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Time:  MWF period 7 

Room:  FLI 113

Email:  avince@ufl.edu

Office:  438 Little Hall

Office hours:  MWF period 5 and by appointment

Textbook:  Complex Variable and Applications   9th edition

                   Brown and Churchill

Complex analysis is not only of use in other branches of mathematics, but also in various fields of engineering. The course, like calculus, concerns functions of a single variable and covers limits, derivatives, integrals, and series. However, because the variable is a complex number, rather than a real number, the subject has a completely different flavor than calculus – in my opinion simpler and more elegant.

Homework

See canvas

Topics

     Complex numbers            
     rectangular and polar form
     Analytic functions   
     limits and the derivative  
     Cauchy-Riemann equations
     harmonic functions
     Examples   
     exponential and log functions   
     complex exponents
     trig functions
     linear fractional transformations    
     Integrals
     contour integral
     antiderivatives
     Cauchy-Goursat Theorem (and Morera's Theorem)
     Cauchy Integral Formula     
     Liouville's theorem and the Fundamental Theorem of Algebra
     maximum modulus principal 
     Series 
     geometric series
     power series
     Taylor series
     Laurent series
     Residues and poles
     isolated singularities
     residue theorem
     residues at poles
     behavior of a function near a singularity
     Evaluating real integrals

Grades

Four exams, a few questions on each exam.  The lowest grade is dropped if all four exams are taken.  Each exam has equal weight.

Exam 1.  February 3

Exam 2.  February 26

Exam 3.  March 26

Exam 4.  April 21

There will be four homework assignments, each due the class before the corresponding exam.  Students will have a chance to present their solutions.  The homework itself will count toward the final grade.

The exams will be graded on a sliding scale, the harder the exam, the more lenient the  grading.  Out of 100, it will never be stricter than 90A, 80B, 70C, 60D.

Exam and homework grades will be posted on the canvas Grades section within a week, but usually sooner.

Campus Resources

The course will be conducted in accordance with the Academic Honesty Policy  and policy regarding the use of copyrighted material.

Students with disabilities requesting accommodations should first register with the Disability Resource Center by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.

Academic advise and tutoring, as well as health advise (physical and mental) is available to students.

Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found at: Attendance Policies

Information on current UF grading policies for assigning grade points may be found at: Grades

Students are expected to provide feedback on the quality of instruction in this course by completing a course evaluation online via GatorEvals. Students will be notified when the evaluation period opens and can complete evaluations through the email they receive from GatorEvals or in their Canvas course menu under GatorEvals.