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CALCULUS, GEOMETRY AND VECTOR ANALYSIS
Dr. Debasish Sengupta
First Published: 2024
ISBN: 978-93-94107-88-5
Pages: 520

CONTENTS

UNIT I : CALCULUS
- Chapter 1 : Differentiability of a Function; Higher Order Derivatives
- Chapter 2 : Indeterminate Forms
- Chapter 3 : Integration by Successive Reduction
- Chapter 4 :Length of a Plane Curve
- Chapter 5 : Area enclosed by a Plane Curve
- Chapter 6 :Volumes and Surfaces of Revolution

UNIT II : GEOMETRY
- Chapter 7 : Conics in Two Dimensional Rectangular Cartesian System of Co-ordinates
- Chapter 8 : Conics in Polar System of Co-ordinates
- Chapter 9 : Quadric Surfaces (Quadrics or Conicoids)
- Chapter 10 : Generating Lines

UNIT III : VECTOR ANALYSIS
- Chapter11 : Vector Algebra; Applications to Geometry and Mechanics
- Chapter 12 : Calculus of Vector Functions (Single Variable)

ABOUT THE BOOK: This textbook is prepared to serve as an updated companion to the students studying mathematics in the undergraduate major and minor courses of studies as introduced in NEP. The book comprises of twelve chapters which are considered in three basic units. The first unit considers Calculus which, in six chapters, discusses thoroughly the criterion of differentiability of functions, higher order derivatives, indeterminate forms, integration by successive reductions and certain applications of integral calculus which enable one to determine the length of a plane curve, area enclosed by plane curves, volume and surface of revolutions of a region enclosed by plane curves. The second unit considers Geometry which, in four chapters, analyses a depth discussions on the basic concepts of conics under the Cartesian and Polar system of co-ordinates, Quadric surfaces (Conicoids) and Generating lines. Finally the third unit considers Vector Analysis which, in its two chapters, discusses thoroughly the complete concept of vector with certain of its applications in algebra and geometry, differentiation and integration of vector functions of single variable. Each chapter is designed with sufficient number of worked-out examples and exercise for the practice purpose of the students. However the book is sure to be an excellent companion to all aspiring students studying mathematics in the undergraduate level of studies in any university of India.

ABOUT THE AUTHOR: Dr. Debasish Sengupta has a brilliant academic record. He has published many research articles on Stability theory and Eigenvalue problems of a System of second order Differential Equations with a turning point in a number of reputed national and international journals. He has taught many important topics on mathematics like Advanced Geometry of two and three dimensions, Vector algebra and Analysis, Differential Equations, Advanced higher algebra, Real and complex analysis, to the students of undergraduate and postgraduate levels under the University of Calcutta. Dr. Sengupta has also authored five other books (i) Application of Calculus, (ii) Introduction to Differential Equations, (iii) Elementary Multivariate Calculus and (iv) Advanced Geometry and Vector and (v) Advanced Calculus (Applications) published by Books & Allied (P) Ltd. designed primarily for the students studying mathematics at the undergraduate and postgraduate levels but are also useful for the students studying Engineering and Physics Honours.