After successful completion of the course, students are able to understand and apply the differential calculation with functions in several variables (approximate functions linearly, set up and apply Taylor series, calculate and classify local extremes, apply Newton methods, apply the implicit function theorem). Furthermore, the students should understand Banach spaces and Hilber spaces with their applications and be able to use the Fourier series as a solution method. Finally, the students should acquire the basic knowledge of complex functions and be able to use the methods of complex analysis.
Scalar and vector fields: Differentiation, extremal values Normed spaces: Banach and Hilbert space, L^2(a,b), Sturm-Liouville problem. Complex analysis.
Regular tutorials with a discussion of assignments.
Hompepage: https://www.asc.tuwien.ac.at/~ewa/AnaII_Uebung_2022/
Written tests: There will be two tests with 3 assignments each. Each assignment is worth 6 points. This means that the maximal number of points is 36. To positively complete the lecture 18 points are required.
The marks are organized as follows: < 18:5, >= 18:4, >= 22:3, >= 27:2, >= 32:1.
An addition test at the beginning of the following term replaces the result of the worse of the two regular tests.
