MATH 365 - COMPLEX VARIABLES

SPRING 2007

INSTRUCTOR: Dr. Stan Gurak

OFFICE: Serra 159A  

PHONE: 260-4017

OFFICE HOURS:  
M  10 - 11 (also 11 - 12 in S 133A)         
TTH  8:10 - 9:10 (also 12:10- 1:10 in S 133A)             
& by appointment


     The course is a one semester introduction in the theory and application of functions of a complex variable.  As it is an abstract mathematics class, sound reasoning and mathematical rigor are emphasized throughout the course.  Students are expected to be familiar with making sound arguments and constucting proofs.
     The class text is COMPLEX VARIABLES & APPLICATIONS by Brown & Churchill, 7-th ed.. We shall cover Chapters 1-8 of the text with additional topics chosen from Chapters 9 and 10.  The course begins with the basic algebraic properties of complex numbers and their geometric representation in the complex plane (Chap. 1).  The principal aim, thereafter, is to develop a theory of calculus for functions of a complex variable analogous to that for functions of a real variable (as studied in Calculus I and II).  We primarily study analytic functions - those differentiable in the complex sense (Chap. 2,3,8) and which happen to have nice series expansions about their singularities (Chap. 5,6).  There is an analog of the Funda- mental Theorem of Calculus for integrals involving complex variables and familiar tests for convergence of power series.  A secondary objective is to give an introduction to application of residues and of conformal mappings (Chap. 7,9,10).  The course prerequisites are MATH 160 and 250.

     The grading for the course is apportioned as follows:

Homework 15%      

Hour exams(2)/Quizzes 50%       

Final Exam 35%

     There will be NO makeup exams and late homework will be severely penalized.  The class exams are tentatively scheduled for Mar. 13 and May 3.   Homework will generally be due each Tuesday.  Also, there will be weekly quizzes, generally given on Thursdays, to test the previous week's work.  Your combined quiz grades will count as one hour test.  At the end of the semester I will drop either your combined quiz score or one of the hour test scores, whichever is lowest. The final exam is comprehensive and worth 35% of your grade.  It is scheduled in class for THURSDAY, MAY 17 from 8 am to 10 am.