Math 537 syllabus

Complex Analysis

Course Description: Arithmetic of complex numbers; regions in the complex plane; limits, continuity and derivatives of complex functions; elementary complex functions; mappings by elementary functions; contour integration; power series; Taylor series; Laurent series; calculus of residues; conformal representation; applications. Credit for both MA 537 and MA 437 is not allowed.

Prerequisite: MA 238 Minimum Grade of C or MA 338 Minimum Grade of C

Suggested Textbook:   Complex Variables and Applications by Brown and Churchill, Ninth Edition, McGraw-Hill, Inc.
Course Coverage:   Chapters 1-7.

Learning outcomes: Upon the successful completion of the course a student will

  • know major theorems of complex analysis, including their proofs:  Cauchy-Riemann Equations, Cauchy Theorem, Cauchy Integral Formula, the Maximum Modulus Principle, Liouville Theorem, the Residue Theorem, Rouche Theorem