Math 656 March 10, 2011
Midterm Examination
This is a closed-book exam; neither notes nor calculators are allowed. Explain your work
Note: points add up to 108. You only need 100 points.
1) (14pts) De
Math 656 March 10, 2011
Midterm Examination Solutions
1) (14pts) Derive the expression for sinh1 z (arcsinh z) using the definition of sinh w in terms of
exponentials, and use it to find all values of
Math 656 FINAL EXAM May 11, 2010
This is a closed-book exam; neither notes nor electronic devices are allowed. Please explain all work.
1) (20pts) Categorize all zeros and singularities of the followi
Math 665 FINAL EXAM May 13, 2010
1) Categorize all zeros and singularities of the following functions, find two lowest-order non-zero terms in the
Laurent or Taylor series of f(z) near the given point
Math 656 * Homework 20
Due Thursday April 21, 2011
dx
1 x
1. Calculate
6
Integrand has 3 simple poles in upper half-plane:
3 i
;i
z1,2,3 (1)1/6 (ei i 2 k )1/6 cfw_ei /6 , i, ei 5 /6
2
Method 1 Cl
Math 656 * Homework 19
Due Monday April 18, 2011
1. Calculate the following improper integrals:
+
(c)
x
0
dx
(assume a > 0, otherwise intergal does not converge)
5
+ a5
Close the contour along the bou
Math 656 * Homework 17
Due Thursday April 7, 2011
1. The proof that a function is uniquely defined by its values on any set in D which has a
limit point in D, follows directly from the proof of the Id