Calculus: Concepts and Methods
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Calculus: Concepts and Methods

Ken Binmore, Joan Davies

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eBook - PDF

Calculus: Concepts and Methods

Ken Binmore, Joan Davies

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About This Book

The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.

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Information

Publisher
Cambridge University Press
Year
2002
ISBN
9781139632751
Topic
Mathematik
Subtopic
Mathematische Analyse
2.3.
Some
elementary
functions
ā™¦
x
y
0
x
y
0
n
even
n
odd
2.3.2
Exponential
functions
ā™¦
Let
Q
be
the
set
of
rational
numbers
or
fractions,
e.g.
1
/
2,
3,
āˆ’
7
/
5.
Given
a
real
number
a
>
0,
we
can
plot
a
graph
of
y
=
a
r
for
each
r
āˆˆ
Q
.
x
y
r
a
r
yĀ 
=Ā 
a
r
0
x
y
yĀ 
=Ā 
a
x
For
irrational
numbers
(e.g.
Ļ€,
e),
we
assign
values
to
a
x
in
such
a
way
as
to
ā€˜ļ¬ll
up
the
holesā€™
in
the
graph
of
y
=
a
r
.
The
function
f
:
R
ā†’
(
0
,
āˆž
)
then
deļ¬ned
by
It
is
worth
recognizing
that
a
x
has
a
constant
base
and
a
variable
exponent
whereas
x
n
has
a
variable
base
and
a
constant
exponent.
y
=
f
(
x
)
=
a
x
has
a
graph
which
is
continuous
for
all
x
and
is
always
increasing.
2.3.3
Trigonometric
functions
ā™¦
In
what
follows,
the
angle
x
is
always
to
be
understood
as
measured
in
radians,
where
one
radian
is
indicated
by
the
ļ¬gure
on
the
right.
Because
the
total
circumference
of
a
circle
of
radius
1
is
2
Ļ€
,
53

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