# Higher Mathematics I

The students of Electrical Engineering and Physics develop the requisite basic mathematical knowledge and skills for further studies. After completion of the course, the students are familiar with the mathematical concept of convergence. They are able to recognize convergence of sequences, series and functions and to calculate their limits. They understand the properties of real functions, rational functions, polynomials, sequences and series and their relevance in depicting nature or technical systems. They will also master the basic methods of linear algebra, in particular they will be able to solve systems of linear equations and to apply this to concrete problems. Finally, they will learn the basic terms of differential calculus, the method of taking a derivative and the application to curve sketching and optimizing problems.

Topics

Among others, the followinig topics are covered: addition and multiplication of real numbers, axioms of order, axiom of completeness, induction, absolute values, elementary inequalities; real functions, limit, continuity: functions, polynomials and rational numbers, sequences of numbers, limits of functions, properties of continuous functions, infinite series, power series; the vector space $\mathbb{R}^n$, geometry in $\mathbb{R}^n$, geometric properties of complex numbers; linear algebra: vector spaces, linear mappings, linear equations systems, determinants, eigenvalues and eigenvectors, symmetric matrices, quadratic forms, principal axis theorem; introduction to differential calculus: derivative and differential, calculation of derivatives, mean value theorem

Prerequisites/Assessment

Electrical Engineering:

The tutorial classes supplement the independent studies and are strongly recommended. The workload for this kind of activity is counted as self-study for the corresponding course. 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 an exam of an oral exam (graded); type and duration of the exam will be announced at the beginning of the course.

Literature

1. K.Meyberg, P. Vachenauer: Höhere Mathematik 1,2, Berlin, 2001
2. K.Burg, H.Haf, R. Wille: Höhere Mathematik für Ingenieure I (Analysis) und II (Lineare Algebra), 2006,2003
3. G. Bärwolff: Höhere Mathematik für Naturwissenschaftler und Ingenieure, Heidelberg, 2006