Math 300: Introduction to Complex Variables


Instructor information


Location and Time

MWF 8:00-9:00 in BUCH A102


Textbook

We will use the textbook

Fundamentals of Complex Analysis with Applications to Engineering and Science (Third Edition), by E. Saff and A. Snider.

Homework problem sets will be from Saff & Snider. You can also refer to the free online textbook

A First Course in Complex Analysis by Beck, Marchesi, Pixton and Sabalka.


Topics

1.The complex numbers. (Saff & Snider sections 1.1 - 1.6)

2.Analytic functions. (Saff & Snider sections 2.1 - 2.5)

3.Examples of Complex Functions. (Saff & Snider sections 3.1 - 3.3, 3.5)

4.Complex Integration. (Saff & Snider sections 4.1 - 4.7)

5.Taylor and Laurent Series (Saff & Snider sections 5.1 - 5.6)

6.The residue theorem (Saff & Snider sections 6.1 - 6.4)


Homework, tests and grades

There will be weekly homework assignments, usually due on Mondays. You will be required to upload files in pdf format (either scanned handwritten solutions, or prepared with a typesetting program such as LaTeX) on the course canvas page. A selection of problems will be graded. Late homework will not be accepted, even if you have a good excuse. To compensate, I will drop the lowest homework score. Even if you miss the deadline, its a good idea to do the problems, since this is the best way to prepare for the tests and exam. You are welcome to discuss the homework problems with your friends, but are expected to hand in your own work.

There will be two midterm exams on October 11 and November 8 in class and a final exam during the exam period.

The following weightings will be used in computing your final grade:

Homework (lowest score dropped): 10%
Midterms: 2 x 20%
Exam: 50%

If you miss a test for a legitimate reason, please fill out an academic request form and bring it to me. The weight of the test will be transfered onto the final exam.


Class notes, Homework assignments

To hand in homework, upload a pdf file on the canvas page before the due date.

Date Reading Topics Problems
Wed Sept 4 1.1 Introduction, arithmetic operations (Saff&Snider) 1.1: 6a, 8, 10, 20abc 30 due: Mon Sept 9
Fri Sept 6 1.2, 1.3 Modulus, conjugate .
Mon Sept 9 1.4. 1.5 Triangle and reverse triangle inequatlities. Complex exponential, polar form of a complex number. (Saff&Snider) 1.2: 7def, 16, 17, 1.3:11,13,23, 1.4: 3c, 12b, 1.5 5ae 11 16 due: Mon Sept 16
Wed Sept 11 . Trig identity example: . The argument and the principal argument , geometry of multiplication .
Fri Sept 13 1.6 Brief discussion of Julia sets. Here are some pictures: Julia sets, Roots of unity. Factorization of , roots of an arbitrary complex number . .
Mon Sept 16 2.1 Properties of sets in the plane, Complex functions intro (Saff&Snider) 1.6: 1ab, 2ab, 3ab, 4ab, 5ab, 6ab, 7ab, 8ab, 2.1:3abcd, 5abcd, 6abc, 10a, 11a due: Mon Sept 23

Files and Demos

Homework solutions: solutions1.pdf, solutions2.pdf

Geometry of complex multiplication

Here is a scan of the problems in Chapter 1. chapter1problems.pdf which you can use while the bookstore orders more copies of the text.

Here are some examples of describing sets with complex notation: setdescriptions.pdf.


UBC notice

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