MATH 3851
Complex Variables
Winter 2013

This is the homepage for MATH 3851 (Complex Variables). This page will be updated throughout the term with important information for our course, including homework assignments, review materials, solutions to assignments, and more. CHECK IT FREQUENTLY!


  • Solutions for our practice final exam and for HW8 have been posted.
  • The date listed for our final is incorrect! It will be on FRIDAY, March 15th. More details will be given in class, and review materials will be posted over the coming week.
  • The due date for Homework 8 has been changed to Wednesday, March 13th, at the BEGINNING of class.
Course Information

Instructor: Ronnie Pavlov
Office: John Greene Hall 304
Phone: (303)-871-4001
Office hours: Wednesday 2-3, Thursday 10-12, in John Greene 304

Graduate TA: Gabriel Giron-Garnica
Office: John Greene Hall 313
Phone: (303)-871-3311
Office hours: Tues. 2-3, Thurs. 2-4, in John Greene Hall 313


Text: Complex Variables and Applications, 8th Edition, by Brown and Churchill.

This book is available at the DU Bookstore.

We will cover Chapters 1-5 of the textbook, and as much of Chapter 6 as we can.

Course summary

The purpose of this course is to develop the theory of calculus for functions whose input and output are both complex numbers. It turns out that differentiability is a much stronger property for such functions, and as a result there are many beautiful theorems that one can prove. For example, the integral of any differentiable function around a closed loop in the complex plane is 0! We will also be able to use this theory to prove some surprising results, such as the Fundamental Theorem of Algebra, which states that any polynomial with complex coefficients has a complex root.

We can also prove some results which, on the surface, seem to have nothing at all to do with complex numbers. For instance, suppose we want to find the integral over the real line of the function 1/(1 + x^10). This can be done with only a few lines by using complex analysis, even though the indefinite integral of this function takes many pages to write down. (try plugging it into Mathematica sometime!)

The only prerequisites for this course are our calculus sequence, up through Math 2080 (Multivariable Calculus.) Though our emphasis will still be mostly on computation and applications, this course will be more theoretical than a Calculus course, and I will require you to be able to understand and write simple "proofs."

The most important advice I can give you for this course is to honestly evaluate your own progress. Mathematics, perhaps more than any other subject, allows for constant easy self-evaluation; either you know how to complete exercises from the section on your own, without outside help, or you do not. If you are having trouble, come see me or Gabriel! Either of us will be happy to discuss any aspect of the class which is causing trouble, either informally after class or during office hours. A difference of even a few days in seeking help can make a huge difference, so BE PROACTIVE!

Grading scheme

Your term grade will consist of weekly homework assignments, a midterm exam, and a final exam, broken down in the following way:

40% Final exam
30% Midterm
30% Homework


Late assignments will have a percentage subtracted according to the following policy:

3-7 days late: -50%
>7 days late: not accepted


You will have one midterm exam, on Wednesday, February 13th, during class time in our classroom. Your final exam will be on Friday, March 15th, also during class time in our class room.
Important Documents

None yet!

Course Policies

Students in this course are expected to abide by the University of Denver’s Honor Code and the procedures put forth by the Office of Citizenship and Community Standards. Academic dishonesty - including, but not limited to, plagiarism and cheating - is in violation of the code and will result in a failing grade for the assignment or for the course. As student members of a community committed to academic integrity and honesty, it is your responsibility to become familiar with the DU Honor Code and its procedures: see