Dictionary of Conformal Mapping
Part IV

Example 38.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,
here  , ,   and  , , ,
and the angles are  .

Details 38.

Example 39.  The conformal mapping  ,
here  , , ,   and  , , , .

Details 39.

Example 40.  The conformal mapping  .

Example 41.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,
here  , ,   and  , , ,
and the angles are  .
Also  .

Details 41.

Example 42.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,
here  , ,  and  , ,  and the angles are  ,
(additionally for we would have ).
Also  ,  also  .

Details 42.

Example 43.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,
here  , , ,   and  , , , ,
and the angles are  .
Also  .

Details 43.

Example 44.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,
here , ,  and  , ,  and the angles are  ,
(additionally for we would have   and  , ).
Also  .

Details 44.

Example 45.  The conformal mapping  ,
here  , ,   and  , , .

Details 45.

Example 46.  The conformal mapping  ,
here  , ,   and  , , .

Details 46.

Example 47.  The conformal mapping  .
It can be constructed via the Schwarz-Christoffel integral  ,
here  , ,   and  , , ,  and the angles are  .
Also  .

Details 47.

Remark.  When we compare Examples 31, 41, 45, 46, 47 we see that there are many conformal mappings whose range is a right angle channel. Many of the other examples can also be done in several alternate ways.

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
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