### MATH 5046: Introduction to Complex Variables

**Description:** Complex plane, Riemann sphere, polar coordinates and Euler's formula, complex differentiable functions and Cauchy-Riemann equations, harmonic conjugates, conformal maps. Elementary functions: exp, sin, cos, log, Log, powers. Integration along simple curves, simply connected domains, Cauchy-Goursat theorem, Cauchy integral formula. Power series and the disk of convergence, Taylor and Laurent series, classification of singularities. Cauchy's residue theorem and its use in evaluating real-valued integrals. Not open to students who have passed MATH 3146. Open for master's credit but not doctoral credit toward degree in mathematics.

**Offered:** Spring

**Credits:** 3

**Sections: **Fall 2009 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

08027 | 5046 | 001 | Lecture | TuTh 2:00-3:15 | MSB307 | Madych, Wolodymyr |