Lecture Analysis 1/2 for mathematicians and physicists
We use the excellent script of Michael Struwe, see the first link on
scripts. We also provide additional reading material on the script and on coding concepts from the lecture course further down on this page. The course material is aimed ot be self-contained, so the script (together with the exercises and the addendum) contains ALL the relevant material of the course. The coding material in SAGE together with some acquaintance acquired in the exercises should allow to illustrate in a precise manner most of the concepts of the course yourself.
All code from here can also be found in a commented form on the excellent code-webpage Codotron.
- Addendum for chapter 1, 2, 3, 4, 5, 6, 7, 8 and 9.
- Worksheet on convergence in Sage. We mainly use Sage for numerical or symbolic implementations. You can either install Sage locally on your computer, for instructions look at the installation guide, or use sage online here by creating a working account. To run the code, just copy and paste it into the first cell of your newly created worksheet and evaluate it, or upload the worksheet. Sage is based on the general purpose scripting language Python and thus inherits its syntax, so be aware to reproduce the line identations in the code correctly after pasting it into the notebook cell.
- Worksheet on functions in Sage.
- Short Worksheet on algebra of polynomials in Sage.
- Short Worksheet on Riemannian integration and Short Worksheet on Differential Equations in Sage.
- Short Worksheet on implicit functions and their graphical representation in Sage.
- A short calculation concerning conic sections in Sage.
- Sage-Musterlöung für Serie 5, Serie 6, Serie 7, Serie 8, Serie 9, Serie 10, Serie 11, Serie 12 und Serie 13.
- Additional reading material on completeness and incompleteness phenomena can be found in Martin Goldstern's introductory paper on Completeness.