After successful completion of the course, students are able to:

• calculate simple numerical procedures manually
• manually approximate functions
• perform quadratic interpolations in everyday life
• discretize differential equations
• apply boundary conditions and solve eigenvalue problems
• convert higher order differential equations into first order differential equations
• perform error calculations and error estimates for numerical methods
• apply simple numerical methods to specific problems
• explain the advantages and disadvantages as well as the differences between numerical methods
• describe the limits of the applicability of simple numerical methods

• basics of numerical arithmetic
• basics of numerical linear algebra
• methods for solving nonlinear equations
• approximations of functions
• numerical differentiation and integration
• boundary value problems, initial value problems, eigenvalue problems

oral presentation

This course is taught in English.

 

Exam modalities:

• a non-programmable calculator is allowed.
• questions are in English but help/vocabulary list can be provided. Answers preferably in English, but German is also accepted.
• documents are not allowed.
• paper sheets are provided.

Dahmen & Reusken (2006): Dahmen, W. & Reusken, A. (2006), Numerik für Ingenieure und Naturwissenschaftler, Springer, Berlin, Heidelberg. (e 29,95) Freund et al. (2007): Freund, R. W., Hoppe, R. H. W., Stoer, J. & Burlisch, R. (2007), Stoer/Bulirsch: Numerische Mathematik 1, Springer, Berlin, Heidelberg. (e 24,95) Golub & van Loan (1989): Golub, H. G. & van Loan, H. G. (1989), Matrix Computations, Johns Hopkins University Press. (e 34,95) Hanke-Bourgeois (2002): Hanke-Bourgeois, M. (2002), Grundlagen der numerischen Mathematik und des wissenschaftlichen Rechnens, Teubner, Wiesbaden. (e 52,00) Huckle & Schneider (2006): Huckle, T. & Schneider, S. (2006), Numerische Methoden, Springer, Berlin, Heidelberg. (e 21,00) Moler (2004): Moler, C. B. (2004), Numerical Computing with MATLAB, SIAM, Philadelphia.(e 40,99) Press et al. (1992): Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. (1992), Numerical Receipes in C, Cambridge University Press, Cambridge. (umfangreich, vergriffen) Quarteroni & Saleri (2006): Quarteroni, A. Saleri, F. (2006), Wissenschaftliches Rechnen mit MATLAB, Springer, Berlin, Heidelberg. (e 29,95) Stoer & Burlisch (2005): Stoer Stoer, J., Burlisch, R. (2005), Numerische Mathematik 2, Springer, Berlin, Heidelberg. (e 26,95) iv