Analysis II Exam Preparation Course: Multivariable Calculus

A preparation course (Prüfungsvorbereitungskurs) taught in German in the spring semester of 2021 for Prof. Tristan Rivière’s Analysis II class, together with the script written to accompany it.

The material works through topology, differential calculus in several dimensions, optimisation, implicit functions and diffeomorphisms, multiple integrals, and the major integral theorems — Green’s, Gauss’s and Stokes’s. The script is deliberately written to build intuition first and formalism second, bringing the theory closer to how students actually reason about it.