Math 685/CSI 700/OR 682 Spring '08

Mondays 4:30-7:10pm Innovation Hall 105
Instructor: Maria Emelianenko
Email: memelian @
Office: 226A Science and Tech I
Office hours: Mondays 1-3pm and by appt.

 Site contents:  Syllabus  Matlab  Announcements  Lecture notes  Projects  Schedule and homework  Links  Help info  Gradelist  Anonymous Feedback Form

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:
- A standalone student version of the product is available from Mathworks website for a reasonable price.

Some MATLAB tutorials you might want to read:
[01/22/08]  Welcome! Our first meeting is on Monday, Jan. 28. 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!

[01/29/08]  Homework 1 has been posted, to be discussed in class on 02/04/08.
PLEASE CHECK YOUR GMU MAILBOX! If you don't have a message from me from today, it means the email I have on file for you does not function properly. Please let me know about this asap!

[02/05/08]  Homework 2 has been posted, to be discussed in class on 02/11/08.
Project assignments are available. I will ask you to specify the problem you are working on and your group members in class on 02/11/08.

[02/12/08]  Homework 3 has been posted, to be discussed in class on 02/18/08 - these are some of the most important questions, that I expect you to be able to answer, so it makes sense to practice.
Project 1 reports are due in class on 02/18/08 (please note that some typos have been corrected in Problems 1 and 2). No late submissions will be accepted without valid excuse. Although we will not have enough time to do group presentations for this project, I will expect you to participate in the discussion and report on your observations.

[02/19/08]  Project 2 has been posted, due two weeks from now. You can start working on it, and we will go through the analytical techniques once again in class on 09/25/08. No additional practice problems this week.

[03/04/08]  Take-home midterm is given, due in class on 03/24/08. Only individual effort is allowed on the midterm, in contrast with project assignments.

[03/06/08]  Hints were added to problems 4 and 5, newer version of the midterm assignment sheet posted online.

[03/26/08]  Homework 4 has been posted, to be discussed in class on 03/31/08.

[04/01/08]  Project 3 has been posted, due two weeks from now. Make sure you understand the problem formulations and ask questions in case anything is unclear - I will add more details then. No additional practice problems this week.

[04/16/08]  Project 4 has been posted, due three weeks from now. Make sure you understand the problem formulations and ask questions in case anything is unclear - I will add more details then.

[04/28/08]  The description of Project 4 has been slightly modified: [1] definition of the midpoint method had an extra 0.5 factor that has been removed; [2] and the initial value x=L/2 has been provided for the problem 2.2. Please make sure you take these clarifications into account!
Lecture notes
Lecture notes will be posted here as the course progresses.
Reading assignments and selected homework problems will follow our main text: M. Heath "Scientific Computing: An introductory survey", 2nd edition.

Lecture #1: Jan 28 [slides: PPT]

Lecture #2: Feb 4 [slides: PPT] [notes: PDF]

Lecture #3: Feb 11 [slides: PPT] [notes: PDF]

Lecture #4: Feb 18 [slides: PPT] [notes: PDF]

Lecture #5: Feb 25 [slides: PPT] [notes: PDF]

Lecture #6: March 3 [slides: PPT] [notes: PDF]

Lecture #7: March 17 [notes: PDF]

Lecture #8: March 24 [slides: PPT][notes: PDF]

Lecture #9: March 31 [slides: PPT][notes: PDF]

Lecture #10: April 7 [slides: PPT][notes: PDF]

Lecture #11: April 14 [notes: PDF]

Lecture #12: April 21 [slides: PPT][notes: PDF]

Lecture #13: April 28 [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.

Project 1
(given 02/05/08, due in class 02/18/08)
Choose one of the following problems and complete them in groups of two or individually:
[Problem1.1]   demo
[Problem1.2]   demo
[Problem 1.3]  

Project 2
(given 02/19/08, due in class 03/03/08)
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.

[1] 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)
[2] Growth in world population (total population vs. year) based on the following [data]
     (source: US Bureau of the Census, Intl. Database, 1996)
[3] 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)

Midterm exam: [pdf]

Project 3
(given 04/01/08, due in class 04/14/08)
Complete the assignment in groups of no more than three or individually. Description: [pdf]
Choose one of the following datasets for problem #2.

[1] Page rank. Using the code provided ([m]), generate the matrix representing the hierarchical structure of a portion of the world wide web, starting with (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.

[2] 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.

Project 4
(given 04/16/08, due in class 05/05/08)
Complete the assignment in groups of no more than three or individually. Description: [pdf]

You will be expected to make a 15-min presentation on one of the projects of your choosing on May 5th in class. Each group will choose one project they like to make a presentation on (not necessarily the last one). However, while project 4 assignments will be accepted up till last class, 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: 45%
- Project presentations: 15%
- Take-home midterm exam: 25%
- Class participation: 15%

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.
Tentative schedule
  Adobe reader needed to view .pdf files is available here

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.
Reading assignment: Chapter 1.


Computer arithmetic. Systems of linear equations.
Reading assignment: Chapter 2.
Homework assignment (practice): [pdf]    MATLAB codes: roundoff error: [.m], factorial: [.m]


Solving linear systems.
Reading assignment: Chapter 2.
Kees Vuik handout: be ready to discuss one of the cases in detail in class on 02/11/08.
Homework assignment (practice): [pdf]     MATLAB codes: [dir],
Tom Minka's lightspeed Matlab toolbox: [link]


Linear systems. Least squares.
Reading assignment: Chapter 3.
Project 1 due: please submit the reports in class and code via email, one per group.
Homework assignment (practice): [pdf]    MATLAB codes: [dir]


Least squares. Interpolation.
Reading assignment: Chapters 3, 7.
Start working on Project 2.


Reading assignment: Chapters 7, 4.
Interpolation. Eigenvalue problems.    Demos: [dir]
Google PageRank problem: [ppt], [pdf]
Project 2 due: please submit the reports in class and code via email, one per group.
Please start working on the Take-home midterm exam.


Spring break, no class

Reading assignment: Chapter 4.
Eigenvalue problems. Iterative methods.
Computer graphics problem: [pdf]


Reading assignment: Chapter 5.
Nonlinear equations.
MATLAB codes: [dir]
Take-home midterm exam due


Reading assignment: Chapter 6.
Homework assignment (practice): [pdf]


Reading assignment: Chapters 6,9.


Invited lecture: you are welcome to attend (CMASC series)
Class starts at 6pm. Reading assignment: Chapter 9.
Project 3 due: please submit the reports in class and code via email, one per group.


Review Chapter 9. Start working on Project 4.
Some useful resources:
[Pplane and Dfield software for Project 4]
[MATLAB optimization]
[ODE functions in MATLAB]
Reading assignment: Chapter 10.


Finish working on Project 4, start preparing the final presentation
Reading assignment: Chapter 11.
MATLAB codes: [dir]

Project 4 due: please submit the reports in class and code via email, one per group.
Final project presentations.

Help info and contacts
If you are looking for help, these are some of your options:
  • 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
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.

Useful links
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 ( 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