Externally indexed torrent

If you are the original uploader, contact staff to have it moved to your account

Textbook in PDF format

The Concept of an Analytic Function.
The complex numbers.
Point sets in the complex plane.
Functions of a complex variable.
General Properties of Rational Functions.
The n-th power.
Polynomials.
Rational functions.
Linear Transformations.
Basic properties of linear transformations.
Mapping problems.
Stereographic projection.
Mapping by Rational Functions of Second Order.
The Exponential Function and its Inverse. The General Power.
Definition and basic properties of the exponential function.
Mapping by means of the exponential function. The logarithm.
The general power.
The Trigonometric Functions.
The sine and cosine.
The tangent and the cotangent.
The mappings given by the functions tan z and cot z. Their inverse functions.
The mappings given by the functions sinz and cosz. The functions arc sin z and arc cos z.
Survey of the Riemann surfaces of the elementary functions.
Infinite Series with Complex Terms.
General theorems.
Power series.
Integration in the Complex Domain. Cauchy's Theorem.
Complex line integrals.
The primitive function.
Cauchy's theorem.
The general formulation of Cauchy's theorem.
Cauchy's Integral Formula and its Applications.
Cauchy's formula.
The Taylor expansion of an analytic function.
Consequences of Cauchy's integral formula.
The Laurent expansion.
Isolated singularities of an analytic function.
The inverse of an analytic function.
Mapping by a rational function.
The Residue Theorem and its Applications.
The residue theorem.
Application of the residue theorem to the evaluation of definite integrals.
The partial-fraction expansion of cotxz.
The argument principle.
Applications of the argument principle.
Harmonic Functions.
Preliminary considerations.
Gauss's mean-value theorem. The maximum and minimum principles.
Poisson's formula.
The harmonic measure.
The Dirichlet problem.
Harnack's principle.
Analytic Continuation.
The principle of analytic continuation.
The monodromy theorem.
The inverse of a rational function.
Harmonic continuation. The reflection principle.
Entire Functions.
Infinite products.
Product representation of the function w = sin xz.
The Weierstrass factorization theorem.
Jensen's formula. The growth of entire functions.
Periodic Functions.
Definitions of simply and doubly periodic functions.
Reduction of simply periodic functions to the exponential function.
The basic properties of doubly periodic functions.
The Weierstrass -function.
The Weierstrass - and a-functions.
Representation of doubly periodic functions by means of the a-function.
The differential equation of the function o(z).
Representation of doubly periodic functions as rational functions of p and p'.
Addition theorem for doubly periodic functions.
Determination of a doubly periodic function with prescribed principal parts.
Mapping by a doubly periodic function of order 2.
Elliptic integrals.
The Euler I'-Funcfion.
Definition of the U-function.
Stirling's formula.
The product representation of the U-function.
The Riemann T-Function.
Definition and the Euler product formula.
The Theory of Conformal Mapping.
The Riemann mapping theorem.
Construction of the solution.
Boundary correspondence under conformal mapping.
The connection between conformal mapping and the Dirichlet problem.
The conformal mapping of polygons.
Triangle functions.
The Picard theorem