# Higher Mathematics II

After completion of the course, the students can use elementary and advanced methods to solve definite and indefinite integrals.
They are familiar with the approximation of real functions by taylor series and the concept of well-posedness for ordinary differential equations. They know methods for solving linear and nonlinear differential equations as well as methods for solving systems of differential equations. Finally, they are proficient in differential calculus of several variables as well as its application to multidimensional optimization.

Topics

Among others, the following topics are covered: The definite integral; definition and basic properties, conditions for integrability, integral inequalities and mean value theorems; Fundamental theorems of calculus. Applications: first and second fundamental theorem, partial integration and substitution, the indefinite integral, integration of rational functions, Taylor series and applications, introduction to ordinary differential equations, an applications to systems of linear equations, further special differential equations of first order, ordinary differential equations of second order (I), improper integrals; funcions in several variables: continuity, differentiaton, curves in the plane and in space, extension of differential calculus and its applications.

Prerequisites/Assessment:

Electrical Engineering:

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

Physics:

There are no prerequisites for the module. Admission to the module eyamination is acquired by written homework. An additional admission requirement for the module examination is regular presence in the exercise classes. The assissment 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), 2006,2003G.
3. Bärwolff: Höhere Mathematik für Naturwissenschaftler und Ingenieure, Heidelberg, 2006