Krishna's
TEXT BOOK on
D ifferential C alculus
(For B.A. and B.Sc. Ist Semester students of Kumaun University)
Kumaun University Semester Syllabus w.e.f. 2016-17
By
A.R. Vasishtha A.K. Vasishtha
Retired Head, Dept. of Mathematics M.Sc., Ph.D.
Meerut College, Meerut C.C.S. University, Meerut
Kumaun
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
, P reface
This book on Differential Calculus has been specially written according to the latest
Syllabus to meet the requirements of the B.A. and B.Sc. Semester-I Students of all
colleges affiliated to Kumaun University.
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, M.D., 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.
July, 2016 — Authors
, Syllabus
D ifferential C alculus
B.A./B.Sc. I Semester
Kumaun University
First Semester – Second Paper
B.A./B.Sc. Paper-II M.M.-50
PAPER II: DIFFERENTIAL CALCULUS
Limit, Continuity and Differentiability: Functions of one variable, Limit of a function (
- Definition), Continuity of a function, Properties of continuous functions, Intermediate
value theorem, Classification of Discontinuities, Differentiability of a function,Rolle 's
Theorem,Mean value theorems and their geometrical interpretations, Applications of
mean value theorems.
Successive Differentiation, Expansions of functions and Indeterminate forms:
Successive Differentiation, nth Differential coefficient of functions,Leibnitz
Theorem;Taylor 's Theorem, Maclaurin 's Theorem,Taylor 's and Maclaurin 's series
expansions .
dx
Tangents and Normals: Geometrical meaning of , Definition and equation of Tangent,
dy
Tangent at origin, Angle of intersection of two curves, Definition and equation of Normal,
Cartesian subtangent and subnormal, Tangents and Normals of polar curves, Angle
between radius vector and tangent, Perpendicular from pole to tangent, Pedal equation of
curve, Polar subtangent and polar subnormal, Derivatives of arc (Cartesian and polar
formula).
Curvature and Asymptotes: Curvature, Radius of curvature; Cartesian, Polar and pedal
formula for radius of curvature, Tangential polar form, Centre of curvature, Asymptotes of
algebraic curves, Methods of finding asymptotes, Parallel asymptotes.
Singular Points and Curve Tracing: Regular points and Singular Points of a curve, Point
of inflection, Double Points, Cusp, Node and conjugate points, Curve tracing.
TEXT BOOK on
D ifferential C alculus
(For B.A. and B.Sc. Ist Semester students of Kumaun University)
Kumaun University Semester Syllabus w.e.f. 2016-17
By
A.R. Vasishtha A.K. Vasishtha
Retired Head, Dept. of Mathematics M.Sc., Ph.D.
Meerut College, Meerut C.C.S. University, Meerut
Kumaun
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
, P reface
This book on Differential Calculus has been specially written according to the latest
Syllabus to meet the requirements of the B.A. and B.Sc. Semester-I Students of all
colleges affiliated to Kumaun University.
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, M.D., 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.
July, 2016 — Authors
, Syllabus
D ifferential C alculus
B.A./B.Sc. I Semester
Kumaun University
First Semester – Second Paper
B.A./B.Sc. Paper-II M.M.-50
PAPER II: DIFFERENTIAL CALCULUS
Limit, Continuity and Differentiability: Functions of one variable, Limit of a function (
- Definition), Continuity of a function, Properties of continuous functions, Intermediate
value theorem, Classification of Discontinuities, Differentiability of a function,Rolle 's
Theorem,Mean value theorems and their geometrical interpretations, Applications of
mean value theorems.
Successive Differentiation, Expansions of functions and Indeterminate forms:
Successive Differentiation, nth Differential coefficient of functions,Leibnitz
Theorem;Taylor 's Theorem, Maclaurin 's Theorem,Taylor 's and Maclaurin 's series
expansions .
dx
Tangents and Normals: Geometrical meaning of , Definition and equation of Tangent,
dy
Tangent at origin, Angle of intersection of two curves, Definition and equation of Normal,
Cartesian subtangent and subnormal, Tangents and Normals of polar curves, Angle
between radius vector and tangent, Perpendicular from pole to tangent, Pedal equation of
curve, Polar subtangent and polar subnormal, Derivatives of arc (Cartesian and polar
formula).
Curvature and Asymptotes: Curvature, Radius of curvature; Cartesian, Polar and pedal
formula for radius of curvature, Tangential polar form, Centre of curvature, Asymptotes of
algebraic curves, Methods of finding asymptotes, Parallel asymptotes.
Singular Points and Curve Tracing: Regular points and Singular Points of a curve, Point
of inflection, Double Points, Cusp, Node and conjugate points, Curve tracing.
