MATH 485
Complex Analysis Fall 2019
Division III Quantative/Formal Reasoning

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The calculus of complex-valued functions turns out to have unexpected simplicity and power. As an example of simplicity, every complex-differentiable function is automatically infinitely differentiable. As examples of power, the so-called ¿residue calculus¿ permits the computation of ¿impossible¿ integrals, and ¿conformal mapping¿ reduces physical problems on very general domains to problems on the round disc. The easiest proof of the Fundamental Theorem of Algebra, not to mention the first proof of the Prime Number Theorem, used complex analysis.
The Class: Type: lecture
Limit: 40
Expected: 30
Class#: 1595
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation: evaluation will be based primarily on homework, classwork, and exams
Prerequisites: MATH 350 or MATH 351 or permission of instructor
Unit Notes: this course is not a senior seminar, so it does not fulfill the senior seminar requirement for the Math major
Distributions: Division III Quantative/Formal Reasoning
QFR Notes: Advanced mathematics course with weekly or daily problem sets.

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