Complex analysis, the study of functions of a complex variable, emerged in its modern form during the 19th century primarily from the seminal investigations by Cauchy, Riemann, and Weierstrass. Their distinct approaches -- Cauchy based his analysis on complex differentiability, Riemann studied mappings between domains in the complex plane, and Weierstrass relied on power series representations of functions -- are inextricably linked and have become to define the modern-day theory of analytic functions. Apart from its own intrinsic interest and beauty, complex analysis is studied as an indispensable tool in practically every major field of mathematics, and it has found applications in such varied subjects as computer graphics, cryptography, fluid mechanics, quantum theory, tomography, and so on.
MTH 611 Complex Analys will be taught as an introductory course to the theory of analytic functions. Topics covered will include:
We will use the book Ash, Novinger, Complex Variables, 2nd Ed., Dover 2007, as the course text. A pdf-version of the book can be downloaded gratis at http://www.math.uiuc.edu/~r-ash/CV.html.
The course is offered concurrently with MTH 619 Topics in Analysis, CRN 59554Instructor: Juha Pohjanpelto
Prerequisites: Basics of differentiation and integration as covered e.g. in MTH 411.
|Learning objectives: Upon successfully completing this course a student|
|• comprehends the notion of an analycity for complex functions and recognizes a large variety of analytic functions.|
|• is capable of evaluating contour integrals involving complex functions and
is familiar with the Cauchy integral theorems.
||• comprehends the maximum principle and recognizes its basic applications to the study of analytic functions.
||• appreciates Laurent expansions of analytic functions and is adept in applying the ensuing techniques to evaluating definite integrals.
||• is acquainted with the key applications of analytic functions.|
Grading: Your course grade will be based on a mid-term exam, a final exam, and four homework assignments. The midterm exam counts 30%, the final exam 40%, and the homework assignments 30% towards the course grade.
You can view the course calendar by clicking here
| ||Lars Ahlfors, Complex Analysis, McGraw-Hill, 1979.|
| ||Jerrold Marsden, Michael Hoffman, Basic Complex Analysis, W. H. Freeman, 1998.|
| ||Raghavan Narasimhan, Complex Analysis in One Variable, Birkh&aum;user, 1979.|
| ||Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976.|
| ||Walter Rudin, Real and Complex Analysis, McGraw-Hill, 1986.|
Course Catalog DescriptionOSU Academic Dishonesty Policy
Disability Access Services