## Numerical Mathematics for Chemists

### MNF-chem5014

**Contents**

- introduction to programming basics (Fortran)
- representation of numbers, errors, problem condition
- numerical differentiation
- numerical integration
- search for roots and extrema
- differential equations
- systems of linear equations
- matrix diagonalization
- interpolation, regression

**Course material**

script (corrections/small changes may occur during the semester)

exercise sheet 1: simple programming

exercise sheet 2: errors and differentiation (program for equidistant logspace, and error plot for the 3 finite-difference formulae)

exercise sheet 3: integration and random numbers (example program stub on how to use the Fortran90/95 random number seed routine)

exercise sheet 4: differential equations

exercise sheet 5: root finding and minimization

exercise sheet 6: systems of linear equations

exercise sheet 7: interpolation and regression (necessary data for exercise sheet 7: doublemin.dat, doublemin.true, wiggle.dat, wiggle.true, kinetic.dat)

exercise sheet 8: matrix diagonalization (optionally: jacobi.f90, eigsrt.f90, jacobi-manual)

**additional material**

WS15/16 script (Henrik Larsson’s extended version, based on my old Diploma lecture “computer applications in physical chemistry”; contains an Octave introduction).

Short introduction to Fortran, with a few simplistic example programs.