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

  • 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: 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

    Answer key to Problem Set 1

    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

    Answer key to Problem Set 2

    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

    Answer key to Problem Set 3

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

    Answer key to Problem Set 4

    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

    Answer key to Problem Set 5

    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

    Answer key to Problem Set 6

    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

    Answer key to Problem Set 7

    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

    Answer key to Problem Set 8

  • 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.

    Solution for Practice problems for Midterm 1.

    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 1 problems and solutions

  • 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.

    Practice problems for Midterm 2.

    Solutions to practice problems for Midterm 2.

    Midterm 2 problems and solutions.

  • 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.

    Practice final exam (actual Math 300 final exam from 2015).

    Solutions to the practice final exam.

    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.