Example 48.  The conformal mapping  ,  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .  Also  .

Details 48.

Example 49.  The conformal mapping    for  .  

                    The conformal mapping  .

Details 49.

Example 50.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , , ,   and  , , , ,  and the angles are  , , , .  

Details 50.

Example 51.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , , ,   and  , , , ,  and the angles are  , , , .  

Details 51.

Example 52.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .  Also  .

Details 52.

Example 53.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  .

Details 53.

Example 54.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .  Also  .

Details 54.

Example 55.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .

Details 55.

Example 56.  The conformal mapping
.   
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .

Details 56.

 Example 57.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  , here  , ,  , ,  and the angles are  ,   (if we include then ).

Details 57.

Example 58.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,  , ,  and the angles are  ,
(if we include then ).       

Details 58.

Example 59.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .

Details 59.

Example 60.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .  

Details 60.

Example 61.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  , , .

Details 61.

Example 62.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  ,   and  , ,  and the angles are  , ,  (if we include then ).

Details 62.

Example 63.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  ,   and  , ,  and the angles are  , ,  (if we include then ).

Details 63.

Example 64.  The conformal mapping  .  
It can be constructed via the Schwarz-Christoffel integral  ,  here  , ,   and  , , ,  and the angles are  ,, .

Details 64.

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

    Chapter 11. Applications of Harmonic Functions

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

Return to the Complex Analysis Project

 

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