# MAT-23306 Multivariate Mathematics Applied

## Course

Credits 6.00

 Teaching method Contact hours Tutorial 72 Practical 12 Independent study 0
 Course coordinator(s) dr. ir. JD Stigter Lecturer(s) dr. JHJ van Opheusden EE Deinum prof. dr. J Molenaar dr. ir. JD Stigter dr. ir. LG van Willigenburg CR Zelissen Examiner(s) dr. JHJ van Opheusden dr. ir. JD Stigter

English

### Assumed knowledge on:

MAT-14903 Mathematics 2 and MAT-15003 Mathematics 3.

### Contents:

- linear algebra: matrices, eigenvalues and eigenvectors;
- complex numbers;
- ordinary differential equations: separation of variables and variation of constants; systems of linear differential equations; systems of non-linear differential equations and classification of steady states;
- numerical methods for ordinary differential equations: difference quotients and the Euler method; systems of differential equations; trapezoidal rule and Runge-Kutta; discretization errors; error propagation, stability and stiffness;
- integration in two or three dimensions: limits of integration; coordinate systems and the Jacobian;
- introduction to partial differential equations: flow models, diffusion and convection; boundary and initial conditions; steady states;
- vector fields: flow fields and force fields; the gradient and the laws of Fick, Fourier and Darcy; the potential function; divergence and the Laplace operator;
- Fourier series for partial differential equations: separation of variables and the Sturm-Liouville problem; boundary value problems and Fourier series;
- use of computer software.

### Learning outcomes:

After successful completion of this course students are expected to be able to:
- explain and apply concepts, methods and techniques from linear algebra, calculus, vector calculus and numerical mathematics;
- apply mathematical knowledge, insights and methods to solve problems in the technological sciences using a systematic approach;
- critically reflect upon the results;
- correctly report mathematical reasoning and argumentation;
- interpret and evaluate the results in terms of the (physical, chemical, biological) problem that was modelled mathematically;
- use mathematical software (Maple) in elaborating mathematical models.

### Activities:

- preparing for lectures and tutorials by self-study and doing exercises;
- active participation in lectures and tutorials;
- doing the exercises;
- computer practical (compulsory).

### Examination:

- written test with open questions and/or multiple choice questions (100%).
- practical (with compulsory attendance) has to be completed with the grading 'passed'.
A sufficient practical result remains valid for a period of one study year.

### Literature:

M. de Gee, "Mathematics that Works volume 4: Time-dependent Systems". ISBN 978-90-5041-161-5. Available: WUR-shop.
M. de Gee, "Mathematics that Works volume 5: Processes in Space and Time". ISBN 978-90-5041-170-7. Available: WUR-shop.

Programme Phase Specialization Period Compulsory for: BSW Soil, Water, Atmosphere BSc 1AF BES Environmental Sciences BSc C: Environmental Technology 1AF MES Environmental Sciences MSc 1AF MML Molecular Life Sciences MSc C: Physical Biology 1AF