Chapter 1. Functions: Limits and Continuity
1.1
Functions
It is common that the values of one variable depend on the values of another. E.g. the area A of a region on the plane enclosed by a circle depends on the radius r of the circle (A = r2, r > 0 .) M
CH 5 - Three Dimensional Space
In this chapter, we shall study
Coordinate System
Vectors
- scalar (dot ) product
- vector (cross) product
Lines
Planes
Vector functions
Special curves
1
5.1. The Cartesian Coordinate System
One dim
0
right-handed
syst
CH 6 Fourier Series
Why study Fourier Series First recall Taylor series
Functions should have any order of derivative
Many super smooth functions (not ALL) can be
represented by Taylor series
f ( x) f (a ) + f '(a )( x a ) + f "(a )( x a ) 2 + . + f ( n )
MA 1505
Group D
Chew Tuan Seng
[email protected]
Group D
(LT 7)
Mon 8-9
Wed 12-2
Tutorial from week 3
Webcast
1
I will follow the contents of the lecture notes
but my presentation is different
If you attend my lectures,
I suggest you use my power point sl
CH 4 Series
In this Chapter, we shall study
Sequences cfw_an
series
a
n 1
n
a
n 1
n
lim sn
n
Power Series
Taylor series of f
and when we have f ( x)
?
1
Sequences
A sequence of real numbers
:
2
Limits of Sequences
if an tends to L as n becomes la
Chapter 1 Additional Notes
Functions: Limits and Continuity
Rules of Limits
If lim f (x) = L and lim g(x) = L, then the followxa
xa
ing statements are easy to verify:
(1) lim (f g)(x) = L L;
xa
(2) lim (f g)(x) = LL;
xa
L
f
(3) lim (x) = provided L = 0;
x
CH 2 - Differentiation
2.1 Derivative
Geometrical meaning of derivative
y = f(x)
P
Problem Find the slope
of the tangent to the curve
y = f(x) at P(a, f(a).
1
The slope of PQ
QB
= tan =
PB
f ( a + h) f ( a )
=
h
B
The slope of the tangent
to the curve y
MA 1505
Group D
Chew Tuan Seng
[email protected]
Group D
(LT 7)
Mon 8-9
Wed 12-2
Tutorial from week 3
Webcast
1
I will follow the contents of the lecture notes
but my presentation is different
If you attend my lectures,
I suggest you use my power point sl
Chapter 2. Dierentiation
2.1
2.1.1
Derivative
Derivative
Let f (x) be a given function. The derivative of f at
the point a, denoted by f (a), is dened to be
f (x) f (a)
xa
xa
f (a) = lim
()
provided the limit exists.
An equivalent formulation of () is
f (
Chapter 1. Some Basics
1.1
Functions
It is common that the values of one variable depend
on the values of another. E.g. the area A of a region on the plane enclosed by a circle depends on
the radius r of the circle (A = r2, r > 0 .) Many
years ago, the Sw
CH 2 - Differentiation
2.1 Derivative
Geometrical meaning of derivative
y = f(x)
P
Problem Find the slope
of the tangent to the curve
y = f(x) at P(a, f(a).
1
The slope of PQ
QB
= tan PB
f ( a h) f ( a )
h
B
The slope of the tangent
to the curve y = f(x)