Analysis 3

Intergralsätze, Lebesgue-Integral und Anwendungen

Lecture Notes

This introductory text is based on lectures within a three-semester course on "Real Analysis", given by the author at Heidelberg University. The present third part treats the Riemann integral over lines and surfaces and the integral formulas of Gauß and Stokes. Further, the Lebesgue integral and the corresponding function spaces are introduced. Then, applications are discussed in the theory of Fourier integrals, for basic problems in the calculus of variations and in the theory of partial differential equations. Contents and
presentation are particularly oriented towards the needs of applications in the theory of differential equations, in Mathematical Physics and in Numerical Analysis. The understanding of the contents requires besides the material of the preceding parts of this series, "Analysis 1 (Differential- und Integralrechnung für Funktionen einer reellen Veränderlichen)" and "Analysis 2 (Differential- und Integralrechnung für Funktionen mehrerer reeller Veränderlichen)", only some basic prior knowledge of Linear Algebra. For supporting
self-study each chapter contains exercises with solutions collected in the appendix.