Example 16.  The conformal mapping  .  
The image of the horizontal strip    is the punctured plane  .  

Details 16.

Example 17.  The conformal mapping  .
The image of the  plane    is the horizontal strip  .  

Details 17.

Example 18.  The conformal mapping  .
The image of the vertical strip    is the w-plane slit along the two rays and .

Details 18.

Example 19.  The conformal mapping  .  
The image of the vertical strip    is the unit disk  .

Details 19.

Example 20.  The conformal mapping  .
The image of the upper half-plane    is the semi-infinite strip  .

Details 20.

Example 21.  The conformal mapping  .  
The image of the upper half-plane    is the semi-infinite strip  .

Details 21.

Example 22.  The conformal mapping  .  
The image of the upper half-plane    is the horizontal strip  ,  
and  , , and and  , , and .  

 Details 22.

 Example 23.  The conformal mapping    .  
The image of the portion of the unit disk    that lies in the upper half-plane   is the upper half-plane  .  Furthermore, the upper semicircular portion of the boundary is mapped onto the line negative u-axis, and the segment    is mapped onto the positive u-axis.

Details 23.

Example 24.  The conformal mapping    .   
The image of the upper half-plane    is the upper-half plane    slit along the vertical segment  .  

Details 24.

Example 25.  The conformal mapping  .   
The image of the upper half-plane    is the portion of the upper half-plane    that lies outside the unit circle  .  

Details 25.

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