MATH 686 (Section 001)
Spring 2008

Numerical Solution of Differential Equations

ABOUT THE COURSE

• Lectures: T (7:20 pm - 10:00 pm)
• Venue: Science and Technology I (Room 242)
• Course Syllabus
  

INSTRUCTOR

• Office:MATH 222B
• Office Hours: T (6:00 pm - 7:00 pm), Tr (3:00 pm - 4:00 pm) and by appointment
  
• E-mail: pseshaiy@gmu.edu

EXPECTED LEARNING OUTCOMES

1. Understanding the theoretical and practical aspects of the use of numerical methods for differential equations

2. Implementing numerical methods for a variety of multidisciplinary applications

3. Establishing the limitations, advantages, and disadvantages of the numerical methods used in practice

LECTURES

• Modeling Process
• Two-Point Boundary Value Problems
• Partial Differential Equations: Part I

ABOUT MATLAB

• Introduction to the MATLAB problem solving environment
• Accessing MATLAB
  • MATLAB is installed in the computer labs in the Johnson Center in rooms 340, 341, and 343 and in Innovation Hall in room 301. Check the following website for hours of operations.
  • MATLAB is also installed on the Mason cluster (osf1). To use this version of MATLAB, you must activate your account on the Mason cluster (osf1). If you haven't done this before, you must activate your mason account. See the web page below for instructions to activate your account and set up a password .
  • One may also access the Mason cluster (and hence, MATLAB) from home using the Secure Shell software.
• Matlab Tutorials
  • UNIVERSITY BASED MATLAB LINKS
  • University of Florida
  • University of Michigan (Control Tutorials for Matlab)
• Please find below the MATLAB programs that you may use for your assignment involving solutions to nonlinear equations. Note that all these program will expect user inputs upon execution.
  • Newton-Raphson Method (newton_raphson.m)
  • Secant Method (secant_method.m)

COURSE EVALUATION

There will be six homework assignments during the semester each worth 10% assigned every other week, that will include both theoretical and computational problems. The solutions must be neatly written up and handed in on time to receive full credit as they add towards 60% of the total grade. Students must also prepare for inclass presentations based on their homework which will be worth 10%. There will be one midterm exam worth 10% that will be based on the various mathematical techniques presented in the class during the semester. There will be one final exam which will be worth 20% and will be held on Tuesday May 13, 2008 from 7:30 pm - 10:15 pm.

OPPORTUNITIES

• NASA Higher Education Opportunities: Applications are now being accepted for NASA's Graduate Student Researchers Project. Through GSRP, NASA awards fellowships for graduate study leading to research-based master s or doctoral degrees in science, mathematics and engineering fields related to NASA research and development. GSRP supports approximately 300 graduate students annually. Applicants must be currently enrolled or accepted as full-time students at an accredited U.S. college or university. Applicants must also be U.S. citizens. All application materials must be received no later than Feb. 1, 2008. For more information, visit: Graduate Student Researchers Project .
  
  
• Space Telescope Science Institute Summer Student Program: The Space Telescope Science Institute has announced its Summer Student Program for college undergraduates. The program will run 10 weeks from June through August 2008. STScI is located in Baltimore, Md., on the Homewood campus of Johns Hopkins University. The Summer Student Program is centered upon one-on-one student interaction with a scientist working at the Institute. The diverse range of scientific interests includes the study of Earth's solar system, interacting binary stars, quasars at the edge of the universe and the quest for intelligent life elsewhere. The goal is to place students in a true research environment where students will participate directly in research, including data acquisition, reduction and interpretation. At the end of the program, students will present their summer's work at an informal symposium of their peers and mentors. The Summer Student Program is oriented toward upper-division college undergraduates, typically students between their junior and senior years. Most participants are physics or astronomy students, but applications are welcome from anyone with enough interest and experience in science who wants to take part in a research experience. Foreign students are welcome to apply. Applications are due Feb. 20, 2008. For more information, including answers to frequently asked questions, visit Space Telescope Science Institute Summer Student Program . Please e-mail any questions about this opportunity to summerintern@stsci.edu .
  
  
• GMU 2008 Aspiring Scientists Summer Internship Program : The George Mason University Aspiring Scientists Summer Internship Program was established in 2007 by Dr. Lance Liotta and Dr. Emanuel Petricoin III for high school, undergraduate, and graduate students to gain hands on experience in laboratories at the Prince William George Mason University Campus. Students are exposed to cutting edge technology and have the opportunity to work in areas of science including but not limited to Proteomics, Genomics, Neuroscience, Biochemistry, and Environmental Science. Hard work often pays off with participants’ names published in scientific journals and their work presented at scientific conferences. In addition to gaining invaluable laboratory experience pivotal for college applications and resumes, students also have the opportunity to meet with scientists from varying disciplines in the scientific field during career day presentations.
  The 2008 Aspiring Scientists Summer Internship Program will begin on Monday June 23, 2008 and will conclude with a poster session and reception on Monday August 18, 2008. Two hard copies of the application (see website) for the 2008 George Mason University Aspiring Scientists Summer Internship Program and one recommendation letter completed by a teacher or administrator from his/her school must be received by 5:00pm March 3, 2008.
  
  
• Student Summer Program on Multiscale Modeling and Analysis : The University of Texas at Austin invites applications for a summer program on Multiscale Modeling and Analysis (July 21-August 8, 2008). This is a three-week program on multiscale modeling and analysis for advanced undergraduate and 1st year graduate students. This program will contains 5-6 short course, each consisting of 4-6 one-hour lectures. The lectures will be complemented by problem sessions in the afternoons conducted by senior graduate students. The prerequisites of the course are advanced calculus and linear algebra. Some familiarity with numerical analysis and computer programming will be helpful.
  
  
• NCAR: Numerical Techniques for Global Atmospheric Models : The National Center for Atmospheric Research (NCAR) announces a Summer Colloquium on Numerical Techniques for Global Atmospheric Models, June 1-13, 2008, NCAR, Boulder, Colorado, U.S.A. Hosted by the Advanced Study Program, Climate and Global Dynamics Division, and Computational and Information Systems Laboratory at NCAR. Additional support is provided by NASA. The colloquium will survey the latest developments in numerical methods for the dynamical cores of Atmospheric General Circulation Models. The course will engage students in the primary options available for global models such as the choice of the computational grids, numerical methods, resolutions, prognostic variables or model equations. Students will participate in lectures and tutorial sessions, but devote a large fraction of time to research projects to be developed in small groups. Each group will be assigned to a specific dynamical core with which they will run idealized test cases. Model-specific tutors will provide expert advise during the hands-on experience. Students will gain in-depth knowledge of the numerical techniques and scientific performance of the dynamical core in question. The goal is to survey the advantages and trade-offs of different computational approaches and grids for climate and weather research. We invite graduate students from the atmospheric sciences, applied mathematics and other relevant disciplines to apply. The application deadline is March 1, 2008. More information can be found at Colloquium Website and the Wiki for the colloquium. For further information please send an Email to Peter H. Lauritzen (pel@ucar.edu).
  
  
• FIrst opportunity : The High Performance Computing Modernization Program Office will be hosting 50 interns at 12 HPC labs and testing centers nationwide (list is online). Interns will be doing work in electromagnetic, acoustics, weapons testing, design of sensors, signal processing, software development, oceanography, meteorology, biotechnology, cluster development, molecular modeling, biochemical engineering, etc. We would like your help in recruiting science, technology, engineering, and mathematics students. Below is basic information about the internship that can be posted on list-servs, websites, or internal bulletin boards where promising students might take interest. If you need additional information, please reply to Email: JEOM-Summer-Intern@hpcmo.hpc.mil.

• DoD/High Performance Computing Modernization Program Office Joint Educational Opportunities for Minorities : (Deadline: March 10, 2008) The Joint Educational Opportunities for Minorities (JEOM) internship is an opportunity for science, technology, engineering, and mathematics students (graduate or undergraduate) to learn how to conduct research and work on exciting and rewarding projects at national laboratories and test centers across the country (a list of locations is online at JOEM .) For eligibility, applicants must be enrolled full-time in an undergraduate or graduate program in science, technology, engineering, and mathematics (STEM) disciplines. All individuals are welcome to apply, including white men, women, minorities, and citizens from other countries. Students will not be required to enlist in any of the military Services (Army, Navy, or Air Force). To apply, Submit an online application at JOEM . Also, send a transcript, resume, and two letters of recommendation to:
  HPCMP
  JEOM Program Manager
  10501 Furnace Road, Suite 101
  Lorton, VA 22079-2632
  703-812-4440-Tel
  703-690-0971-Fax
  email: JEOM-Summer-Intern@hpcmo.hpc.mil
  The application deadline is March 10, 2008; faxes or emails are acceptable. If you have problems with the online application, a paper version is posted on the HPCMP JEOM webpage. JEOM offers a competitive stipend, travel expenses to/from the internship location, and an opportunity to network with leaders in the science and technology community at a technical conference and Summer Colloquium in Seattle, Washington. For more information, email: JEOM-Summer-Intern@hpcmo.hpc.mil.

• Mathematical modeling in industry XII : A workshop for graduate students, August 6-15, 2008. Here are details of past workshops .
  
  
• Industrial Mathematical & Statistical Modeling Workshop for Graduate Students : Details will appear here .

ACADEMIC INTEGRITY

DISABILITY ACCOMODATION