Contents

systems of sets, (σ-algebras)

measures,  Lebesgue measure

Caratheodory theorem

measurable functions, approximation theorems

integral w.r.t. a measure, L^p 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