`sommese@nd.edu`

**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.

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

AnalyticContinuation
Analytic continuation by means of differential equation marching methods

A Short Introduction to the Euler Characteristic

Computing analytic one-forms on smooth curves

**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)** **Answers**

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)** **Answers**

Pg.
80: 3.

Pg.
90: 3, 4, 6.

Pg.
101: 1abde, 2acd.

**Homework 4 (Due Tuesday, February 10)** **Answers**

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

**Homework 5 (Due Thursday, February 19)** **Answers**

Pg.
216: 1abce, 3, 5.

Pg.
235: 1bd, 2abehi.

**Homework 6 (Due Thursday, February 26)** **Answers**

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

**Homework 7 (Due Thursday, March 5)** **Answers**

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

**Homework 8 (Due Tuesday, March 24)** **Answers**

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)** **Answers**

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

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

**Homework 10 (Due Thursday, April 16)** **Answers**

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) ****Answers**

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)
****Answers**

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

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