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Course Outline
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Topics |
Complex numbers: algebra and geometry, square roots, polar coordinate, n-th roots |
Analytic functions: Cauchy-Riemann 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 Lax-Milgram theorem |
Series: Taylor's and Laurent's series expansions, convergence, algebra for power series.
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Residues and Poles: Cauchy's residue Theorem, zeros of analytic functions
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Application of Residues: computation of integrals, branch cuts, Laplace transform |
Mappings: examples provided by elementary functions |
Conformal Mapping and applicationss |
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Textbook
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Official textbook
James Ward Brown, Ruel V. Churchill,
"Complex Variables and Applications", Ninth edition,
McGraw-Hill Education, New York, 2014
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Homework
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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
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Final Exam
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Friday April 29th, 8:00-10:50am
Skiles 271
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to calendar)
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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.
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Grades
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90% for an A |
Homeworks |
35% |
Grade distribution |
80% for a B |
Final |
65% |
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70% for a C |
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60% for a D |
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