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

requirements

none

recommended knowledge

Content of lectures "Mathematik 1-2"