Cauchy's Theorem for starlike domains, Cauchy's integral Theorem Flashcards
1
Q
What is the complex fundamental theorem of calculus (FTC)?
A
2
Q
Define the length of a contour.
A
3
Q
What is the proposition about the upper bound of the following?
A
4
Q
Prove the following proposition.
A
5
Q
What do you use to create this inequality?
A
- Triangle inequality for the numerator
- Reverse traingle inquality for the denominator
6
Q
Finish the following theorem.
A
7
Q
Define starlike
A
8
Q
Give two examples of a domain which is starlike, and then two non starlike domain.
A
- Starlike - ℂ, D(a,r)
- Not starlike - ℂ - {0}, D(a,r) - {a}
9
Q
What is the theorem about starlike domains and triangles?
A
10
Q
Finish the following proposition.
A
11
Q
If we are not given a parametrization of a closed contout which way around it do we go?
A
Anti-clockwise
12
Q
Finish the following proposition.
A
13
Q
What is Cauchy’s Theorem for starlike domains?
A
14
Q
What is Cauchy’s Integral Formula theorem?
A
