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.
