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# Introduction to Complex Variables (MATH 300 202)

This page contains information on section 202. For information on section 201, see here.

## Time and location

• Mondays, Wednesdays, Fridays 13:00-14:00 (from January 4 till April 6)
• Math Annex 1100

## Textbook

E.B. Saff, A.D. Snider, Fundamentals of Complex Analysis with Applications to Engineering, Science and Mathematics, third edition.

## Course description

We will begin by discussing the complex numbers and functions of a complex variable, then proceed to develop differential and integral calculus in this setting. The resulting theory is very beautiful and in many ways quite different from the "usual" calculus for functions of either one or several real variables. Complex analysis has many applications to science, engineering and other areas of mathematics. We will go over (most of) chapters 1-6 in the text, covering the following topics:
• complex numbers,
• complex derivatives and analytic functions,
• elementary functions,
• contour integration,
• Cauchy's theorem,
• Cauchy's Integral Formula,
• Taylor series,
• Laurent series, singularities and residues.
The specific sections to be covered, subject to minor changes along the way, are 1.1-1.6, 2.1-2.6, 3.1-3.3, 3.5, 4.1-4.6, 5.1-5.3, 5.4, 5.5-5.6, 6.1, 6.2, 6.3.

The prerequisites can be found here.

## Office hours

The term grade will be calculated in two ways and the higher grade will be used.
• Homework (20%)
• Every week, due on Wednesday, at the beginning of the class.
• The first assignment is due on Wednesday, January 11.
• Your two lowest assignment grades will be disregarded in the final grade.
• Quizzes (40% or 20%)
• Every other week on Friday
• The first quiz is on Friday, January 20.
• There will be 5 quizzes in total.
• Your final quiz grade will be the average of your 4 best quizzes.
• Final exam (40% or 60%)

## Homework

There will be homework assignments every week. The due is on Wednesday, at the beginning of the class. A portion of the assignments will be marked.
• Assignment 1 (due Wednesday, January 11)
• Section 1.1: 8, 17, 20(b, c), 32
• Section 1.2: 5, 7(c, f, h), 16, 20
• Section 1.3: 3, 7(f, g), 12, 13
Note: Those of you who registered for the course on Tuesday 10 or later may still hand-in their assignments on Friday 13.
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 2 (due Wednesday, January 18)
• Section 1.4: 2(c), 4(c), 8, 11, 16, 18(a,c)
• Section 1.5: 4(b), 5(b,c,d), 6, 9, 10, 16
• Section 1.6: 2-8 for (a,b,d)
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 3 (due Wednesday, January 25)

• Assignment 4 (due Wednesday, February 1)
• Section 2.3: 3, 4(b) [use the definition directly], 7(c), 13, 14
• Section 2.4: 2, 4, 6, 7, 12, 14
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 5 (due Wednesday, February 8)

• Assignment 6 (due Wednesday, February 15)
• You may skip questions 3 and 6 of section 3.3 for now. For question 13 of section 3.2, use the definition of complex sinh and cosh on page 114.
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 7 (due Wednesday, March 1)
• Enjoy the break!
• A visualization of the exponential map for problem II.
• A visualization of the logarithm map for problem III.
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 8 (due Wednesday, March 8 Friday, March 10)
• Deadline extended to March 10.
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 9 (due Wednesday, March 15)
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 10 (due Wednesday, March 22)
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 11 (due Wednesday, March 29)
• Section 5.1: 1(b, c, f), 6, 10, 16
• Section 5.2: 2, 4, 5(b, e, g), 11(b), 13, 15, 18(a)
• Section 5.3: 7, 8, 12, 18 (compare with Prob. 2.3.14, assignment 4)
• Section 5.5: 1(b, c), 5, 6
• Solutions are posted on Connect.
• You can collect your papers from the MLC.

• Assignment 12 (not to be turned in)

## Quizzes

There will be a quiz every other week on Friday.
• Quiz 1 (Friday, January 20)
• Sections 1.1-1.6
• Solutions
• You can collect your papers from the MLC.

• Quiz 2 (Friday, February 3)
• Up to and including section 2.5 (as far as it is covered before Friday)
• Solutions
• You can collect your papers from the MLC.

• Quiz 3 (Friday, February 17 March 3)
• Up to and including section 3.5
• Solutions
• You can collect your papers from the MLC.

• Quiz 4 (Friday, March 10 March 17)
• Chapter 4 and before
• Solutions
• You can collect your papers from the MLC.

• Quiz 5 (Friday, March 24 March 31)
• Chapter 5 (as far as it is covered before Friday) and before
• Solutions
• You can collect your papers from the MLC.

## Final exam

• Time and location
• The final exam will cover the entire course (see the syllabus on top of the page) with an emphasis on chapters 4, 5, and 6.
• No books, notes or calculators will be allowed on the exam.
• Practice final exam (actual final exam from 2015) with solutions
• Other past exams
• Review sessions
• Monday, April 10, 10:30-12:00, Math Annex 1100
• Wednesday, April 12, 13:00-14:30, Math Annex 1100
• The grades are submitted. (new)