Quick links on this page: News | Introduction | Class coordinates | Instructor information | Exam Schedule | Grading | Homework Policy | Textbook
Quick links to Math 43 pages: Homework Assignments | Syllabus and schedule | Exam page | Final exam page
Math 43 is an introduction to the theory of functions of a single complex variable. In other words, Math 43 is about calculus on single variable functions which accept and take values in complex numbers instead of real numbers. We will discuss differentiation and integration of complex functions, and explore the many consequences that complex differentiability implies. A major goal of this class is to discuss the Cauchy integral theorem and its corollaries. We will also discuss product factorizations of everywhere complex differentiable functions (entire functions), and if time permits, we will examine applications to the gamma and (Riemann) zeta functions, and a proof of the Prime Number Theorem.
Although the official ORC pre-requisite for this class is only multivariable calculus, some knowledge of real analysis will be handy. We will not assume any real analysis background, but will quickly discuss and review relevant ideas that subject when necessary.
|Lectures||MWF 10:00am - 11:05am|
|X-hour||Th 12:00pm - 12:50pm|
|Office Hours||MWF 3:00pm - 4:00pm, or appointment|
There will be four 45 minute midterms, administered during the X-hour, and a final exam. A limited amount of notes will probably be permitted during each exam, but no computational aids will be allowed on exams.
If you are unable to be at any of these exams, please contact me as soon as possible so we can setup alternate test-taking arrangements.
Your grade in this class will be determined by homework and exams.
Weekly written assignments will consist of questions which usually cover the material from the previous week. Questions will typically involve computing a certain quantity or proving a particular statement. In either case, answers must be justified using clear and reasonably complete arguments. Written homework will be due on Monday afternoons.
There will be four 45 minute midterm exams, administered during the X-hour, and a final exam. They will probably be limited open note exams.
Each of the above contributes to your final grade in the following fashion:
Written homework assignments will be posted at the homework page of this website, and will be usually due about a week after they are posted. Late assignments will only be accepted when granted an extension, which must be requested from the instructor several days in advance. In general, extensions will only be granted for health-related reasons or family emergencies. Exceptions may be made for school-related travel.
The homework collaboration policy for this class is more or less in line with other Dartmouth math classes. You are allowed to collaborate with others on homework, but must write your own solutions. A good rule of thumb is that you should never be copying phrases or sentences from anyone else or any source. You may use theorems, lemmas, etc. that we have covered from the textbook, but in general you should not use theorems, lemmas, etc. from sections of the book we have not covered or from external sources. Also, please write down the people you collaborated with and outside sources (namely, anything besides the required textbook) you consulted on your homework assignments.
The required book for this class is Complex Analysis, by Elias Stein and Rami Shakarchi, ISBN 978-0691113852. This relatively new book is one part of a series of texts on real and complex analysis that grew out of teaching the analysis sequence for undergraduates at Princeton University. As this sequence is one of the best, if not the best, analysis sequence for math majors in the country, the quality of the exposition and choice of topics in this book (and the other books in this series) are fantastic. Elias Stein is one of the leading world authorities in analysis (in particular, harmonic analysis), and has had decades of experience teaching top undergraduate and graduate students. Another plus of this book is that it contains a lot of content, yet is reasonably priced.
There are many books about complex analysis. The following are a few books which might be worth consulting: