Computational Science

Syllabus

• Floating point representation, arithmetic and error analysis.
• Numerical Linear Algebra, linear systems of equations, decompositions, Least Squares, Singular Value decomposition, condition, stability.
• Solving non-linear equations, iterative methods, order of convergence, Fixed-point theory, Newton's iteration, multi-point methods, polynomial zeroes.
• Introduction to symbolic computation, exact arithmetic, data representation, operations on polynomials.
• Interpolation methods, splines.
• Numerical quadrature, Euler-Mclaurin summation.
• Ordinary differential equations, discretization, error analysis, multi-step methods, Runge-Kutta methods, adaptive methods.
• Introduction to partial differential equations, discretization, boundary problems.

Reference

The topics mentioned above are treated in

• Introduction to Numerical Analysis
• Springer Verlag
• Series: Texts in Applied Mathematics , Vol. 12
• Stoer, J., Bulirsch, R.
• 3rd ed., 2002, XV, 768 p.

(The text covers more topics and some topics in more detail than what is expected in this course.)

Related courses

Linear Algebra (including finite arithmetic, numerical stability):
http://www.math.ethz.ch/education/bachelor/lectures/hs2008/other/linalg_INFK

Introduction to Computational Science
http://www.icos.ethz.ch/education/courses/courses_icos/intro_comp_science

Scientific Computing: Introduction to Differential Equations
http://intra.csb.ethz.ch/education/spring_08/sc/index_en.html

Availability of previous exams

The current policy is not to release any previous exam.

However, some old exams for the related courses above were made available in the past, and can be obtained at the student organization VIS. These exams have a similar format as the foundation exam, but their syllabus may not fully coincide.