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Complex Variables Midterm 2 Study Sheet Silas K Grossberndt 1 De▯nitions 1.1 Converges and limit Let snfor n 2 N and s be complex numbers. Then n converges to s, written as sn! s if 8▯ > 0 there is a positive integer N snt js ▯ sj < ▯8n > N The point s is then called the limit of the sequence. 1.2 Pointwise Convergence Let fn 8n 2 N and f be complex valued functions de▯ned on set S. n ! f pointwise on S means fn(z) ! f(z)8z 2 S i.e. 8z 2 S;8▯ > 0;9N = N ▯;z2 N : jn (z) ▯ f(z)j < ▯;8n > N 1.3 Uniform Convergence Using the above notation,nf ! f uniformly (on S) means 8▯ > 0;9N = N 2 N : jf (z) ▯ f(z)j < ▯;8n > N;;8z 2 S ▯ n 1.4 Conti

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School: Columbia University in the City of New York

Department: Science and Math

Course: Complex Variables

Professor: Patrick gallagher

Term: Spring 2017

Tags: Math and complex

Cost: 50

Name: Midterm 2 study guide

Description: Definitions and theorems for midterm 2

Uploaded: 03/30/2017

10 pages

Math 3007 Week 1 notes

8 pages

Final definitions

10 pages

Math 3007 Week 1 notes

8 pages

Final definitions

10 pages

Math 3007 Week 1 notes

8 pages

Final definitions

convergernt

convergernt Description

School: Columbia University in the City of New York

Department: Science and Math

Course: Complex Variables

Professor: Patrick gallagher

Term: Spring 2017

Tags: Math and complex

Cost: 50

Name: Midterm 2 study guide

Description: Definitions and theorems for midterm 2

Uploaded: 03/30/2017

10 pages

Math 3007 Week 1 notes

8 pages

Final definitions

10 pages

Math 3007 Week 1 notes

8 pages

Final definitions

10 pages

Math 3007 Week 1 notes

8 pages

Final definitions

convergernt
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