MATH 640A, Fall 2002

Continues as MATH 640B in the winter quarter.
Catalog Description for 640ABC:
Approximation by piecewise polynomial functions, variational principles, variational formulation of partial differential equations. The Rayleigh-Ritz-Galerkin method, convergence of approximations, time-dependent problems, isoparametric elements and nonconforming finite element methods, applications.
Real story:
In 640A (call number 04203) we will start at the beginning of numerical analysis, and cover topics such as linear algebra, nonlinear equations, approximation, and differentiation and integration. The pace will depend on what you already know, but by the end everyone should understand these topics very well.
In 640B we will learn how to solve ordinary and partial differential equations. The catalog description (which I inherited), is of the finite-element method for solving partial differential equations. We will cover it, along with other approaches.
If we manage to finish all this by the end of the winter quarter, then in 640C we will switch to a project format, where you each choose a topic of interest, we all study them a bit, and you study your topic in depth.
Prerequisites:
The catalog lists Math 510 Linear Algebra, which makes sense, and Math 570 Complex Variables, which does not. I require
  • Mastery of Calculus and Linear Algebra
  • The mathematical sophistication to learn material independently from a book.
  • Knowledge of Matlab or a programming language. Less-prepared students should consider Math 544, which offers similar material in a less strenuous setting.
  • Instructor:
    Martin Mohlenkamp, mohlenka@ohio.edu, (740)593-1283, 554 Morton Hall.
    Office hours: Monday 3-4pm, Tuesday 2-3pm, and Thursday 1-2pm.
    Web page:
    http://www.ohio.edu/people/mohlenka/20031/640A.
    Class hours/ location: 
    MT(W)HF 9:10-10am in 215 Morton Hall (note change in room).
    Text:
    Numerical Analysis: Mathematics of Scientific Computing, 3rd edition, by David Kincaid and Ward Cheney, Brooks/Cole, 2002.
    Homework:
    There will be weekly homework assignments. Late homeworks are penalized 3 points for each 24 hour period or part thereof, with no excuses accepted, and a strict deadline to catch up before each exam. You are strongly encouraged to work together, but you must acknowledge any help you receive. Homework will be a mixture of paper and pencil problems and programming. Having your programs work is essential, but style and proper commenting also count. I will support Matlab and C, but you can use another language if you prefer. Each week one problem will be designated a Good Problem, and will be graded partly on presentation. The idea is to practice writing mathematics regularly but in small pieces.
    Exams:
    There will be one midterm exam, and a final exam on Thursday 21 November at 10:10am in 215 Morton Hall.
    Grade:
    Based on homeworks 50%, midterm exam 20%, and the final exam 30%. Grades are not the point.
    Policies:
    I will not count attendance, but you need to attend in order to learn. Academic dishonesty will be considered as professional dishonesty and harshly punished.
    Special Needs:
    If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met.
    Resources:

    Martin Mohlenkamp
    Last modified: Mon Jun 2 11:51:00 EDT 2003