# MATH V3007- Final Exam Guide - Comprehensive Notes for the exam ( 131 pages long!)

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Published on 4 Dec 2017
School
Columbia University
Department
Mathematics
Course
MATH V3007
Professor
Columbia
MATH V3007
FINAL EXAM
STUDY GUIDE
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Complex Numbers
Tuesday, January 17, 2017
2:41 PM
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## Document Summary

Abel and tauber theorems are related to power series. Let sn for n n and s be complex numbers. Then sn converges to s, written as sn s if > 0 there is a positive integer n s. t |sn s| < n > n the point s is then called the limit of the sequence. Using the above notation, fn f uniformly (on s) means. > 0, n = n n : |fn(z) f (z)| < , n > n, , z s. Let s be a subset of c, f a (complex-values) function de ned on s. let z0 be a point in s. we say f is continuous at z0 if. > 0, > 0 : |f (z) f (z0)| < , z s with |z z0| < . Of course may depend on , z0 and f. we say f is continous on s if f is continuous at each point of s.