## Mathematics 300, Introduction to Complex Variables, Section 201. January - April 2017, Mathematics Annex, rm. 1100, TuTh 14:00-15:30

• Instructor : Zinovy Reichstein
Office: 1105 Math Annex
Phone: 822-3929
E-mail: reichst at math.ubc.ca

• 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 I plan to cover, 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, 5.5-5.6, 6.1, 6.3.

• Office Hours (through April 5, 2017) :
Tuesday 10:30-11:30, in 1105 Math Annex
Wednesday 2:30-3:30, in 1105 Math Annex
Thursdays 11-12, in LSK 300B
Fridays 11-12, in LSK 300B
• Homework will be posted on line and collected in class, ususally on a weekly basis. A portion of each assignment will be marked.

Problem set 1, due in class Thursday, January 12
Section 1.1. Problems 10, 20, 30, 32
Section 1.2. Problems 8, 14, 16
Section 1.3 Problems 4, 12

Problem set 2, due in class Thursday, January 19
Section 1.4. Problems 4, 12
Section 1.5. Problems 16, 18
Section 2.1 Problems 4, 6
Section 2.2 Problem 14

Problem set 3, due in class Thursday, January 26
Section 2.3. Problems 4, 10, 14
Section 2.4. Problems 2, 6, 12
Section 2.5 Problems 2, 6, 12, 14

Problem set 4, due in class Tuesday, February 7
Section 3.1 Problems 4, 6, 8, 10, 12, 14, 18, 22

Problem set 5, due in class Thursday, March 2
Section 3.2 Problems 6, 12, 18, 20
Section 3.3 Problems 2, 6, 16
Section 3.5 Problems 2, 4, 9

Problem set 6, due in class Tuesday, March 14
Section 4.1 Problems 4, 8
Section 4.2 Problems 6, 10, 14
Section 4.3 Problems 4, 12
Section 4.4 Problems 10, 12, 16
Section 4.5 Problems 4, 6, 15
Section 4.6 Problems 4, 8, 14

Problem set 7, due in class Tuesday, March 28
Section 5.1 Problems 8, 20
Section 5.2 Problems 4, 14, 15, 16, 18
Section 5.3 Problems 2, 4, 6, 12

Problem set 8, due in class Thursday, April 6
Section 5.5 Problems 4, 5, 6
Section 5.6 Problems 2, 8, 17, 18
Section 6.1 Problems 2, 4, 6, 7
Section 6.3 Problems 1, 2, 3, 11

• Exams There will be two midterms and a final exam. The midterms will be given in class Thursday, February 9 and Thursday, March 16. The final exam is scheduled for Thursday, April 13 at 3:30pm in WESB 100. No books, notes or calculators will be allowed on any of the exams.
• Midterm 1 will cover sections 1.1 - 1.6, 2.1 - 2.5 and 3.1 from the text.

Practice problems for Midterm 1. This is an actual midterm given in Math 300 in 2015 by my colleague Malabika Pramanik.

More practice problems for Midterm 1. This is another actual midterm given in Math 300 in 2015, this one by my colleague Kalle Karu. Solutions posted on connect.

• Midterm 2 will cover sections 3.2, 3.3, 3.5, and 4.1-4.6 from the text. The main focus of Chapter 3 is on exponential, trigonometric, hyperbolic, logarithmic, power and inverse trig. functions. Chapter 4 covers complex integration, culminating in the Cauchy Integral formula and its numerous corollaries. You should also review the material covered prior to Midterm 1 (e.g., the Cauchy-Riemann equations or partial fractions, etc.) This material is foundational and may be needed to solve some of the Midterm 2 problems.
• The final exam will cover the entire course (sections 1.1-1.6, 2.1-2.6, 3.1-3.3, 3.5, 4.1-4.6, 5.1-5.3, 5.5-5.6, 6.1, 6.3), with an emphasis on Chapters 4, 5 and 6.

Other past Math 300 final exams can be found here .

• Review sessions for the final exam:
Monday, April 10, 10:30-12, in Mathematics Annex 1100
Wednesday, April 12, 1:00-2:30, also in Mathematics Annex 1100

• Marking scheme : I will compute the total term mark in two ways,

Total 1 := Homework (20%) + Midterm 1 (20%) + Midterm 2 (20%) + Final exam (40%), and

Total 2 := Homework (20%) + Best midterm (20%) + Final exam (60%),

and use the higher of these two numbers.