Exercise 8.  Use formulas (10-26) and (10-27) to find the following:

Exercise 8 (d).  .

Solution 8 (d).

Answer.   .  

Solution.   Using Formulas (10-26) and (10-27), we get  

                          

Then  

                    

We are done.   

Aside.  We can look at some graphs of the mapping  .

                                        .  

We are really done.   

Aside.  We can let Mathematica double check our work.

We are really really done.   

Aside.   We can compare the above answer with the one obtained using formula (5-45) in Section 5.5.  

(5-45)              ,

and the principal value

                       .
                       
                       .

Then

                       

                       

We can let Mathematica do the computations.

This solution is complements of the authors.

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