Schedule and homework
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MATLAB is an interactive programming language for general scientific and technical computation with powerful graphics and library functions.
We will be using MATLAB environment for all homework problems and I expect you to be able to get access to it. Here is some relevant information.
- Some guidelines for accessing and using MATLAB are available here: http://math.gmu.edu/introtomatlab.htm
- A standalone student version of the product is available from
Mathworks website for a reasonable price.
Some MATLAB tutorials you might want to read:
[01/15/10] Welcome! Our first meeting is on Monday, Jan. 25. If you have time, please try to familiarize yourself with the software to prepare
for the fruitful work this semester. Hope it will be an enjoyable one!
[02/15/10] Due to the snow cancellation last week, we will have one additional class at the end of the semester, on Friday May 7, same time/place.
[02/16/10] Project 1 has been posted, due two weeks from now on March 1. Make sure you understand the problem formulations and ask questions in case anything is unclear - I will add more details then. Don't forget to do the weekly practice problems!
[02/22/10] I have posted Project 2, due three weeks from now on March 22. Please look at it before the break and ask questions if something is not clear, since we won't be meeting on Monday March 8. You can start working on it once you are done with Project 1.
[03/22/10] Midterm Exam is now available (see schedule for the file to download). Please work on it indivudually and submit in class on April 5.
[04/05/10] I have posted Project 3, due three weeks from now on April 26. You will have one week after that to work on your final presentation.
[04/26/10] Final Presentations are going to be held in class on May 7 (Friday) - please give yourself enough time to prepare!
[04/26/10] Final Exam is now available(see schedule for the file to download). Please work on it indivudually and submit it in class on May 7, or no later than May 12 via email or to my office.
Lecture notes will be posted here as the course progresses.
There is no required textbook, but the following reading sources are recommended in addition to lectures:
1) Michael Heath: Scientific Computing. An Introductory Survey
2) Diane O'Leary: Scientific Computing: with case studies
Here are also several textbooks that are available for free online
through SpringerLink (with GMU login), they will be useful at
different times during the semester as we cover relevant topics.
3) Otto, Denier: An Introduction to Programming and Numerical Methods in MATLAB
4) Atkinson, Han: Theoretical Numerical Analysis
A Functional Analysis Framework
5) Varga: Matrix Iterative analysis
6) Jorge Nocedal and Stephen J. Wright: Numerical Optimization
Springer Series in Operations Research and Financial Engineering, 2006
7) Holmes: Introduction to Numerical Methods in Differential Equations
Lecture #1: Jan 25 [slides: PPT] [notes on Matlab: PDF] [Numerical disasters: PDF]
Lecture #2: Feb 1 [slides: PPT] [notes: PDF]
Lecture #3: Feb 15 [slides: PPT] [notes: PDF]
Lecture #4: Feb 22 [slides: PPT] [notes: PDF]
Lecture #5: March 1 [slides: PPT] [notes: PDF]
Lecture #6: March 15 [slides: PPT][notes: PDF]
Lecture #7: March 22
Lecture #8: March 29 [slides: PPT] [notes: PDF]
Lecture #9: April 5 [slides: PPT] [notes: PDF]
Lecture #10: April 12 [notes: PDF]
Lecture #11: April 19 [slides: PPT] [notes: PDF]
Lecture #12: April 26 [slides: PPT]
Lecture #13: May 3 [slides: PPT] [notes: PDF]
- There will be approximately 3 group projects given during the semester.
- You may work in groups of no more than 3 people and submit your work in one group report.
- You will be expected to give a 15-minute presentation after the completion of the final project
- Don't hesitate to seek my help with these problems as well as with any other questions about the course.
(given 02/16/10, due in class 03/01/10)
Choose one of the following problems and complete them in groups or individually:
(given 02/22/10, due in class 03/15/10)
Complete both the theoretical and numerical parts of the assignment in groups of no more than three or individually. Description: [pdf]
Choose one of the following datasets for problem #4. Export the relevant columns from Excel into a text file and use MATLAB commands "data=load('filename.txt')" to read the data into the matrix structure.
 Gas prices: make a least squares approximation for the end of the year gas price (Dec price vs. year) based on the following [data]
(source: Bureau of Labor Statistics, 2004)
 Growth in world population (total population vs. year) based on the following [data]
(source: US Bureau of the Census, Intl. Database, 1996)
 Correlation between world-wide life expectancy and availability of physicians (female life expectancy vs. people per physician) based on the following [data]
(source: The World Almanac 1993)
(given 04/05/10, due in class 04/26/10)
Complete the assignment in groups of no more than three or individually. Description: [pdf]
Choose one of the following datasets for problem #2.
 Page rank. Using the code provided ([m]), generate the matrix representing the hierarchical structure of a portion of the world wide web, starting with http://www.gmu.edu (or some other site) as a root. Run the power iteration to determine the dominant eigenvector and find out which 10 websites get the highest ranking in this domain.
 Weather forecast. Generate a Markov chain for weather prediction. Namely, write down a matrix P, such that P(1,1) and P(1,2) are the probabilities that a sunny day is followed by a sunny day or a rainy day, respectively, and P(2,1), P(2,2) are the probability of a rainy day to be followed by a sunny day or another rainy day, in that order. A Markov chain is a system that has n possible states and passes through a series of transitions from one state to another, according to these probabilities Pij. Explain how power iteration can be used to make long-term weather predictions based on this set of transition probabilities. Compute the solution for the choice of P=[0.9 0.1; 0.5 0.5] and comment on your results.
You will be expected to make a 15-min presentation on one of the projects of your choosing on May 7th in class. Each group should choose one project they like to make a presentation on (not necessarily the last one). I encourage you to leave yourselves enough time to prepare the slides! Although the presentations will be based on group projects, every member of the group is supposed to talk about some part of the project. Each group should be prepared to have the slides available online or have a laptop/flash drive at the time of their talk. If your have any questions on the way the presentations will be conducted, please ask me at any time.
Final grade in the course will be determined as follows:
- Theoretical and computational assignments and projects: 35%
- Take-home midterm exam: 25%
- Take-home final exam: 30%
- Project presentations: 10%
Weekly practice problems will be given that will not count towards the final grade, unless specifically noted. I strongly encourage all participants to do these exercises in order to gain the necessary grasp of the material and perform well on exams and graded assingments. I will discuss solutions in class every week.
I expect all class participants to abide to the rules and regulations specified in the official
GMU Honor code.
Adobe reader needed to view .pdf files is available
Prerequisites for the course include basic knowledge of calculus, linear algebra and differential equations, as well as programming skills.
We will build upon this prior knowledge to learn how to formulate, analyze and solve real problems arising in the fields on science and engineering.
In addition to computational techniques the course will includes theoretical development as well as implementation, efficiency, and accuracy
issues in using algorithms and interpreting results. Specific topics include linear and nonlinear systems of equations, polynomial interpolation,
numerical integration, and introduction to numerical solution of differential equations.
Introduction to MATLAB and scientific computing.
roundoff error: [.m],
Computer arithmetic. Systems of linear equations.
[hw2.pdf] MATLAB codes: [flops.m], [prob1.m], [prob2.m]
No class due to snow.
Solving linear systems.
[hw3.pdf] MATLAB codes: [PALU.m], [sherman.m]
Linear systems. Least squares.
Least squares. Interpolation.
Project 1 due.
Spring break, no class
Interpolation. Eigenvalue problems.
Eigenvalue problems. Iterative methods.
Project 2 due.
Midterm Exam: [pdf]
Motivation for eigenvalue problems: [pdf]
Google eigenvector problem: [pdf]
Take-home midterm exam due.
Numerical Integration and Differentiation.
Initial value problems for ODEs.
Boundary Value problems for ODEs.
Project 3 due.
Final Exam: [pdf]
Final project presentations.
Help info and contacts
If you are looking for help, these are some of your options:
If you have concerns or suggestions that you'd rather leave anonymous, please use the anonymous feedback form.
I need to know what you think in order to make the learning process effective, so any feedback is valuable to me.
- Try coming to my office hours: M 1-3pm.
- If you have conflict with my office hours, talk to me after class or email me, I'll try to make an
appointment for you at a different time. Or you can try to stop by my office at any time if you have a quick question
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
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)
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)
(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:
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,
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