A Course in Calculus and Real Analysis: Undergraduate Texts in Mathematics
Autor Sudhir R. Ghorpade, Balmohan V. Limayeen Limba Engleză Hardback – 4 iun 2006
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Specificații
ISBN-13: 9780387305301
ISBN-10: 0387305300
Pagini: 432
Dimensiuni: 156 x 235 x 26 mm
Greutate: 0.77 kg
Ediția:2006
Editura: Springer
Colecția Springer
Seria Undergraduate Texts in Mathematics
Locul publicării:New York, NY, United States
ISBN-10: 0387305300
Pagini: 432
Dimensiuni: 156 x 235 x 26 mm
Greutate: 0.77 kg
Ediția:2006
Editura: Springer
Colecția Springer
Seria Undergraduate Texts in Mathematics
Locul publicării:New York, NY, United States
Public țintă
GraduateDescriere
Calculus
is
one
of
the
triumphs
of
the
human
mind.
It
emerged
from
inv-
tigations
into
such
basic
questions
as
?nding
areas,
lengths
and
volumes.
In
the
third
century
B.
C.
,
Archimedes
determined
the
area
under
the
arc
of
a
parabola.
In
the
early
seventeenth
century,
Fermat
and
Descartes
studied
the
problem
of
?nding
tangents
to
curves.
But
the
subject
really
came
to
life
in
the
hands
of
Newton
and
Leibniz
in
the
late
seventeenth
century.
In
part-
ular,
they
showed
that
the
geometric
problems
of
?nding
the
areas
of
planar
regions
and
of
?nding
the
tangents
to
plane
curves
are
intimately
related
to
one
another.
In
subsequent
decades,
the
subject
developed
further
through
the
work
of
several
mathematicians,
most
notably
Euler,
Cauchy,
Riemann,
and
Weierstrass.
Today,calculus
occupies
a
centralplacein
mathematics
and
is
an
essential
component
of
undergraduate
education.
It
has
an
immense
number
of
app-
cations
both
within
and
outside
mathematics.
Judged
by
the
sheer
variety
of
the
concepts
and
results
it
has
generated,
calculus
can
be
rightly
viewed
as
a
fountainhead
of
ideas
and
disciplines
in
mathematics.
Real
analysis,
often
called
mathematical
analysis
or
simply
analysis,
may
be
regarded
as
a
formidable
counterpart
of
calculus.
It
is
a
subject
where
one
revisits
notionsencountered
in
calculus,
but
with
greaterrigor
and
sometimes
with
greater
generality.
Nonetheless,
the
basic
objects
of
study
remain
the
same,
namely,
real-valued
functions
of
one
or
several
real
variables.
This
book
attempts
to
give
a
self-contained
and
rigorous
introduction
to
calculusoffunctionsofonevariable.
Cuprins
Numbers
and
Functions.-
Sequences.-
Continuity
and
Limits.-
Differentiation.-
Applications
of
Differentiation.-
Integration.-
Elementary
Transcendental
Functions.-
Applications
and
Approximations
of
Riemann
Integrals.-
Infinite
Series
and
Improper
Integrals.
Recenzii
“Ghorpade
and
Limaye
(both,
Indian
Institute
of
technology,
Bombay)
have
written
a
very
coherent
and
rigorous
advanced
calculus
text
on
functions
of
one
variable.
…
Theorems
are
carefully
proven
and
exercises
(without
solutions
are
provided.
…
Recommended.
Upper-division
undergraduates.”
(
R.
L.
Pour,
Choice,
February,
2018)
“A Course in Calculus and Real Analysis by S.R. Ghorpade and B.V. Limaye (Springer UTM) is a rigorous, well-presented and original introduction to the core of undergraduate mathematics — first-year calculus. … This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously.” (N.J. Wildberger, Gazette of the Australian Mathematical Society, Vol. 35 (3), 2008)
From the reviews:
"The book is a self-contained and rigorous introduction to calculus of one variable. It covers the programme of the first-year in mathematical analysis. The main goal of the book is a clear and successful presentation of the basic ideas of analysis. The reader can see an attention of the authors to help students in understanding and further developing of the basic notions of the subject. … are illustrated by a number of interesting examples and remarks. In some sense it is a book for self-education." (Sergi V. Rogosin, Zentralblatt MATH, Vol. 1100 (2), 2007)
“A Course in Calculus and Real Analysis by S.R. Ghorpade and B.V. Limaye (Springer UTM) is a rigorous, well-presented and original introduction to the core of undergraduate mathematics — first-year calculus. … This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously.” (N.J. Wildberger, Gazette of the Australian Mathematical Society, Vol. 35 (3), 2008)
From the reviews:
"The book is a self-contained and rigorous introduction to calculus of one variable. It covers the programme of the first-year in mathematical analysis. The main goal of the book is a clear and successful presentation of the basic ideas of analysis. The reader can see an attention of the authors to help students in understanding and further developing of the basic notions of the subject. … are illustrated by a number of interesting examples and remarks. In some sense it is a book for self-education." (Sergi V. Rogosin, Zentralblatt MATH, Vol. 1100 (2), 2007)
Notă biografică
Textul de pe ultima copertă
This
book
provides
a
self-contained
and
rigorous
introduction
to
calculus
of
functions
of
one
variable.
The
presentation
and
sequencing
of
topics
emphasizes
the
structural
development
of
calculus.
At
the
same
time,
due
importance
is
given
to
computational
techniques
and
applications.
The
authors
have
strived
to
make
a
distinction
between
the
intrinsic
definition
of
a
geometric
notion
and
its
analytic
characterization.
Throughout
the
book,
the
authors
highlight
the
fact
that
calculus
provides
a
firm
foundation
to
several
concepts
and
results
that
are
generally
encountered
in
high
school
and
accepted
on
faith.
For
example,
one
can
find
here
a
proof
of
the
classical
result
that
the
ratio
of
the
circumference
of
a
circle
to
its
diameter
is
the
same
for
all
circles.
Also,
this
book
helps
students
get
a
clear
understanding
of
the
concept
of
an
angle
and
the
definitions
of
the
logarithmic,
exponential
and
trigonometric
functions
together
with
a
proof
of
the
fact
that
these
are
not
algebraic
functions.
A
number
of
topics
that
may
have
been
inadequately
covered
in
calculus
courses
and
glossed
over
in
real
analysis
courses
are
treated
here
in
considerable
detail.
As
such,
this
book
provides
a
unified
exposition
of
calculus
and
real
analysis.
The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.
The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.
Caracteristici
Introduces
the
principles
of
real
analysis,
as
a
formidable
counterpart
to
calculus
Offers self-contained introduction to the calculus of functions of one variable
The text is sequenced to emphasize the structural development of calculus
Places appropriate emphasis on computational techniques and applications
Offers self-contained introduction to the calculus of functions of one variable
The text is sequenced to emphasize the structural development of calculus
Places appropriate emphasis on computational techniques and applications