MATH 640A (04438), Fall 2003

Numerical Analysis

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 we will start at the beginning of numerical analysis with some preliminaries (chapter 1), and computer arithmetic (chapter 2). We will then cover nonlinear equations (chapter 3), and linear algebra (chapters 4 and 5). If time allows, we will cover approximation (chapter 6). The pace will depend on what you already know, but by the end everyone should understand these topics very well.
Prerequisites:
The catalog lists Math 510 Linear Algebra and Math 570 Complex Variables. 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 544/545/546, which offers similar material.
    Instructor:
    Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1283, 554 Morton Hall.
    Office hours: Monday 3-4pm, Tuesday 10-11am, Thursday 3-4pm, and Friday 10-11am.
    Web page:
    http://www.ohio.edu/people/mohlenka/20041/640A.
    Class hours/ location: 
    MT(W)HF 1:10-2pm in 313 Morton Hall.
    Text:
    Numerical Analysis: Mathematics of Scientific Computing, 3rd edition, by David Kincaid and Ward Cheney, Brooks/Cole, 2002.
    Homework:
    There will be homework assignments about once a week. 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, on a date to be determined later. The final exam is on Friday 21 November at 12:20pm in our regular classroom.
    Grade:
    Based on homeworks 50%, midterm exam 20%, and the final exam 30%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-. Grades are not the point.
    Missed or Late work:
    Late homeworks are penalized 5% for each 24 hour period or part thereof, excluding weekends and holidays.
    Attendance:
    Attendance is assumed but is not counted in your grade. It is your responsibility to find out any announcements made in class.
    Academic Dishonesty:
    You are strongly encouraged to work together on the homework, but you must acknowledge in writing what help you received and from whom. The midterm and final exam must be your own work, and without the aid of calculators or notes. Dishonesty will result in a zero on that work, and possible failure in the class and a report to the university judiciaries.
    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:
  • LaTeX: LaTeX help 1.1; A sample LaTeX file, samplelatex (.tex, .dvi, .ps, .pdf); A sample of latex with figures incorporated: latexfig.tex and the sample figure lfig.eps.
  • MATLAB: Ohio University Matlab Central; Colorado MATLAB Help Desk; Local Matlab Quick Reference (.pdf) and Survival Guide (.pdf); Official MATLAB Documentation; Random web Introduction to MATLAB, MATLAB Summary and Tutorial, and A Practical Introduction to MATLAB.
  • Schedule

    Subject to change.  
    Week Date Homework/ Test/ etc.
    1 Sep 8 Introduction
    Sep 9
    Sep 11  
    Sep 12  
    2 Sep 15
    Sep 16 Homework 1 (.pdf) due; Layout ( .pdf)
    Sep 18  
    Sep 19  
    3 Sep 22
    Sep 23 Homework 2 (.pdf) due; Flow ( .pdf)
    Sep 25  
    Sep 26
    4 Sep 29
    Sep 30 Homework 3 (.pdf) due.
    Oct 2
    Oct 3
    5 Oct 6  
    Oct 7 Homework 4 (.pdf) due; Symbols ( .pdf)
    Oct 9
    Oct 10
    6 Oct 13  
    Oct 14
    Oct 16 Test on Chapters 1-3, 5-7pm in 219 Morton; study guide .pdf
    Oct 17
    7 Oct 20  
    Oct 21
    Oct 23 Homework 5 (.pdf) due; Logic ( .pdf)
    Oct 24  
    8 Oct 27  
    Oct 28 Homework 6 (.pdf) due
    Oct 30
    Oct 31
    9 Nov 3  
    Nov 4 Homework 7 (.pdf) due
    Nov 6
    Nov 7  
    10 Nov 10  
    Nov 11 Veteran's Day, no class
    Nov 13 Homework 8 (.pdf) due; Graphs ( .pdf)
    Nov 14
    11  Nov 17  
    Nov 21 Final Exam 12:20-2:20pm Friday, in our classroom

    Martin J. Mohlenkamp
    Last modified: Mon Nov 17 11:58:13 EST 2003