Calculus (Hardbound - 2013)

Calculus is a branch of mathematics that deals with limits and the differentiation and integration of functions of one or more variables. In it, analysis or calculation is made using a special symbolic notation. It has two major branches: (i) differential calculus, which concerns the rates of change and slopes of curves, and (ii) integral calculus, which concerns the accumulation of quantities and the areas under curves. These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Calculus is widely used to solve many problems that algebra alone cannot. It is a major part of modern Mathematics. A course in calculus is considered a gateway to other, more advanced courses in Mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

The book has been prepared to cater to the needs of students of Mathematics at undergraduate level. The subject matter has been divided into three sections. Section-I explains, in three chapters, limit and continuity, types of discontinuities and differentiability of functions; differentiation and Leibnitz Theorem; and partial differentiation and Euler’s Theorem on homogeneous functions.

Section-II deals with tangents and normals with evaluations thereof; curvature and various formulas relating to it; asymptote, the condition of the existence of asymptote and other pertinent aspects; the two types of singular points, i.e. the point of inflexion and multiple points and their applications in concavity and convexity; and tracing of various types of curves.

Section-III takes up Mean Value Theorems; Maclaurin series; the concepts of maxima and minima; and indeterminate forms, De L’Hospital’s Rule and algebraic methods used to shorten the work of evaluating the given limits which assume the indeterminate forms.

Equations, theorems, rules and problems have been explained in simple language and lucid manner for easy understanding by the readers. Illustrative examples have also been given. There are exercises in all the chapters to give the students a feel of the type of questions they should expect in the examination. Answers to all the exercises have been provided. The book will be very useful for the students of Mathematics. It will also help those preparing for competitive examinations involving mathematical problems.

Hari Kishan is Senior Reader in Mathematics at Kishori Raman Postgraduate College, Mathura, affiliated to Dr. Bhim Rao Ambedkar University, Agra. He has 36 years experience of teaching degree classes. He completed his M.Sc. from B.S.A. College, Mathura in 1971 and obtained a record percentage of marks for which he was awarded Gold Medal by Agra University. He received Ph.D. in Mathematics (Fluid Dynamics) in 1981 from the same university. His topic of research was “Flow of Homogeneous or Stratified Viscous Fluids”. He has published numerous research papers in several mathematical journals of repute. Besides, he is a well-known author of a large number of books on Mathematics including Trigonometry, Integral Calculus, Coordinate Geometry of Two Dimensions, Matrices, Modern Algebra, Theory of Equations, Dynamics, Statics, Hydro Statics, Real Analysis, Numerical Analysis and Sure Success in Convergence.