Analysis III

  A blackboard displaying the formula for integration in spherical coordinates Copyright: © private


The course Analysis III is intended to give students a deepened understanding of multivariable differential calculus which they can apply to the investigation of submanifolds. Students are introduced to integration in higher dimensions and presented with examples of making intuitive geometric terms computable by expressing them with the means of analysis. This course concludes the set of introductory lectures in analysis and provides a foundation for more specialized lectures.


Among others, the following topics are covered: inverse mappings and implicit mappings; extrema under constraints; curves and line integrals; integrals with parameters; basic concepts of integration in \(\mathbb{R}^n\); submanifolds of \(\mathbb{R}^n\), subspace topology, tangential space, charts and metric tensors; integration on submanifolds, integration theorems.


In order to successfully take the course, either Analysis I or Analysis II must have been passed already.

The examination can be written or oral; admission to the exam is gained by solving and submitting exercises.


  1. J. Elstrodt: Maß- und Integrationstheorie, Springer
  2. O. Forster: Analysis 3, Vieweg
  3. H. Führ, A. Krieg, S. Walcher: Analysis III, Skript, RWTH Aachen