
Course Outline

Topics 
Complex numbers: algebra and geometry, square roots, polar coordinate, nth roots 
Analytic functions: CauchyRiemann equations, harmonic functions, reflection principle 
Elementary functions: exponential, logarithm, branches, trigonometric & hyperbolic functions 
Integral: definitions, contour integrals, Cauchy formula, Liouville Theorem, roots of polynomials 
Bounded linear functions, Riesz representation theorem, and the LaxMilgram theorem 
Series: Taylor's and Laurent's series expansions, convergence, algebra for power series.

Residues and Poles: Cauchy's residue Theorem, zeros of analytic functions

Application of Residues: computation of integrals, branch cuts, Laplace transform 
Mappings: examples provided by elementary functions 
Conformal Mapping and applicationss 


Textbook

Official textbook
James Ward Brown, Ruel V. Churchill,
"Complex Variables and Applications", Ninth edition,
McGrawHill Education, New York, 2014
(return to top)


Homework

One compulsory homework will be offered once every 2 weeks
Each homework will be graded. The homework grade will count for 35% of the final grade


Final Exam

Friday April 29th, 8:0010:50am
Skiles 271
(
to calendar)



An absence to the final exam will be graded 0 (zero). However if the absence is justified (disease, injury, ...), the student must (i) warn the instructor as soon as possible, in any case before the end of the exam week, (ii) bring the documents justifying the absence to the Instructor.
Then the student will receive an I (incomplete) and will be responsible to take action during the following semester to complete his/her curriculum.


Grades




90% for an A 
Homeworks 
35% 
Grade distribution 
80% for a B 
Final 
65% 

70% for a C 



60% for a D 
