Titlepage
Contents (LaTeX)	Index

Contents (HTML)

• Contents (HTML)
• Contents (LaTeX)
• Linear differential operators
  • Notations
  • Proof
  • Gradient operator
  • Divergence operator
  • LAPLACE operator
  • CAUCHY-RIEMANN operator
  • Diffusion operator
  • Heat operator
  • Wave operator
  • Polynomial solutions
  • Separation of variables
  • Traveling waves
  • Selfsimilar solutions
  • Proof
  • Examples
  • Motivation
  • Transposed differential operator
  • Examples
  • Proof
  • Conclusions
  • Strong derivative
  • Proof
  • Proof
• Fundamental solutions
  • Connection to DIRAC sequences
  • Ordinary differential operators
  • Motivation
  • Proof
  • Proof
  • Proof
  • Further examples
  • Approximation theorem
• Holomorphic functions
  • Proof and Preliminaries
  • Proof
  • Integral representation
  • Beweis
  • Satz
  • Beweis
  • Beweise
  • Argumentfunktion
  • Logarithmus
  • Wurzelfunktionen
  • Arcusfunktionen
  • Motivation
  • Beweis
  • Beispiele
  • Globale Transformationen
  • Beweis
  • Beweise
  • Beweis
  • Bemerkung zu linearen Transformationen
• Isolated Singularities
  • Beweis
  • Beweis
  • Beweis
  • Beispiele
  • Beweis
  • Beweis
  • Integration rationaler Funktionen
  • Integration periodischer Funktionen
  • Integration von Potenzen
• Harmonic functions
  • Examples of harmonic functions
  • Proof
  • Gravitation potential
  • Power series for  n=2 
  • Integral representation
  • Proof
  • Proof
  • GREEN function of a ball
  • Notation
  • Beweis
  • Potenzreihen im  Rⁿ 
  • Beispiel
  • Beweis
  • Folgerungen
  • Beweis
  • Beweis
  • Beweis
  • Beweis
  • Anwendungen des Maximumprinzips
• Heat equation
  • Proof
  • Integral representation
  • Beweis
  • Integraldarstellung auf  R×Rⁿ 
  • Beweis
  • Beweis
• Wave equation
  • Proof
  • Integral representation
  • Beweis
• Appendix 1
• Appendix 2
• Exercises
  • Exercise 1 (Polar coordinates)
  • Exercise 2 (Polar coordinates)
  • Exercise 3 (Harmonic functions)
  • Exercise 4 (Product ansatz)
  • Exercise 5 (Radial symmetric solutions)
  • Exercise 6 (Transposed operator)
  • Exercise 7 (Stream function)
  • Exercise 8 (Differential equation of stream functions)
  • Exercise 9 (Weak derivative)
  • Exercise 10 (Gravitational potential)
  • Exercise 11 (Jump condition)
  • Exercise 12 (Singularity function)
  • Exercise 13 (Fundamental solution)
  • Exercise 14 (Weak solution)
  • Exercise 15 (Fundamental solution)
  • Exercise 16 (Exponential function)
  • Exercise 17 (Conjugate harmonic function)
  • Exercise 18 (Linear transformations in  C )
  • Exercise 19 (Reflexion principle of SCHWARZ)
  • Exercise 20 (Radius of convergence)
  • Exercise 21 (Trigonometric functions)
  • Exercise 22 (Winding number)
  • Exercise 23 (Boundary value problem)
  • Exercise 24 (Antiholomorphic functions)
  • Exercise 25 (External domain)
  • Exercise 26 (Complex   sin -function)
  • Exercise 27 (Conformal transformation)
  • Exercise 28 (Order of a pole)
  • Exercise 29 (LAURENT series)
  • Exercise 30 (Isolated singularities)
  • Exercise 31 (Improper integrals)
  • Exercise 32 (CAUCHY's residue theorem)
  • Exercise 33 (Fundamental solution)
  • Exercise 34 (DIRICHLET integral)
  • Exercise 35 (Biharmonic equation)
  • Exercise 36 (HARNACK inequality)
  • Exercise 37 (Superharmonic functions)
  • Exercise 38 (GREEN function for halve space)
  • Exercise 39 (Power series in  Rⁿ )
  • Exercise 40 (HARNACK inequality)
  • Exercise 41 (Subharmonic functions)
  • Exercise 42 (LIOUVILLE theorem)
  • Exercise 43 (GREEN function for halve space)
• Tables
  • Griechisches Alphabet
  • Inhalt (LaTeX)
  • Partition into lectures
• Index
• Navigation

	Titlepage
Contents (LaTeX)	Index