# MTH 462 Complex Variables - Spring 2003

Tu-Th 9:30 - 10:45 a.m.  RODM 226

Instructor: Prof. O. Merino, Tyler 220, (401) 874 4442, merino@math.uri.edu

Text: Complex Variables, by Stephen D. Fisher (2nd Edition).  Dover Publications Inc.

Evaluation: 75% homework, 25% final exam.
Homework will be collected on tuesdays. Homework on starred topics in the table below counts as 1/2 of other homework assignments.

On the course:  This is an introduction to the complex plane and to functions of a complex variable.

Prerequisite: MTH 243  or equivalent.

 Date Section Topics Problems Jan 21 1.1 * Complex Numbers and Complex Plane 1f, 3d, 5d, 6f, 11, 13b Jan 23 1.2 * Some Geometry 2, 3, 5, 13, 15, 25, 26 Jan 28 1.3 * Subsets of the Plane 1 -- 8 Jan 30, Feb 4 1.4 Functions and Limits 1, 3, 5, 11, 13, 14, 15, 17, 19, 31, 32, 34, 40 Feb 6, 11 1.5 Exp, Log, and Trig Functions 2 -- 28 even Feb 13, 20 1.6 Line Integrals and Green's Theorem 1 -- 8, 10, 11, 12 Feb 25, 27 2.1 Analytic and Harmonic fns, CR eqs 1a, 1g, 2, 4, 6, 8, 10, 14, 16, 18, 20a Mar 4, 6 2.2 Power Series 1 -- 5, 7 -- 11, 15, 16, 22a, 22b Mar 10- 15 SPRING BREAK SPRING BREAK Mar 18, 20 2.3 Cauchy's Theorem 1, 2, 3, 5, 6, 8 -- 12, 14, 18a, 18c Mar 25, 27 2.4 Consequences of Cauchy's Thm. 1, 2, 4, 6, 9, 10, 12, 14, 17, 20 ,25 Apr 1, 3 2.5 Isolated Singularities 1, 2, 5, 6, 7, 8, 10, 12, 22a, 22b, 22c Apr 8, 10 2.6 The Residue Theorem and Apps. 1, 2, 4, 5, 9, 10, 13, 14, 16, 17, 20, 22 Apr 15, 17 3.1 Zeros of an analytic function 1, 2, 3, 4, 7, 8, 12, 14, 15, 17a, 17c, 20 Apr 22, 24 3.3 * Linear Fractional Transformations 4a -- 4e, 5a, 5b, 7a -- 7d, 8a, 8b Apr 29 3.4 * Conformal Mapping 1, 4, 5, 7a, 7c, 7d, 15 May 1 3.2 * Maximum Modulus and Mean Value 1, 2, 3, 6, 7, 16 May 6 Last day of class

Changes to schedule and homework assignments:

Section 1.5: Skipped pages 50-51. Instead, more time was spent discussing logarithm, $z^(1/2)$ and $z^\alpha$. Problems 26, 28 were dropped and replaced by: Find domain of (a) sin(z)/cos(z), and (b) sqrt(1-z)

Section 2.6: we used two weeks to cover it. Homework week 1 is as in table except for 13,14,16,17 of page 167. Also, we discussed winding number (not in text).

Section 3.1: not discussed and no homework assigned due to class cancellation (weather related). The hw assignment consists of more residue theorem problems: 13,14,16,17 of page 167.

Section 3.2: not discussed (ran out of time!)