Course Contents
Part I: sigma-algebras, measures, outer measures and Carathéodory’s theorem, Lebesgue measure; measurable functions, Lebesgue integral, convergence theorems, Lp-spaces, Fubini’s theorem in R^n change of variables formula.
Part II: Convolution integrals, Fouriertransform; Submanifolds, surface measures, divergence theorem, Green’s theorem, Stokes’ theorem.
Literature
Part I: sigma-algebras, measures, outer measures and Carathéodory’s theorem, Lebesgue measure; measurable functions, Lebesgue integral, convergence theorems, Lp-spaces, Fubini’s theorem in R^n change of variables formula.
Part II: Convolution integrals, Fouriertransform; Submanifolds, surface measures, divergence theorem, Green’s theorem, Stokes’ theorem.
Preconditions
recommended: Analysis and Linear Algebra
Online Offerings
moodle
Part I: sigma-algebras, measures, outer measures and Carathéodory’s theorem, Lebesgue measure; measurable functions, Lebesgue integral, convergence theorems, Lp-spaces, Fubini’s theorem in R^n change of variables formula.
Part II: Convolution integrals, Fouriertransform; Submanifolds, surface measures, divergence theorem, Green’s theorem, Stokes’ theorem.
Literature
Part I: sigma-algebras, measures, outer measures and Carathéodory’s theorem, Lebesgue measure; measurable functions, Lebesgue integral, convergence theorems, Lp-spaces, Fubini’s theorem in R^n change of variables formula.
Part II: Convolution integrals, Fouriertransform; Submanifolds, surface measures, divergence theorem, Green’s theorem, Stokes’ theorem.
Preconditions
recommended: Analysis and Linear Algebra
Online Offerings
moodle
- Lehrende: Tim Binz
- Lehrende: Christian Stinner
Semester: ST 2023