Textbook in PDF format The book offers a practice-oriented introduction to the mathematical methods of electrical engineering. The focus is on the solution of ordinary and partial differential equations using analytical and numerical methods. The analytical methods are opposed to the numerical methods. The differential equations were chosen with a view to the problems of electrical engineering. It is shown how they can also be transferred to mechanics or thermodynamics. Numerous examples and exercises with elaborated solutions facilitate the transfer of knowledge to applications. Topics Required mathematical basics - Coordinate systems - Geometric mean distance - GMD - LCR parallel and series resonant circuit - Current displacement in conductor - Bessel equation and Bessel function - Solution of using Green's functions - Method of Lagrangian multipliers - Differential equations and finite elements - the Method of Moments to the Galerkin Method - Galerkin Method - Galerkin-FEM - Electrostatic field calculation - Galerkin-FEM - heat diffusion - Galerkin-FEM - magnetic field diffusion - Introduction to the finite difference method - Applications of FEM to product development - Virtual product design - Eigenvalue problems - Common features of methods to solve differential equations - Things worth knowing about modelling