Mathematical Analysis III

Lecture notes

The lecture notes will be updated regularly throughout the course. The most recent version is available below.

• The current lecture notes

Exercise sheets

• TD01.pdf
• TD02.pdf
• TD03.pdf
• TD04.pdf
• TD05.pdf

Solutions

The solutions are generated by ChatGPT-6 Astra and are NOT carefully reviewed. Please use these solutions merely as reference, or better as further hints, and devote an honest effort in trying to solve the exercise by yourself.

• TD01-solutions.pdf
• TD02-solutions.pdf
• TD03-solutions.pdf
• TD04-solutions.pdf

Project-oriented problem sets

• Project I. Existence of finite atlas on a manifold
• Project II. Zero sets of smooth functions, part I
• Project III. Zero sets of smooth functions, part II
• Project IV. Existence of many self-diffeomorphisms

References

1. Duistermaat & Kolk, Multidimensional Real Analysis I, II, Cambridge Studies in Advanced Mathematics, Cambridge University Press.
2. Loomis & Sternberg, Advanced Calculus, Revised Edition, Jones and Bartlett Publishers.
3. Loomis, An Introduction to Abstract Harmonic Analysis, D. Van Nostrand Company Inc. Mainly Chapter III.
4. Amann & Escher, Analysis II, III, Birkhäuser.
5. The 2025 lecture notes.