MA 101 (Mathematics I)
Dierentiation : Summary of Lectures
Dierentiability and Derivative: Let D R and let x0 D such that there exists
an interval I of R satisfying x0 I D.
(x
A function f : D R is sa
Denition: Let D(= ) R and let f : D R.
Denition: Let D(= ) R and let f : D R.
We say that f is continuous at x0 D if for each > 0, there
exists > 0 such that f (x) f (x0 ) < for all x D satisfying

MA 101 (Mathematics I)
Integration : Summary of Lectures
Riemann Integral: Motivation
Partition of [a, b]: A nite set cfw_x0 , x1 , ., xn [a, b] such that a = x0 < x1 < < xn = b.
Upper sum & Lower su
MA 101 (Mathematics  I)
Innite Series : Summary of Lectures
An innite series in R is an expression
xn , where (xn ) is a sequence in R.
n=1
More formally, it is an ordered pair (xn ), (sn ), where (x
Differentiability and Derivative: Let D R and let x0 D such
that there exists an interval I of R satisfying x0 I D.
Differentiability and Derivative: Let D R and let x0 D such
that there exists an int
A sequence of real numbers or a sequence in R
is a mapping f : N R.
A sequence of real numbers or a sequence in R
is a mapping f : N R.
Notation: We write xn for f (n), n N
and so the notation for a s
An innite series in R is an expression
n=1
where (xn ) is a sequence in R.
xn ,
An innite series in R is an expression
xn ,
n=1
where (xn ) is a sequence in R.
More formally, it is an ordered pair (xn
Riemann Integral: Motivation
Riemann Integral: Motivation
Partition of [a, b]: A nite set cfw_x0 , x1 , ., xn [a, b] such that
a = x0 < x1 < < xn = b.
Riemann Integral: Motivation
Partition of [a, b]
MA 101 (Mathematics I)
Sequence : Summary of Lectures
A sequence of real numbers or a sequence in R is a mapping f : N R.
Notation: We write xn for f (n), n N and so the notation for a sequence is (xn