# Higher Mathematics III

Upon completion of the course, the students will have mastered integration in higher dimensions, the basic concepts of vector calculus as well as the integration theorems of Gauß and Stokes. They will be familiar with the approximation of real and complex functions by Fourier series. Furthermore, they will have learned the basic concepts of probability theory and how to apply them in modeling random phenomena.

Topics

Among others, the following topics are covered: Functions of several variables (continued): integration of functions of several variables, improper parameter integrals; integration theorems: curve integrals, divergence theorem in the plane and second fundamental theorem for curve integrals in the plane, transformation theorem for several variables, implicit function theorem, parametrization of surfaces, surface integrals, divergence theorem in space, Stoke's theorem; ordinary differential equations (II): exact differential equations, boundary value problems and eigenvalue problems for second order ordinary differential equations; series of functions, in particular Fourier series: introduction, uniform convergence, trigonometric polynomial and trigonometric series, the fundamental theorem of Fourier series; basic concepts of probability theory: probability space, conditional probability and stochastic independence, law of total probability and Bayes' law, random variable and distribution function, mean value, variance and deviation, Chebyshev's inequality and the weak and strong laws of large numbers, central limit theorem

Prerequisites/Assessment:

Electrical Engineering:

In order to take the course, you must have previously been enrolled in HM1 and HM2. The assessment consists of a 90 minute exam.

Physics:

There are no prerequisites for the module. Admission to the module examination is acquired by written homework. An additional admission requirement for the module examination is regular presence in the exercise classes. The assessment consists of a 90 minute exam.

Literature

1. K. Meyberg, P. Vachenauer: Höhere Mathematik 1, 2, Berlin, 2001
2. K. Burg, H. Haf, R. Wille: Höhere Mathematik für Ingenieure, III (Gewöhnliche Differentialgleichungen), IV (Vektoranalysis, Funktionentheorie), 2002, 1994