Complex analysis is concerned with the properties of functions of a complex variable, especially analytic functions which have played a vital role in many branches of pure and applied mathematics, physics and engineering. We will extend the notions of differentiation and integration to the complex setting, and study Cauchy's theorem, singularities, contour integration, conformal mapping, and their applications.
Topics covered include:
- Brief review of complex numbers
- Analytic functions and power series
- Line integrals
- Entire functions
- Cauchy's theorem and isolated singularities
- The residue theorem and its applications
- Contour integration
- Conformal mapping
- The Riemann mapping theorem
- Applications in engineering, physics and number theory
Prerequisites
- Calculus I/II/III plus one higher level course.
- General Physics I, II (PHYS-UA 91, PHYS-UA 93) iand Analysis I are not required, but provide useful background.
Textbook
The course textbook is Complex Analysis by Joseph Bak and Donald J. Newman.Assignments and grading
There will be regular (weekly or biweekly) assignments, an in-class midterm and an in-class final.Grading will be based 30% on assignments, 30% on the midterm, and 40% on the final. Please see NYU's Academic integrity policies.