406-0252-AAL  Mathematics II

SemesterHerbstsemester 2016
DozierendeA. Cannas da Silva
Periodizitätjedes Semester wiederkehrende Veranstaltung
KommentarBelegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.

KurzbeschreibungContinuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations.
LernzielMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Inhalt- Multivariable Differential Calculus:
functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence.

- Multivariable Integral Calculus:
multiple integrals, line and surface integrals, work and flux, Green, Gauss and Stokes theorems, applications.

- Partial Differential Equations:
separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform.
Literatur- Thomas, G. B.: Thomas' Calculus, Parts 2 (Pearson Addison-Wesley).
- Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons).