Lecture notes will be posted here as the course progresses. Reading assignments and biweekly homework assignments will mostly follow our main text: Lawrence Perko: Differential Equations and Dynamical Systems, third edition, Springer-Verlag, 2001.
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Your grade in this course will depend on your performance on one written in-class midterm exams, weekly homework and a comprehensive final. - Midterm I (Oct 27, in class): 25% - Final exam (Tue, Dec 15 4:30pm, same room): 35% - Homework: 25% - Participation: 15%
I expect all class participants to abide to the rules and regulations specified in the official
GMU Honor code.
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If you are looking for help, these are some of your options:
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Every now and then I find interesting information on the web or in press.
I'll be putting this stuff here, since it could help some of you to refresh things you might have forgotten or
to aid with the general understanding of the course.
If you find something useful yourself, please let me know,
I'll be really happy to expand this list with your suggestions.
Basic math reference resources: Partial fractions tutorial Integration tutorial Partial derivative examples A concise Integral Table from Mathwords Calculus review - formulae you have to remember! Huge collection of Math related info at Wolfram Mathworld Software tools available online: ODE Software: powerful Dfield and PPlane Matlab tools (read instructions!) DFDEMO: Direction field Java applet One more direction field Java applet Phase portrait generator (applet by Prof. Mansfield, PSU) Studying ODE (applets for dir. fields, solving systems and more, by M. Rychlik) Differential Equations and Initial Value Problems, applet Systems of ODEs, applet ODE solver Solutia (script for solving DE in standard form) Course notes from different sources ODE modules from Duke Univ. (TRY THESE!) S.O.S. Math - nice short Differential Equations course online S.O.S. Mathematics - CyberExam - sample exams online Nagle's ODE book: Interactive Differential Equations supplement 1st Order ODEs (nice introductory notes by I. Blank, in .ps format) Differential Equations Notes (good notes w/lots of examples by B. Ikenaga, in .ps format) GATech DE course (great notes, by Jason Metcalfe) Miscellaneous links You might need to install current version of Ghostview to be able to view .ps files! ODE Lecture Notes (handwritten notes, more advanced material, by M. Pemberton) Advanced Differential Equations (extended source of notes on DE by S. Newhouse, in .ps format) ODE course for Engineers (nice application examples, by J.R. White) ODE notes (in .pdf, by Peter Wolenski, LSU) Numerical Solution of ODEs (CSEP electronic book) Numerical Solution of ODEs (Advanced course on theory of ODE, .ps file) Numerical Methods (S. Dalziel) Partial Differential Equations Notes (html notes on PDEs by A. Hood) Course Notes: ODE, PDE etc (J. Labute at McGill, in .pdf) Topics in Calculus (has some ODE notes too, by L. Lady) ODE Notes and Exercises (Maple-based exercises, by P. Monk) ODE course: lectures, problem sets, exams etc (by J.N. Kutz, U. Wash) ODE Exams, Worksheets, ... (R.L. Devaney) Mathematical Notes (.pdf notes on ODE by M. Malek, more theoretical) PDE & Vector Calculus Lecture Notes (by W. Zakrzewski, Durham UK) Complex Analysis and Differential Equations (by S.G. Rajeev, Rochester) Difference Equations to Differential Equations (D. Sloughter) Linear Methods ... (E.M. Harrell, J.V. Herod) Hilbert Space Methods for PDEs (R.E. Showalter) Topics in Integral and Differential Calculus (T. Kawasaki) ODE Projects (A.C. Heinricher) Maple Worksheet Repository Graphical Tools (applets) Taylor polynomial applets: 1, 2, 3, 4 Java Examples etc. (J. Feldman) Damped Harmonic Motion, applet Interactive Math Programs (calculus and DE applets from Dartmouth) Kepler's Laws, applet Fourier Synthesis, applet The Lorenz Equations, applet Nonlinear Klein-Gordon wave equation (applet by Paul Garrett) Heat equation, applet Java calculus, applets MathServ DE Toolkit Math Archives: ODEs, PDEs Math Forum - Differential Equations (notes, problems, puzzles, discussions etc) Differential Equations and more (calculus.net project) ODE Project at BU Sampler of applets (performance analysis, by Paul Garrett, UMN) Famous Curves Applet Index (spirals, involutes and more) Math Reference Tables |