Reelle und komplexe Zahlen, Grenzwerte, Folgen, Reihen, Potenzreihen, stetige Abbildungen, Differential- und Integralrechnung einer Variablen, Einführung in gewöhnliche Differentialgleichungen

Introduction to differential and integral calculus in multiple variables.

In this lecture we treat problems in applied analysis. The focus lies on the solution of quasilinear first order PDEs with the method of characteristics, and on the study of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation, and the wave equation.

Functions; Differential and integral calculus for functions of one variable; power series. The mathematical methods are applied in a large number of examples from mechanics, physics and other areas which are basic to engineering.

Functions; Differential and integral calculus for functions of one variable; power series. The mathematical methods are applied in a large number of examples from mechanics, physics and other areas which are basic to engineering.

Introduction to the mathematical foundations of engineering sciences, as far as concerning differential and integral calculus.

The lecture course covers basic notions of mathematical logic, set theory, algebra, elementary number theory, graph theory, and combinatorics.

No description available.

Group theory: groups, representation of groups, unitary and orthogonal groups, Lorentz group. Lie theory: Lie algebras and Lie groups. Representation theory: representation theory of finite groups, representations of Lie algebras and Lie groups, physical applications (eigenvalue problems with symmetry).

Examples of partial differential equations. Linear partial differential equations. Separation of variables. Fourier series, Fourier transform, Laplace transform. Applications to solving commonly encountered linear partial differential equations (Laplace's Equation, Heat Equation, Wave Equation).