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ADVANCED CALCULUS (Applications) by Dr. Debasish Sengupta

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Dr. Debasish Sengupta
First Published: 2020
Second Edition: 2023
Reprints: 1
ISBN: 978-93-94107-66-3
Pages: 504


- Chapter 1 : Hyperbolic Functions
- Chapter 2 : Differentiability of a Function; Higher Order Derivatives
- Chapter 3 : Indeterminate Forms
- Chapter 4 : Integration by Successive Reduction

- Chapter 5 : Preliminaries
- Chapter 6 : Curvature, Evolute and Involute
- Chapter 7 : Envelope
- Chapter 8 : Concavity, Convexity, and Point of Inflexion
- Chapter 9 : Rectilinear Asymptotes
- Chapter 10 : Length of a Plane Curve
- Chapter 11 : Area enclosed by a Plane Curve
- Chapter 12 : Volumes and Surfaces of Revolution
- Chapter 13 : Tracing of Curves and Surfaces

- Chapter 14 : Applications in Business, Economics and Life Sciences

ABOUT THE BOOK: “Advanced Calculus (Applications)” has been written to cater to students who are studying Mathematics at the undergraduate level. There are fourteen chapters in the book which are divided into three units. Four important chapters on Hyperbolic functions, Successive differentiations, Indeterminate forms and Successive reduction formulae are discussed in the first unit. Nine chapters concerned with the applications of Differential and Integral Calculus to characterise certain geometrical entities like Tangent, Normal, Singular points, Curvature, Envelope, Concavity, Convexity, Asymptotes, Quadrature, Rectification, Surface-area and volume of solids of revolution, Tracing of curves, conics and conicoids etc. under the rectangular cartesian and polar system of co-ordinates are thoroughly dealt with in the second unit. The third unit containing the last chapter deals with the application of calculus in Business, Economics, and Life sciences. In each chapter, numerous solved examples have been presented after discussion of the theories, and many problems are included in the exercises for the readers to work out and gain confidence in tackling problems in the final examinations. The book is sure to be a good companion for all aspiring students studying mathematics at the advanced levels.

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 several 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 at the University of Calcutta. Dr. Sengupta has also authored four other books (i) Application of Calculus, (ii) Introduction to Differential Equations, (iii) Elementary Multivariate Calculus, and (iv) Advanced Geometry and Vector 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.

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