Math 421, Autumn, 2019

• Taught by Tim Reluga, 424 McAllister Hall
• Textbook: Complex variables for scientists and engineers, 2nd edition, by Paliouras and Meadows
• Syllabus

• You can pick up your copy of the final exam from me on Monday morning, December 16th, in my office.
• You will have 48 hours to complete the exam and return it to me. Return the exam to my office in a sealed envelop – slide under my door if I’m not in.
• The exam is closed-book, 120 minutes. You should not use any resources. But, you can email me if a question comes up.

Homeworks

• Homework 1, due Wednesday, Sept. 4. Here is a scan of the book exercises.
• Homework 2, due Wednesday, Sept. 11. P+M Ch. 1 sec. 2, exercises 1-10. Here is a scan for those without a textbook yet.
• Homework 3, due Wednesday, Sept. 17 (due date updated). P+MSec 4, # 1,2,4,6,7,11,12, Sec 5, #1,3,10, and …
  • Suppose we have two complex numbers \(a\) and \(b\), and we’d like to know if they are perpendicular or not. Use the various things we’ve learned about complex number multiplication to find a formula involving \(a\) and \(b\) that is only true when the two complex numbers are perpendicular.
  • Use polar coordinates to prove that there exists a \(\delta\) such that for every \(z\) where \(0 < |z|<\delta\), \(|z^2| < |z|\). solution
  • Find a formula for \(\delta\) in terms of \(\epsilon\) that can be used to show \(\lim_{z \rightarrow 0} (z+i)^2 = -1\). solution discussion
• Homework 4, due Wednesday, September 24
• Homework 5, due Wednesday, October 2
• Homework 6, due Wednesday, October 9
• Homework 7, due Wednesday, October 23
• Homework 8, due Wednesday, October 30
• Homework 9, due Wednesday, November 6
• Homework 10, due Wednesday, November 13
• Homework 11, due Wednesday, November 20
• Homework 12, due Wednesday, December 4
• Homework 13, due Wednesday, December 11

Quiz solutions

• Quiz 1
• Quiz 2
• Quiz 3
• Quiz 4 was done in class
• Quiz 5
• Quiz 6
• Quiz 7
• Quiz 8

Lectures

• Lecture supplements to our textbook, hilighting places where we’ve diverged a little.

• Complex variables quick reference sheet (in development – please provide feedback.)

• Proof debugging practice

References

• An online interpretter for the python programming language that can be used as a basic complex-number calculator.

• Complex Analysis Project has lots of material.

• Paul’s online notes on complex variables