Fall Semester 2003

Numerical Methods I


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This course is the second year core for Computational Science. It is an integrated course with 3 hours of lectures and 1.5 hours of computional laboratory per week, and will run over two semesters.

The course covers the standard techniques of numerical computation from a theoretical as well as a practical perspective with a particular emphasis on large-scale high-performance computation, and provides the foundation for more specialized third year courses in computation and modeling.

It is assumed that participants have the mathematical background equivalent to two semesters of Engineering and Science Mathematics - attendance of the first year B track (Multivariable Calculus, ODE; Linear Algebra, Fourier Methods, Probability) is highly recommended but not formally required - or Analysis I/II and Linear Algebra I.

The course is appropriate as a home school elective for students of all majors with a particular interest in computation. It is recommended that students commit to this course for the full year. Students interested in a more compact introduction to methods of numerical computation are advised to take the one-semester Engineering and Science Mathematics 4A (Numerical Methods) instead.

Topics covered throughout the year are: computer arithmetic, condition of algorithms, systems of linear equations including iterative methods, computation of eigenvalues, interpolation and least square methods, numerical quadrature, numerical solution of ordinary differential equations, linear and nonlinear optimization, expectation-maximization algorithms, Monte-Carlo methods, introduction to parallelization and visualization.

Contact Information:
Instructor:Marcel Oliver
Office hours:  WThF after class in Research I, 107

TA/grader:Shaowu Tang
Office hours:  TBA

Lab Assistant:Vlad Lazar

Time and Place:
Lectures:  WF 9:45-11:00 in West Hall 4
Lab:Th 15:45-18:00 in the Research II Lecture Hall

Reommended Textbooks:

Additional Reading:

Homework and Projects:
The weekly homework/project sheets are handed out each Wednesday. The code should, moreover, be sent in a single email to to Shaowu Tang. You should be able to present and explain the code in the Thursday lab session following submission.

Collaborative project work in groups of two or three is permissible provided:

  • Each member of the group maintains and submits their own runnable version of the code.
  • You state who you collaborated with (e.g. as comments in the source files).
  • Each member of the group is able to explain the code without help from others.

You may consult books and internet resources, provided you always quote the source.


Class Schedule

03/09/2003: Introduction
05/09/2003: Computer arithmetic, condition of algorithms
10/09/2003: Solving scalar nonlinear algebraic equations: bisection, Newton's method
12/09/2003: Solving scalar nonlinear algebraic equations: analysis of Newton's method, secant method
17/09/2003: Matrix norms and condition numbers
19/09/2003: Linear systems: Gauss elimination
24/09/2003: LU decomposition without pivoting
26/09/2003: LU decomposition with pivoting; error analysis
01/10/2003: QR decomposition; least square solutions to linear systems
03/10/2003: Public Holiday
08/10/2003: Iterative methods: Jacobi and Gauss-Seidel method
10/10/2003: Gradient method
15/10/2003: Review for midterm exam
17/10/2003: Midterm Exam
22/10/2003: Conjugate Gradient method
24/10/2003: Lagrange interpolation; estimates of the interpolation error; numerical differentiation
29/10/2003: Lagrange interpolation (continued)
31/10/2003: Splines
05/11/2003: Numerical integration: Newton Cotes formulae
07/11/2003: Numerical integration: Gauss quadrature
12/11/2003: Gauss quadrature (continued)
14/11/2003: Review of ordinary differential equations
19/11/2003: One step methods for ordinary differential equations
21/11/2003: Local truncation error; estimation of the global error; convergence
26/11/2003: Runge-Kutta methods
28/11/2003: Linear multistep methods; Dahlquist equivalence
03/12/2003: Absolute stability
05/12/2003: Review for final exam
12/12/2003: Final Exam, 9:30-11:30, Research II Lecture Hall

Last modified: 2003/12/02
This page: http://math.iu-bremen.de/oliver/teaching/iub/fall2003/cps211.html
Marcel Oliver (m.oliver@iu-bremen.de)