# ACMS 40485, Spring 2015

## Office Hours: After class and by appointment.

Exam Schedule

Exam 1: Take home test will be given out in class on Tuesday Feb. 10 and will be due Thursday, Feb. 12 at start of class. Test and Answers.

Exam 2: Take home test: Handed out Thursday, March 26 at end of class and

due Tuesday, March 31 at start of class. Test and Answers.

Final: Take home test.  Will be sent out on Monday, may 4 and will be due by Friday, May 8, 12:30PM.

# Handouts

RungeFunction Runge’s function showing a potential bad property of inter-polation polynomials

AnalyticContinuation Analytic continuation by means of differential equation marching methods

# Homework

Homework 1

Make sure you understand the review material! (Manipulating complex numbers, basic residue integration, convergence of power series, Laurent series, exponential, log, Euler’s relation, ...)

Homework 2 (Due Tuesday, February 3)

Pg. 44: 1bc, 2bd, 3, 5.

Pg. 59: 1, 2, 3, 6c.

Pg. 79: 1, 8.

Pg. 90: 2.

Homework 3 (Due Thursday, February 5)

Pg. 80: 3.

Pg. 90: 3, 4, 6.

Pg. 101: 1abde, 2acd.

Homework 4 (Due Tuesday, February 10)

Pg. 135: 1, 2, 3ac, 4abce.

Homework 5 (Due Thursday, February 19)

Pg. 216: 1abce, 3, 5.

Pg. 235: 1bd, 2abehi.

Homework 6 (Due Thursday, February 26)

Pg. 235: 3, 5, 6, 7, 8a, 9.

Homework 7 (Due Thursday, March 5)

Pg. 253: 1, 2, 4, 7, 11, 13.

Homework 8 (Due Tuesday, March 24)

Pg. 265: 2, 5.

Pg. 282: 11bc, 12, 13ab, 16, 18.

Pg. 316: 3.

Show the cross-ratio is left unchanged by a linear fractional transformation.

Homework 9 (Due Thursday, April 9)

Pg. 421: 1a, 2, 3, 4.

Pg. 438: 1, 2, 3, 7.

Homework 10 (Due Thursday, April 16)

Pg. 438: 4, 5.

Pg. 447: 1.

What is the Euler characteristic of the complex plane minus the disc consisting of all points of absolute value strictly less than 1?

What is the Euler characteristic of the complex plane minus the disc consisting of all points of absolute value less than or equal to 1?

Homework 11 (Due Thursday, April 23)

1) Attend the two Trefethen talks.

2) Homogenize

3) Dehomogenize    with respect to the hyperplane z = 0.

4) Find the singular points of

5) Find the singular points of V(

What is the Euler characteristic of the Riemann sphere minus 10 closed disks?

Homework 12 (Due Tuesday, April 28)

What are the analytic one-forms on V(x^4+y^4+z^4)?