# Complex Analysis

**Course:** Math 362, Spring 2017

**Time & Place:** TR 3:10 – 4:30 pm in HEG 308

**Instructor:** Jim Belk (belk@bard.edu)

**Upcoming Office Hours:**

## Announcements

#### In-Class Final

The in-class portion of the final exam will be this Tuesday, May 22nd in class. Here is a study guide for this portion of the final exam:

Here are some practice problems for the final exam, complete with solutions:

Here are the rules for the final exam:

- • You may bring a standard (8.5" × 11") sheet of paper with notes written on the front and back.
- • You may bring a calculator to the midterm if you like, though a calculator is not required.

#### Takehome Final

Here is the takehome final exam:

The final is due next Tuesday, May 22. Late submissions will not be accepted.

#### Homework 9

The last homework assignment can be found at the following link:

The homework is due this Friday. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### Homework 8

The eighth homework assignment can be found at the following link:

The homework is due this Friday. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions. The following notes might be helpful for completing the homework:

#### Homework 7

The seventh homework assignment can be found at the following link:

The homework is due this Friday. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### Homework 6

The sixth homework assignment can be found at the following link:

The homework is due this Friday. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### Midterm Solutions

Here are the solutions to the in-class midterm:

And here are the solutions to the takehome midterm:

#### Takehome Midterm

Here is the takehome portion of the midterm exam:

This is due next Tuesday, April 10th in class. Late submissions will not be accepted.

#### Homework Solutions

Here are the solutions to the first four homework assignments:

#### In-Class Midterm

The in-class portion of the midterm will be this Thursday, April 5th in class. Here is a study guide for this portion of the midterm:

Here are some practice problems for the midterm, complete with solutions:

Here are the rules for the midterm:

- • You may bring a standard (8.5" × 11") sheet of paper with notes written on the front and back.
- • You may bring a calculator to the midterm if you like, though a calculator is not required.

#### Homework 5

The fifth homework assignment consists of the following problems from the textbook.

- Section 4.42 # 1, 3, 7
- Section 4.45 # 2

The homework is due

**after spring break**. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### No Class Next Week

There will be no class next Tuesday or Thursday. Of course, there will also be no class the following week because of spring break.

#### Homework 4

The fourth homework assignment consists of the following problems from the textbook:

- Section 3.34 # 10
- Section 3.35 # 2
- Section 5.56 # 4
- Section 5.59 # 1, 3

The homework is due this

**Tuesday**. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### Reading

Please read Sections 33–35 of Chapter 3, and Sections 55–57 and 59 of Chapter 5.

#### Homework 1 Solutions

Here are the solutions to the first homework assignment:

#### Homework 3

The third homework assignment consists of the following problems from the textbook:

- Section 2.18 # 5
- Section 2.20 # 8
- Section 2.25 # 1, 2
- Section 3.31 # 1

The homework is due this Friday. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### Reading

Please read Sections 22, 24, and 25 of Chapter 2 (skipping Section 23). Please also start to take a look at Chapter 3, including Sections 29–32.

#### Homework 2

The second homework assignment consists of the following problems from the textbook:

- Section 1.11 # 1
- Section 2.14 # 1, 4, 7

The homework is due this Friday. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### Reading

Please read Sections 12 through 21 of Chapter 2. If you haven't had real analysis, you might want to skip over most of the

*ε*-

*δ* proofs in Sections 15–18.

#### Homework 1

The first homework assignment consists of the following problems from the textbook:

- Section 1.8 # 9, 10, 11
- Section 1.10 # 5

The homework is due this Friday. You should feel free to work together with other students in the class, but everyone must write up their own version of the solutions.

#### Practice Problems

Here are some quick practice problems from the textbook. I recommend that you try to solve these problems, but you do not need to turn in your solutions:

- Section 1.3 # 1
- Section 1.4 # 5, 6
- Section 1.5 # 2
- Section 1.8 # 1
- Section 1.10 # 1, 2, 3

#### Reading

Please read Chapter 1 of the textbook as soon as possible. Here is a PDF version of the first chapter for those who don't yet have the book:

The PDF is password-protected. You can open it using the password announced in class.

#### Welcome!

Welcome to Math 362. I will be using this course webpage to post all announcements and documents, including homework assignments, homework solutions, and takehome exams.

## Office Hours

All office hours are in my office (Albee 315).

## Textbook Information

The textbook is

*Complex Variables and Applications* by James Brown and Ruel Churchill. You will need a copy of the textbook for reading and homework problems, but you do not need to bring it to class. Any edition of the textbook will suffice for reading (it is currently in its 9th edition), but I will be using the

**8th edition** for assigning homework problems. You can buy a paperback copy book from Amazon.com for

around $30, or a hardcover copy for

about $105.

## Course Policies

#### Introduction

This course will cover the basic theory of functions of one complex variable. Topics will include the geometry of complex numbers, holomorphic and harmonic functions, Cauchy’s theorem and its consequences, Taylor and Laurent series, singularities, residues, elliptic functions and/or other topics as time permits.

#### Prerequisites

The prerequisites are a familiarity with partial derivatives and with Taylor series. Any one of Math 241, Math 245, or Physics 221 should be sufficient.

#### Homework

There will be a written homework assignment due each Friday. You are encouraged to work with other students in solving the homework problems, but you should write your own solutions, and you must acknowledge anyone that you work with. Your solutions should be written clearly and in complete sentences, with enough detail that another student in the class would be able to follow your reasoning. You are encouraged to write your homework solutions in LaTeX, but this is not required.

#### Exams and Grading

The grade will be based on the weekly homework and two exams:

Homework | 50% |

Midterm Exam | 25% |

Final Exam | 25% |

The exams will most likely have both a takehome component and an in-class component.