2. Sequences and Series of Functions

Question 1

Definition 2.1
Pointwise convergence.

Question 2

Definition 2.8
Uniform convergence.

Question 3

Definition 2.10
Uniformly Cauchy

Question 4

Theorem 2.11
(f_n) is uniformly Cauchy iff.

Question 5

Theorem 2.13
f_n cts. uniformly convergent implies..

Question 6

Theorem 2.14
The space of bounded, continuous functions with (which?) norm is…

Question 7

Theorem 2.16
if f_n is integrable and uniformly converges to f…

Question 8

Theorem 2.19
f : \Omega \subset R^2 -> R cts with \Omega closed, bounded…

Question 8

Theorem 2.20
If f : [a,b] x [c,d] -> R is continuous, then I(t)

Question 9

Theorem 2.21
If f and \partial_{t} f are continuous on [a,b]x[c,d] then…

Question 10

Theorem 2.22
if f : [a,b] x [c,d] cts then… Fubinis

Question 11

Theorem 2.24
(f_n) \in C^1([a,b]) with f_n -> f and f’_n ->-> g then..

Question 12

Definition 2.25
Partial sum.
Pointwise and uniform convergence of sum.

Question 13

Theorem 2.26
f_k : [a,b] -> R integrable, S_n ->->S, then…

Question 14

Theorem 2.27
f_k : [a,b] -> R \in C^1 st \sum f_k -> and \sum f_k’ converges uniformly, then…

Question 15

Theorem 2.28
Weierstrass M-test