Mathematics 430 and 630
Complex Variables (3)
Dr. Chris Caldwell
This course and the course text are between the level of the prerequisite Multivariate Calculus (320) and the capstone courses Algebra and Real Analysis (461-2 and 481-2). In many ways this course is a continuation of the calculus, but we are now doing the work using complex (rather than real) variables. This involves a reexamination of the transcendental functions (for example, what should ln(i), sin(i) and ii mean?), then an application of differentiation and integration to functions of complex variables. Look at the catalog description of the course:
Algebraic operations and geometry of complex numbers, definitions of limit, continuity, and analytic functions, differentiation, mappings of simple functions, line integrals, Cauchy integral formula, Laurent series, evaluation of real integrals using the residue theorem.
You have seen these ideas (though not all of these words) before: 'Analytic' is a generalization of 'differentiable,' 'Laurent series' are just a generalization of (complex) Taylor series... This is both good news and bad news. The good news is that since you have seen these ideas, what we learn this semester will not be totally new and should fit well in you recall from previous courses (especially calculus). The bad news is that I will expect you to remember som calculus--so you might need to keep your old calculus book handy.
The title of our course is complex variables (as opposed to complex analysis) which indicates the department's intention that the course emphasize application rather than proof. But this is a senior level math course, so you will get a dose of proof (especially at the beginning of the course)! We will not, however, do anywhere near as much proof as in Abstract Algebra or Real Analysis; and will will be much less formal about it.
The suggestions are the same for most any mathematics class:
I want you to succeed and will gladly help you, but you must start by working on the homework and reading the text (even if you cn not do it, at leasts start). Many of the other faculty member might also be able to answer some questions (if they have time), but few have taught this course recenty.
Homework will be assigned daily but sporadically collected. At the beginning of the following class period I may ask students to present parts of the homework as "board problems." I expect you to use your homework as notes. We will have about four, fifty minute tests and a comprehensive final. The homework should give you an excellent idea what the test question will look like. The course grade will probably be determined as follows:
Letter grades will then be assigned at my discretion (but at any time in the semeser I will gladly tell you were you are "grade-wise" and usually do so after every test).
The text for this course is: Complex Variables and Applications by Brown and Churchill, 4th edition. Publisher McGraw-Hill. ISBN: 978-0073051949. We will cover much of chapters one through nine. See also the department syllabus.