Appendix 2

Titlepage

Tables

Index

Exercises
[chap:Aufgaben]

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Aufgabenzettel 1

Exercise 1 (Polar coordinates)

Exercise 2 (Polar coordinates)

Exercise 3 (Harmonic functions)

Exercise 4 (Product ansatz)

Aufgabenzettel 2

Exercise 5 (Radial symmetric solutions)

Exercise 6 (Transposed operator)

Exercise 7 (Stream function)

Exercise 8 (Differential equation of stream functions)

Aufgabenzettel 3

Exercise 9 (Weak derivative)

Exercise 10 (Gravitational potential)

Exercise 11 (Jump condition)

Aufgabenzettel 4

Exercise 12 (Singularity function)

Exercise 13 (Fundamental solution)

Exercise 14 (Weak solution)

Exercise 15 (Fundamental solution)

Aufgabenzettel 5

Exercise 16 (Exponential function)

Exercise 17 (Conjugate harmonic function)

Exercise 18 (Linear transformations in C )

Exercise 19 (Reflexion principle of SCHWARZ)

Aufgabenzettel 6

Exercise 20 (Radius of convergence)

Exercise 21 (Trigonometric functions)

Exercise 22 (Winding number)

Exercise 23 (Boundary value problem)

Aufgabenzettel 7

Exercise 24 (Antiholomorphic functions)

Exercise 25 (External domain)

Exercise 26 (Complex sin -function)

Exercise 27 (Conformal transformation)

Aufgabenzettel 8

Exercise 28 (Order of a pole)

Exercise 29 (LAURENT series)

Exercise 30 (Isolated singularities)

Exercise 31 (Improper integrals)

Aufgabenzettel 9

Exercise 32 (CAUCHY's residue theorem)

Exercise 33 (Fundamental solution)

Exercise 34 (DIRICHLET integral)

Exercise 35 (Biharmonic equation)

Aufgabenzettel 10

Exercise 36 (HARNACK inequality)

Exercise 37 (Superharmonic functions)

Exercise 38 (GREEN function for halve space)

Exercise 39 (Power series in Rⁿ )

Aufgabenzettel 11

Exercise 40 (HARNACK inequality)

Exercise 41 (Subharmonic functions)

Exercise 42 (LIOUVILLE theorem)

Exercise 43 (GREEN function for halve space)

Version 1.5
H.W. Alt - 02.01.2007

Appendix 2

Titlepage

Tables

Index

Exercises [chap:Aufgaben]

Exercises
[chap:Aufgaben]