Complex Analysis     MATH 305

Homework Assignment #5

Due Thursday, March 17, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to the primary course text by Brown and Churchill. Unless otherwise indicated, all parts of a problem (a), (b), etc. should be completed. You are encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.

Important: Please list the names of any students or faculty who you worked with on the assignment. Also cite any references (website, other texts, etc.) that you may have used while working on this assignment.

Sections 24 and 25 (pp. 77 - 78): #1a, 1b, 2b, 2c, 4c, 7
Hints: cosh y = (ey + e-y)/2 and sinh y = (ey - e-y)/2. It is easy to check that d/dy(cosh y) = sinh y and d/dy(sinh y) = cosh y. A point z0 is called a singular point if the function is not analytic at z0, but is analytic at some point in every neighborhood of z0. For #7, follow the argument of a similar theorem proved in class.

Section 26 (pp. 81 - 83): #1b, 1c, 5
Bonus question: #7. You will need to justify the remarks in the Suggestion given in the text.

Section 29 (pp. 92 - 93): #1, 3, 10
Note: exp(z) = e^z

Sections 30 - 31 (pp. 97 - 98): #1, 2, 4, 8