# course: Mathematics 3

number:
150114
teaching methods:
lecture with tutorials
media:
black board and chalk
responsible person:
Dr. rer. nat. Annett Püttmann
lecturer:
Dr. rer. nat. Annett Püttmann (Mathematik)
language:
german
HWS:
4
CP:
see examination rules
offered in:
winter term

## dates in winter term

• start: Tuesday the 27.10.2020
• lecture Tuesdays: from 08:00 to 10.00 o'clock in Online
• tutorial (alternativ) Wednesdays: from 08:15 to 10.00 o'clock in Online
• tutorial (alternativ) Wednesdays: from 08:15 to 10.00 o'clock in Online
• tutorial (alternativ) Wednesdays: from 10:15 to 12.00 o'clock in Online
• tutorial (alternativ) Wednesdays: from 10:15 to 12.00 o'clock in Online

## Exams

##### Die Angaben zu den Prüfungsmodalitäten (im WiSe 2020/2021 | SoSe 2021) erfolgen vorbehaltlich der aktuellen Situation. Notwendige Änderungen aufgrund universitärer Vorgaben werden zeitnah bekanntgegeben.
 Form of exam: written Registration for exam: FlexNow Date: 26.05.2021 Begin: 10:30 Duration: 120min description of exam: verschobener Prüfungstermin WiSe 20/21 Rooms : HZO 10,  HZO 20 Individual appointments of students to each exam location will be issued by the responsible chair.
##### Die Angaben zu den Prüfungsmodalitäten (im WiSe 2020/2021 | SoSe 2021) erfolgen vorbehaltlich der aktuellen Situation. Notwendige Änderungen aufgrund universitärer Vorgaben werden zeitnah bekanntgegeben.
 Form of exam: written Registration for exam: FlexNow Date: 01.09.2021 Begin: 12:30 Duration: 120min Rooms : HIA ,  HIB Individual appointments of students to each exam location will be issued by the responsible chair.

## goals

Proficiency in applying the following mathematical methods to solve

• odinary differential equations
• partial differential equations

## content

1. ordinary differential equations
• initial value problems, Picard-Lindelöf theorem
• separation of variables, 1st order linear ODE, Bernoulli ODE, Riccati ODE, exact ODE, integrating factor
• linear ODE of order n
• poperties
• Wronski determinant, variation of constants
• reduction of order
• Euler ODE
• (generalized) power series solution
• boundary value problems
• systems of ODEs
2. partial differential equations
• Quasilinear partial differential equations
• method of characteristics
• Linear partial differential equations of second order
• definition and classification, normal form
• wave equation - method of d'Alembert
• wave equation and heat equation - Fourier method
• Poisson's equation and Dirichlet problem
• application of Laplace transform and Fourier transform to PDEs

none

## recommended knowledge

Content of lectures "Mathematik 1-2"

## miscellaneous

Diese Veranstaltung wird im Wintersemester 2020/2021 im Online-Format via Zoom angeboten. Die Koordination der Kursaktivitäten erfolgt über Moodle. Der Kurs wird ab dem 20.10.2020 verfügbar sein.

Kursname: "Mathematik III für ET/IT" (150114-WiSe20/21) Schlüssel: Dirichlet