Dictionary of Conformal Mapping
Part I

Common Mappings

Example 1.  The conformal mapping in polar coordinates.  Example 2.  The conformal mapping in rectangular coordinates.  Example 3.  The conformal mapping in polar coordinates.  Example 4.  The conformal mapping in rectangular coordinates.  Example 5.  The conformal mapping .  The image of the half-plane is the unit disk .  Example 6.   The conformal mapping .  The image of the right half-plane is the unit disk   Example 7.  The conformal mapping .  The image of  the unit disk is the left half-plane .  Example 8.  The conformal mapping .  The image of the upper half-plane is the upper half-plane .  Example 9.  The conformal mapping .  The image of the upper half-plane is the upper half-plane .  Example 10.  The conformal mapping .  The image of the disk is the right half plane .  Example 11.  The conformal mapping .  The image of the upper half-plane is the exterior of the circle .  Example 12.  The conformal mapping .

The image of the region inside the unit disk and outside the circle is the annulus .

For this mapping and and .  Example 13.  The conformal mapping .

The image of the region that lies outside the the unit circle and outside the circle is the annulus .

For this mapping and and .  Example 14.  The conformal mapping .

The image of the region that lies in the left half plane and outside the the unit circle is the annulus .

For this mapping and and .  Details 14.

Example 15.  The conformal mapping ,  where , , and , ,   Details 15.

1. Conformal Mapping Dictionary - Part I
2. Conformal Mapping Dictionary - Part II
3. Conformal Mapping Dictionary - Part III
4. Conformal Mapping Dictionary - Part IV
5. Conformal Mapping Dictionary - Part V

Chapter 2. Complex Functions

6. Complex Functions and Linear Mappings
7. The Mappings and 8. Complex Limits and Continuity
9. Branches of Complex Functions
10. The Reciprocal Transformation Chapter 5. Elementary Functions

11. The Complex Exponential Function
12. The Complex Logarithm Function
13. Complex Exponents and Powers
14. Trigonometric and Hyperbolic Functions
15. Inverse Trigonometric and Hyperbolic Functions

Chapter 10. Conformal Mapping

16. Basic Properties of Conformal Mappings
17. Mobius Transformations - Bilinear Transformations
18. Mappings Involving Elementary Functions
19. Mappings by Trigonometric Functions

Chapter 11. Applications of Harmonic Functions

20. Preliminaries
21. Invariance of Laplace's Equation and the Dirichlet Problem
22. Poisson's Integral Formula for the Upper Half Plane
23. Two-Dimensional Mathematical Models
24. Steady State Temperatures
25. Two-Dimensional Electrostatics
26. Two-Dimensional Fluid Flow
27. The Joukowski Airfoil
28. The Schwarz-Christoffel Transformation
29. Image of a Fluid Flow
30. Sources and Sinks

Return to the Complex Analysis Project

(c) 2008 John H. Mathews, Russell W. Howell