INSTRUCTOR: Dr. Botsko

TEXT: Complex Variables and Applications, 7^th edition by Churchill and Brown

COURSE CONTENT:

We will cover chapters 1, 2, 3, 4, 5, 6, and part of 7 of the above text. A list of topics includes:

1. The complex number system
2. Some Topology in the complex plane
3. Complex mappings
4. Limits and continuity
5. Differentiation and the Cauchy-Riemann equations
6. Analytic functions
7. Harmonic functions
8. The elementary complex functions
9. Line integrals and Green's Theorem
10. The Cauchy Integral Theorem and Formula
11. The Maximum Modulus Theorem
12. The Fundamental Theorem of Algebra
13. Series of complex numbers and functions
14. Taylor and Laurent series
15. The Residue Theorem
16. Evaluation of improper integrals
17. Definite integrals involving sine and cosine

OBJECTIVES:

Students are expected to know the definitions and fundamental theorems of Complex Variables, to be able to prove propositions, to develop proficiency in applying the problem-solving techniques treated in the course, and to be able to make connections between Complex Variables and other branches of mathematics. Class discussions and exams will be used to assess the level to which these objectives are being attained.

EXAMS:

There will be 2 exams and a final and you will be given a week's notice for each exam.

GRADING POLICY:

The final will count as 1/3 of your grade as will each of the two in class exams. The grading system will be according to the current SVC bulletin.

CLASS ATTENDANCE:

Please make every effort to keep up with assignments and to attend all classes. A significant number of class cuts in an upper division mathematics course almost always leads to disastrous results. If for some reason class is cancelled, an announcement will be posted on the Blackboard site for this course.

“Saint Vincent College assumes that all students come for a serious purpose and expects them to be responsible individuals who demand of themselves high standards of honesty and personal conduct. Therefore, it is college policy to have as few rules and regulations as are consistent with efficient administration and general welfare.

Fundamental to the principle of independent learning and professional growth is the requirement of honesty and integrity in the performance of academic assignments, both in the classroom and outside, and in the conduct of personal life. Accordingly, Saint Vincent College holds its students to the highest standards of intellectual integrity and thus the attempt of any student to present as his or her own any work which he or she has not performed or to pass any examinations by improper means is regarded by the faculty as a most serious offense.”
Saint Vincent College 2003-2005 Bulletin, page 32.

DISABILITY STATEMENT: 

Students with disabilities who may be eligible for academic accommodations and support services should please contact Mrs. Sandy Quinlivan by phone (724-805-2371), email (sandy.quinlivan@email.stvincent.edu) or by appointment (Academic Affairs-Headmaster Hall).  Reasonable accommodations do not alter the essential elements of any course, program or activity.

TUTORING FOR THE COURSE:

I will be in my office (4th floor of Alfred Hall) at the following times during the week. Do feel free to stop in when you are having any difficulty with the material.

Office Hours:

Monday: 9:30 to 10:30 and 3 to 4

Tuesday: 9:30 to 10:30

Wednesday: 9:30 to 10:30

Friday: 9:30 to 10:30

In addition to my office hours, student tutors will be assigned by the Mathematics Department and their hours will be given to you during the first week of class. You are also free to come to them for help in the course.

For a nice web site on various areas of mathematics, click on Math archives.

Math archives

Student Tutors

A Property of the Complex Logarithm Function

A Proof of the Cauchy Integral Theorem

Assignments and Other Information If this link doesn't work, click here.