# course: Mathematics 3

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

## dates in winter term

• start: Tuesday the 08.10.2019
• lecture Tuesdays: from 08:00 to 10.00 o'clock in HZO 80
• tutorial (alternativ) Wednesdays: from 08:15 to 10.00 o'clock in IA 1/109
• tutorial (alternativ) Wednesdays: from 08:15 to 10.00 o'clock in IA 1/71
• tutorial (alternativ) Wednesdays: from 10:15 to 12.00 o'clock in IA 1/109
• tutorial (alternativ) Wednesdays: from 10:15 to 12.00 o'clock in IA 1/71

## Exam

##### All statements pertaining to examination modalities (for the summer/winter term of 2020) are given with reservations. Changes due to new requirements from the university will be announced as soon as possible.
 Form of exam: written Registration for exam: FlexNow Date: 05.08.2020 Begin: 14:30 Duration: 120min Room : ID 03/445

## 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"