Analysis III
Lecture: Mo, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam: date to be announced
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
Teacher: Michael Růžička
Assistant: Luciano Sciaraffia
Language: in German
The Analysis III lecture deals with measure and integration theory, with particular emphasis on the Lebesgue measure. These theories are of particular importance for many further lectures in analysis, applied mathematics, stochastics, probability theory and geometry, as well as physics. Main topics are measures and integrals in \(\mathbb R^n\), Lebesgue spaces, convergence theorems, the transformation theorem, surface integrals and Gauss' integral theorem.
Required: Analysis I and II, Linear Algebra I \
Useful: Linear Algebra II
Elective (Option Area) (2HfB21)
Analysis III (BSc21)
Mathematical Concentration (MEd18, MEH21)
Elective in Data (MScData24)
Lecture: Mo, 12-14h, HS II, Albertstr. 23b, Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Sit-in exam 06.08., 14:00-16:00, HS Rundbau, Albertstr. 21
Attention: Change of time and room!
Teacher: Patrick Dondl
Assistant: Luciano Sciaraffia
Language: in English
Linear functional analysis, which is the subject of the lecture, uses concepts of linear algebra such as vector space, linear operator, dual space, scalar product, adjoint map, eigenvalue, spectrum to solve equations in infinite-dimensional function spaces, especially linear differential equations. The algebraic concepts have to be extended by topological concepts such as convergence, completeness and compactness.
This approach was developed at the beginning of the 20th century by Hilbert, among others, and is now part of the methodological foundation of analysis, numerics and mathematical physics, in particular quantum mechanics, and is also indispensable in other mathematical areas.
Linear Algebra I+II, Analysis I–III
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective in Data (MScData24)