hna 's
Kris TEXT BOOK on
C alculus
(For B.A. and B.Sc. Ist year students of All Colleges affiliated to universities in Uttar Pradesh)
As per U.P. UNIFIED Syllabus
(w.e.f. 2011-2012)
By
A. R. Vasishtha
Retired Head, Dep’t. of Mathematics
Meerut College, Meerut (U.P.)
KRISHNA Prakashan Media (P) Ltd.
KRISHNA HOUSE, 11, Shivaji Road, Meerut-250 001 (U.P.), India
, Jai Shri Radhey Shyam
Dedicated
to
Lord
Krishna
Authors & Publishers
, Preface
This book on CALCULUS has been specially written according to the latest
Unified Syllabus to meet the requirements of the B.A. and B.Sc. Part-I Students
of all Universities in Uttar Pradesh.
The subject matter has been discussed in such a simple way that the students will
find no difficulty to understand it. The proofs of various theorems and examples have
been given with minute details. Each chapter of this book contains complete theory
and a fairly large number of solved examples. Sufficient problems have also been
selected from various university examination papers. At the end of each chapter an
exercise containing objective questions has been given.
We have tried our best to keep the book free from misprints. The authors shall be
grateful to the readers who point out errors and omissions which, inspite of all care,
might have been there.
The authors, in general, hope that the present book will be warmly received by
the students and teachers. We shall indeed be very thankful to our colleagues for
their recommending this book to their students.
The authors wish to express their thanks to Mr. S.K. Rastogi, Managing Director,
Mr. Sugam Rastogi, Executive Director, Mrs. Kanupriya Rastogi Director and entire
team of KRISHNA Prakashan Media (P) Ltd., Meerut for bringing out this book
in the present nice form.
The authors will feel amply rewarded if the book serves the purpose for which it is
meant. Suggestions for the improvement of the book are always welcome.
Preface to the Revised Edition
The authors feel great pleasure in presenting the thoroughly revised edition of
the book CALCULUS and wish to record thanks to the teachers and students for
their warm reception to the previous edition.
The present edition has been specially designed, made up-to-date and well
organised in a systematic order according to the latest syllabus.
The authors have always endeavoured to keep the text update in the best
interests of the students community- a gesture which the authors hope would be
appreciated by the students and teachers alike.
Suggestions for the improvement of the book will be thankfully received.
— Authors
, Syllabus
Calculus
U.P. UNIFIED (w.e.f. 2011-12)
B.A./B.Sc. Paper-II M.M. :
Differential Calculus
Unit-1: ε
-δ
definition of the limit of a function, Continuous functions and
classification of discontinuities, Differentiability, Chain rule of Differentiability,
Rolle’s theorem, First and second mean value theorems, Taylor’s theorems with
Lagrange’s and Cauchy’s forms of remainder, Successive differentiation and
Leibnitz’s theorem.
Unit-2: Expansion of functions (in Taylor’s and Maclaurin’s series),
Indeterminate forms, Partial differentiation and Euler’s theorem, Jacobians.
Unit-3: Maxima and Minima (for functions of two variables), Tangents and
normals (polar form only), Curvature, Envelopes and evolutes.
Unit-4(a): Asymptotes, Tests for concavity and convexity, Points of inflexion,
Multiple points, Tracing of curves in Cartesian and Polar coordinates.
Integral Calculus
Unit- 4(b): Reduction formulae, Beta and Gamma functions.
Unit-5: Quadrature. Rectification. Volumes and surfaces of solids of revolution,
Pappus theorem, Double and triple integrals, Change of order of integration,
Dirichlet’s and Liouville’s integral formulae.
Kris TEXT BOOK on
C alculus
(For B.A. and B.Sc. Ist year students of All Colleges affiliated to universities in Uttar Pradesh)
As per U.P. UNIFIED Syllabus
(w.e.f. 2011-2012)
By
A. R. Vasishtha
Retired Head, Dep’t. of Mathematics
Meerut College, Meerut (U.P.)
KRISHNA Prakashan Media (P) Ltd.
KRISHNA HOUSE, 11, Shivaji Road, Meerut-250 001 (U.P.), India
, Jai Shri Radhey Shyam
Dedicated
to
Lord
Krishna
Authors & Publishers
, Preface
This book on CALCULUS has been specially written according to the latest
Unified Syllabus to meet the requirements of the B.A. and B.Sc. Part-I Students
of all Universities in Uttar Pradesh.
The subject matter has been discussed in such a simple way that the students will
find no difficulty to understand it. The proofs of various theorems and examples have
been given with minute details. Each chapter of this book contains complete theory
and a fairly large number of solved examples. Sufficient problems have also been
selected from various university examination papers. At the end of each chapter an
exercise containing objective questions has been given.
We have tried our best to keep the book free from misprints. The authors shall be
grateful to the readers who point out errors and omissions which, inspite of all care,
might have been there.
The authors, in general, hope that the present book will be warmly received by
the students and teachers. We shall indeed be very thankful to our colleagues for
their recommending this book to their students.
The authors wish to express their thanks to Mr. S.K. Rastogi, Managing Director,
Mr. Sugam Rastogi, Executive Director, Mrs. Kanupriya Rastogi Director and entire
team of KRISHNA Prakashan Media (P) Ltd., Meerut for bringing out this book
in the present nice form.
The authors will feel amply rewarded if the book serves the purpose for which it is
meant. Suggestions for the improvement of the book are always welcome.
Preface to the Revised Edition
The authors feel great pleasure in presenting the thoroughly revised edition of
the book CALCULUS and wish to record thanks to the teachers and students for
their warm reception to the previous edition.
The present edition has been specially designed, made up-to-date and well
organised in a systematic order according to the latest syllabus.
The authors have always endeavoured to keep the text update in the best
interests of the students community- a gesture which the authors hope would be
appreciated by the students and teachers alike.
Suggestions for the improvement of the book will be thankfully received.
— Authors
, Syllabus
Calculus
U.P. UNIFIED (w.e.f. 2011-12)
B.A./B.Sc. Paper-II M.M. :
Differential Calculus
Unit-1: ε
-δ
definition of the limit of a function, Continuous functions and
classification of discontinuities, Differentiability, Chain rule of Differentiability,
Rolle’s theorem, First and second mean value theorems, Taylor’s theorems with
Lagrange’s and Cauchy’s forms of remainder, Successive differentiation and
Leibnitz’s theorem.
Unit-2: Expansion of functions (in Taylor’s and Maclaurin’s series),
Indeterminate forms, Partial differentiation and Euler’s theorem, Jacobians.
Unit-3: Maxima and Minima (for functions of two variables), Tangents and
normals (polar form only), Curvature, Envelopes and evolutes.
Unit-4(a): Asymptotes, Tests for concavity and convexity, Points of inflexion,
Multiple points, Tracing of curves in Cartesian and Polar coordinates.
Integral Calculus
Unit- 4(b): Reduction formulae, Beta and Gamma functions.
Unit-5: Quadrature. Rectification. Volumes and surfaces of solids of revolution,
Pappus theorem, Double and triple integrals, Change of order of integration,
Dirichlet’s and Liouville’s integral formulae.
