22C:171/22M:171
Numerical Analysis II
Spring 2007

Contact/class information

Instructor:	David Stewart
Phone:	335-3832
Email:	dstewart(at)math(dot)uiowa(dot)edu
WWW URL:	http://www.math.uiowa.edu/~dstewart/
Office:	MLH 325B
Office hours:	TBA
Class times:	11:30am-12:20pm MWF
Class location:	110 MLH

You can see me outside the office hours provided it is mutually convenient.

Description

22C:171/22M:171 is about the numerical solution of differential equations and matrix computations (linear equations, linear least-squares problems, and eigenvalue/eigenvector problems).

Differential equations arise in almost every model of the physical world (and many economic, biological, social and other systems as well). Since most differential equations are too difficult to solve exactly, numerical methods are commonly used to approximately, but accurately, solve these equations. Numerical methods for solving differential equations are essential for anyone interested in simulating continuous-time systems.

Matrix computations arise in almost every area of computational mathematics. Everyone interested in computational methods in the physical or applied sciences should have some familiarity with methods for solving systems of linear equations. As well, least-squares problems are very common in statistics, approximation, and data analysis. Eigenvalues are used to study stability and resonances in physical systems.

Textbook

Introduction to Numerical Analysis by K. Atkinson, J. Wiley and Sons, 2nd Edition (1989). This course covers chapters six through nine. 22C:170/22M:170 covers the first five chapters.

Syllabus

• Numerical solution of differential equations
  • Euler's method
  • Midpoint rule
  • Runge-Kutta methods
  • multistep methods
  • error analysis (order of accuracy)
  • stability
• Solution of systems of linear equations
  • Gaussian elimination
  • LU factorization
  • error analysis, condition numbers and sensitivity
  • pivoting (partial and complete)
• Least squares problems
  • Normal equations
  • Cholesky factorization
  • QR factorization and orthogonalization
• Eigenvalue and eigenvector problems
  • eigenvalue problems and decompositions
  • symmetric matrices
  • power method
  • inverse power method
  • introduction to the QR algorithm

Assessment

There will be two in-class exams (20% each), homework assignments (40%) which may include some programming, and a programming assignment (20%). There may also be ungraded homework assigned during the course.

Familiarity with MATLAB will be useful during the course. The programming may be done in Matlab, C/C++, Fortran, Java, or other programming languages provided it is acceptable to the instructor.

Notes

1. The course plan may be modified during the semester. Such modifications will be announced in advance during class periods; the student has responsibility for keeping up with such changes. You should also make a habit of reviewing the class web page, which is accessible via:  
   http://www.math.uiowa.edu/~dstewart/classes/ 
   This page will have homework details and other information posted to it as the class progresses.
2. The Department of Mathematics offices are in 14 McLean Hall (MLH). You can contact the chair of the department through the Departmental Secretary at 14 MLH or by calling 335-0714.
3. Please let you instructor know if you have a disability that requires special arrangements. I need to hear from anyone who has a disability which may require some modification of seating, testing or other class requirements so that appropriate arrangements can be made. Please see me after class or during my office hours.
4. Be sure to read the section titled Student Complaints Concerning Faculty Actions in the Schedule of Classes.
5. This course is given by the College of Liberal Arts and Sciences. This means that class policies on matters such as requirements, grading, and sanctions for academic dishonesty are governed by the College of Liberal Arts and Sciences. Students wishing to add or drop this course after the official deadline must receive the approval of the Dean of the College of Liberal Arts and Sciences. Details of the University policy of cross enrollments may be found at:

   http://www.uiowa.edu/~provost/deos/crossenroll.doc .

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