Example 1.  The conformal mapping    in polar coordinates.

Details 1.

Example 2.  The conformal mapping    in rectangular coordinates.

Details 2.

Example 3.  The conformal mapping    in polar coordinates.

Details 3.

Example 4.  The conformal mapping    in rectangular coordinates.

Details 4.

Example 5.  The conformal mapping  .  The image of the half-plane    is the unit disk  .

Details 5.

Example 6.   The conformal mapping  .  The image of the right half-plane    is the unit disk  .     

Details 6.

Example 7.  The conformal mapping  .  The image of  the unit disk    is the left half-plane      

Details 7.

Example 8.  The conformal mapping  .  The image of the upper half-plane    is the upper half-plane  .    

Details 8.

Example 9.  The conformal mapping  .  The image of the upper half-plane    is the upper half-plane  .

Details 9.

Example 10.  The conformal mapping  .  The image of the disk    is the right half plane  .    

Details 10.

Example 11.  The conformal mapping  .  The image of the upper half-plane    is the exterior of the circle  .

Details 11.

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  .

Details 12.

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  .

Details 13.

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

1. Complex Functions and Linear Mappings
2. The Mappings and
3. Complex Limits and Continuity
4. Branches of Complex Functions
5. The Reciprocal Transformation

   Chapter 5. Elementary Functions

6. The Complex Exponential Function
7. The Complex Logarithm Function
8. Complex Exponents and Powers
9. Trigonometric and Hyperbolic Functions
10. Inverse Trigonometric and Hyperbolic Functions

    Chapter 10. Conformal Mapping

11. Basic Properties of Conformal Mappings
12. Mobius Transformations - Bilinear Transformations
13. Mappings Involving Elementary Functions
14. Mappings by Trigonometric Functions
15. Conformal Mapping Dictionary - Part I
16. Conformal Mapping Dictionary - Part II

    Chapter 11. Applications of Harmonic Functions

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

Return to the Complex Analysis Project

 

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