Analysis IICopyright: © private
The course Analysis II is designed to give students a deeper understanding of the fundamental concepts of analysis, in particular of differential and integral calculus in one dimension and of differential calculus in several variables. They will master more advanced methods and concepts of analysis, learn the process of dealing with mathematical problems, continue the development of their mathematical intuition and practice to turn this intuition into precise reasoning. Central examples let the students retrace the evolution of analysis. Analysis II, as the preceding course, offers students an opportunity to aquire basic knowledge and skills for their entire studies.
Among others, the following topics are covered: differentiability: differentiation rules, mean value theorem, taylor series, de l'Hospital, convex functions, applications; function series: pointwise and uniform convergence; Riemann integral ("Regelintegral"), fundamental theorem of calculus, integration methods, improper integrals; normed vector spaces, elementary topolical terms, Banach fixed-point theorem, Heine-Borel; differential calculus of several variables: partial and total differentiability, Schwarz's theorem, Taylor expansion, local extrema.
In order to successfully take the course, knowledge from the module "Mathematisches Propädeutikum" and from Analysis I is necessary.
Admission to the exam is gained by solving and submitting exercises.
- O. Forster: Analysis I, II, Vieweg
- H. Führ, A. Krieg, S. Walcher: Analysis II, Skript, RWTH Aachen H. Heuser: Lehrbuch der Analysis 1, 2, Teubner
- C. Tretter: Analysis I, II, Birkhäuser