______________________________________________________

Time:  MWF period 6 

Email:  avince@ufl.edu 

Office hours:  MWF period 9 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

Sec 3 (Pg 7) #1  
Sec 5 (Pg 13) #1,5  
Sec 6 (Pg 16) #1,2,10a 
Sec 9 (Pg 23) #1,2,5,6  
Sec 11 (Pg 30) #1,2,4   
Sec 12 (Pg 34) #1-4  
Sec 14 (Pg 43) #2,4,8 
Sec 18 (Pg 54)#3b,5,10,11  
Sec 20 (pg 61)#1,8a,9   
Sec 24 (pg 70) #1ac,3ab,4a  
Sec 26 (pg 76) #1c,2c,4c,6 
Sec 29 (pg 85) #4   
Sec 30 (pg 89) #1b,2,6,8ac,10 
Sec 33 (pg 95) #1,2,5,8 
Sec 34 (pg 99) #1   
Sec 36 (pg 103)  #1,2,3,8c      
Sec 38 (pg 107) #5a
Sec 42 (pg 119) # 2,3,4 
Sec 46 (pg 132) #1-6,13      
Sec 47 (pg 138)  #1,2,5,     
Sec 49 (pg 147) #2,3,5     
Sec 53 (pg 159) #1,2,3,4,6 
Sec 57 (pg 170) #1-4,7    
Sec 59 (pg 177) #1,2,3,7,8  
Sec 61 (pg 185) #4        
Sec 65 (pg 195) #1-4,9,11   
Sec 68 (pg 205) #1-6        
Sec 72 (pg 218) #1-4,6,7    
Sec 73 (pg 224) #1,2a,3,4       
Sec 77 (pg 237) #1,2,4      
Sec 79 (pg 242) #1,2        
Sec 81 (Pg 247) #1,2,3b,4,5,7    
Sec 83 (pg 254) #2-5,7           
Sec 84 (pg 257)  #1,4,6      
Sec 86 (Pg 265) #1,2,4,9     
Sec 88 (Pg 273) #1-3         
Sec 91 (Page 282) #1         

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

Three exams, each worth 30%

     Exam 1.  September 

     Exam 2.  November 

     Exam 3.  December 

Five homework assignments, each worth 2%.

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.

Homework will receive full credit if there is an honest attempt to do the problems.

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.