Calculus: Concepts and Methods
eBook - PDF

Calculus: Concepts and Methods

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Calculus: Concepts and Methods

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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Yes, you can access Calculus: Concepts and Methods by Ken Binmore,Joan Davies in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.
2.3.
Some
elementary
functions
♦
x
y
0
x
y
0
n
even
n
odd
2.3.2
Exponential
functions
♦
Let
Q
be
the
set
of
rational
numbers
or
fractions,
e.g.
1
/
2,
3,
−
7
/
5.
Given
a
real
number
a
>
0,
we
can
plot
a
graph
of
y
=
a
r
for
each
r
∈
Q
.
x
y
r
a
r
y 
= 
a
r
0
x
y
y 
= 
a
x
For
irrational
numbers
(e.g.
π,
e),
we
assign
values
to
a
x
in
such
a
way
as
to
‘fill
up
the
holes’
in
the
graph
of
y
=
a
r
.
The
function
f
:
R
→
(
0
,
∞
)
then
defined
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
♦
In
what
follows,
the
angle
x
is
always
to
be
understood
as
measured
in
radians,
where
one
radian
is
indicated
by
the
figure
on
the
right.
Because
the
total
circumference
of
a
circle
of
radius
1
is
2
π
,
53

Table of contents

  1. Cover
  2. Half Title
  3. Dedications
  4. Title Page
  5. Copyright
  6. Contents
  7. Preface
  8. Acknowledgements
  9. 1 Matrices and vectors
  10. 2 Functions of one variable
  11. 3 Functions of several variables
  12. 4 Stationary points
  13. 5 Vector functions
  14. 6 Optimisation of scalar valued functions
  15. 7 Inverse functions
  16. 8 Implicit functions
  17. 9 Differentials
  18. 10 Sums and integrals
  19. 11 Multiple integrals
  20. 12 Differential equations of order one
  21. 13 Complex numbers
  22. 14 Linear differential and difference equations
  23. Answers to starred exercises with some hints and solutions
  24. Appendix
  25. Index