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.
Instructor: | Marcel Oliver |
Email: | m.oliver@iu-bremen.de |
Phone: | 200-3212 |
Office hours: | WThF after class in Research I, 107 |
TA/grader: | Shaowu Tang |
Email: | s.tang@iu-bremen.de |
Phone: | 200-3511 |
Office hours: | TBA |
Lab Assistant: | Vlad Lazar |
Email: | v.lazar@iu-bremen.de |
Phone: | TBA |
Lectures: | WF 9:45-11:00 in West Hall 4 |
Lab: | Th 15:45-18:00 in the Research II Lecture Hall |
Collaborative project work in groups of two or three is permissible provided:
You may consult books and internet resources, provided you always quote the source.
Homework: | 20% |
Projects: | 30% |
Midterm Exam: | 20% |
Final Exam: | 30% |
Cutoff score: | 95% | 90% | 85% | 80% | 75% | 70% | 65% | 60% | 55% | 50% | 45% | 40% |
IUB Points: | 1.0 | 1.33 | 1.67 | 2.0 | 2.33 | 2.67 | 3.0 | 3.33 | 3.67 | 4.0 | 4.33 | 4.67 |
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 |