Complex variables and applications / James Ward Brown, Ruel V. Churchill

Contents;

1. Complex numbers
sums and products
Basic algebra properties
Further properties
Moduli
E.tc

2. Analytic function
Functions of a complex variable
Mappings
Mappings by exponential functions
Limits
E.tc

3. Elementary functions
The exponential function
The logarithmic function
Branches and derivatives of logarithms
E.tc

4. Integrals
Derivatives of functions
Definite integrals of functions
Contours
E.tc

5. Series
Convergence of sequences
Convergence of series
Taylor series
E.tc

6. Residues and poles
Residues
Cauchy's residue theorem
Using a single residue
E.tc

7. Applications of residues
Evaluation of improper integrals
Example
Improper integrals from Fourier analysis
E.tc

8. Mapping by elementary functions
Linear transformations
The transformation
Mappings
E.tc

9. Conformal mapping
Preservation of angles
Scale factors
local inverses
E.tc

10. Applications of conformal mapping
Steady temperatures
Steady temperatures in a half plane
A related problem
E.tc

11. The Schwarz-Christoffel transformation
Mappin the real axis onto a polygon
Schwarz-Christoffel Transformation
Triangles and rectangles
E.tc

12. Integral formulas of the Poisson type
Poisson integral formula
Dirichlet problem for a disk
E.tc

Includes bibliographical references and index