Basic definitions and properties

Question 1

Define the following.

Answer 1

Question 2

Define a domain.

Answer 2

A domain is a non-empty, open, path connected subset of ℂ

Question 3

What does the following mean?

Answer 3

The line integral of f over Ɣ

Question 4

Finish the following equation.

Answer 4

Question 5

Prove the following Lemma.

Answer 5

Question 6

Prove the following Lemma.

Answer 6

Question 7

Define a curve.

Answer 7

Question 8

When is a curve called smooth or C¹?

Answer 8

If Ɣ’ exists and is continuous on [a,b].

Question 9

What is Ɣ’ defined as?

Answer 9

Question 10

Define the integral of f along Ɣ.

Answer 10

Question 11

What is the reparametrisation of curves Lemma?

Answer 11

Question 12

Prove the following Lemma.

Answer 12

Question 13

Define piecwise C¹-curve / contour.

Answer 13