The course consists of two parts A and B. Part A concerns theory and application of vector analysis with scalar and vector fields. General orthogonal coordinates are introduced with the cylindrical and spherical coordinate systems as important examples. The basic vector operations are introduced together with the for calculus important rules they obey. The theorems that relate line-, surface- and volume integrals are derived and applied. Part B concerns application of ordinary and partial differential equations (ODE and PDE) with focus on physical models and numerical solutions of the equation. For ODE, tools like MATLAB and Maple may be used. The students will construct a model based on ODE that describes a physical phenomenom. For PDE we introduce the PDE-solver FEMLAB. This tool is then used to illustrate basic theory and also applied to physical phenomena.