Contents
systems of sets, (σ-algebras)
measures, Lebesgue measure
Caratheodory theorem
measurable functions, approximation theorems
integral w.r.t. a measure, Lp spaces, convergence theorems, transformation theorem
product measures, Fubini's theorem,
Contact time
2 SWS lecture
1 SWS exercise class
Substantive prerequisites
lecture "Fundamentals of Mathematics I + II"
External resources
KIS entry: Lecture Measure and Integration Theory
KIS entry: Exercise class Maß- und Integrationstheorie
OLAT Course: RPTU Maß- und Integrationstheorie SS 2024
Contents
generators, resolvents
Hille-Yosida theorem, Lumer-Phillips theorem
contraction semigroups, analytic semigroups, operator groups
approximations, perturbations
applications to partial differential equation (including heat equation, wave equation, Schrödinger equation)
Contact time
4 SWS lecture
2 SWS exercise class
Substantive prerequisites
lecture "Functional Analysis"
External resources
KIS entry: Lecture Operator Semigroups and Applications to Partial Differential Equations
KIS entry: Exercise class Operator Semigroups and Applications to Partial Differential Equations
OLAT Course: RPTU Operator Semigroups and Applications to PDE Summer 2024
Contents
complex numbers
vectors
vector functions
functions of several variables
partial derivatives
the total derivative
maxima and minima for functions of several variables
the Riemann Integral
the indefinite integral
vector fields
curve integral
Contact time
3 SWS lecture
1 SWS exercise class
Substantive prerequisites
To refresh the knowledge of school mathematics, it is recommended to attend the mathematics preparatory course (Vorkurs) before starting with this course.
Lecture frequency
This lecture is offered each semester.
External resources
KIS entry: Lecture Mathematik 1 für Chemiker*innen
KIS entry: Exercise class Mathematik 1 für Chemiker*innen
OLAT Course: RPTU Mathematik 1 für Chemiker*innen SS 2024
Contents
Linear Algebra
multiple integration
transformation theorem
power series
ordinary differential equations
linear differential equation systems
partial differential equations.
Contact time
3 SWS lecture
1 SWS exercise class
Substantive prerequisites
lecture "Mathematics 1 for Students of Chemistry" from the Bachelor's degree programme in Chemistry
Lecture frequency
This lecture is offered each semester.
External resources
KIS entry: Lecture Mathematik 2 für Chemiker*innen
KIS entry: Exercise class Mathematik 2 für Chemiker*innen
OLAT Course: RPTU Mathematik 2 für Chemiker*innen SS 2024
Contents
multiple integration
transformation theorem
surface integrals
the theorem of Stokes and Gauss
power series
function series
ordinary differential equations
systems of linear differential equations
partial differential equations
Contact time
2 SWS lecture
1 SWS exercise class
Substantive prerequisites
lecture "Mathematics for Biophysics 1"
Lecture frequency
This lecture is offered each summer term.
External resources
KIS entry: Lecture Mathematik 2 für Biophysiker*innen
KIS entry: Exercise class Mathematik 2 für Biophysiker*innen
OLAT Course: RPTU Mathematik 2 für Biophysiker*innen SS 2024
Archive of Lecture Notes
- Functional Analysis, summer term 2019Download 654 KB
- Einführung in die Funktionalanalysis, Wintersemester 2018/19Download 549 KB
- Operator semigroups, winter term 2016/2017Download 901 KB
- Sobolev spaces, winter term 2018/19Download 614 KB
- White Noise Analysis, summer term 2017Download 807 KB