MTH 499- 599: MODELS AND METHODS OF APPLIED MATHEMATICS - Spring 2014
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Instructor: Malgorzata Peszynska, Professor of Mathematics
Class: MWF 2:00-2:50pm, MLM 234
Course information: Credits: 3.00.
Student preparation: the students should have completed MTH 256 or equivalent, and MTH 341.
Class announcement.
Textbook:
  • REQUIRED: Gilbert Strang, Introduction to Applied Mathematics, Wellesley, 1986. Other materials will be available as class notes and handouts.
    In particular, I will be using parts of
    • J.D. Logan, "Applied Mathematics", Wiley 1987
    • P.S. Hansen, "Discrete Inverse Problems. Insight and Algorithms", SIAM 2010
    • D.P. O'Leary, "Scientific Computing with Case Studies", SIAM 2009
    • K. Borre, G. Strang, "Algorithms for Global Positioning", Wellesley-Cambridge, 2012
    • Cleve Moler's books and materials at http://www.mathworks.com/moler/
Syllabus: This class covers various discrete and continuous models along with the necessary mathematical methods. The methods will include linear analysis, equilibrium and minimum principles, calculus of variations, principal component analysis (singular value decomposition) and orthogonal expansions, asymptotic and Fourier analysis, least squares, and constrained and unconstrained optimization. As time permits, a gentle introduction to inverse problems and Monte Carlo techniques will be included. The models will be explored in depth in various guided projects and computer lab activities, none of which require prior computing expertise.

Grading: a grade for the class will be established based on the Homework grade (30%), Lab and project reports grade (30%), and Exam grade (40%) from two exams worth 20% each.
No late HW will be accepted but one lowest HW grade will be dropped.

Exams: Midterm 1: 5/9/14 in class.
Midterm 2: 5/28/14 in class.
There will be no make-up exams.

Attendance: Attendance in class is not taken but students are responsible for the material covered in class. Attendance in lab meetings is required but a pre-arranged absence in one lab meeting can be allowed. (Lab meetings will be scheduled most Fridays and/or other days as schedule permits) Daily schedule will be posted as a guide to the class activities.

Course Learning Outcomes:
    A successful student who has completed MTH 499 will be able to
    • Follow the fundamental ideas of mathematical modeling for various current applications which translate a given problem to one that can be solved using algebra and differential equations.
    • Solve discrete and continuous quadratic minimization problems and the associated positive definite linear models arising from physically motivated equilibrium problems and calculus of variations.
    • Apply the basics of Fourier analysis to selected examples.
    • Use the principles of principal component analysis and least squares for solving, in particular, large underdetermined and overdetermined linear systems.
    A successful student who has completed MTH 599 will be able to:
    • Apply the fundamental ideas of mathematical modeling for various current applications which translate a given problem to one that can be solved using algebra and differential equations.
    • Formulate and solve discrete and continuous quadratic minimization problems and the associated positive definite linear models arising from physically motivated equilibrium problems and calculus of variations.
    • Apply the basics of Fourier analysis and understand its limitations
    • Use the principles of principal component analysis and least squares for solving, in particular, large underdetermined and overdetermined linear systems. Select the most appropriate method for a given application.
Special arrangements for students with disabilities: please contact the instructor and Services for Students with Disabilities prior to or during the first week of the term to discuss accommodations. Students who believe they are eligible for accommodations but who have not yet obtained approval through DAS should contact DAS immediately at 737-4098.
Course drop/add information is at http://oregonstate.edu/registrar/.
Student Conduct: All students are expected to obey to OSU’s student conduct regulations, see OSU’s Statement of Expectations for Student Conduct . See also Academic or Scholarly Dishonesty link.