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Calculus - the most important topic for IIT-JEE aspirants - constitutes a major part of modern mathematics. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics. This book has been written by a pioneer teacher associated with IIT-JEE coaching, Dr. G.S.N. Murti, along with Dr. K.P.R. Sastry, who had an illustrious career in academia. The book has a two-fold advantage: (a) Conceptual strength provided by accurate, precise but sufficient coverage of topics; (b) solved and unsolved problems as per IIT-JEE pattern for strengthening concepts. The main idea is to make students understand the theory behind to enable them to strategize a given problem and tactically solve it. Special Features · Eminent Authorship · Clear, Concise, and Inviting Writing Style, Tone and Layout · Optimum Balance of Theory and Applications Table of Content Pre-Requisites · Sets · Real Numbers · Bounded Set, Least Upper Bound and Greatest Lower Bound · Completeness Property of and Archimedes’ Principle · Relational Numbers, Irrational Numbers and Density Property of Rational Numbers · Intervals · Absolute Value of a Real Number Functions, Limits, Continuity Sequences and Series · Functions: Varieties · Functions and Their Inverse · Even and Odd Functions, Periodic Functions · Graphs of Functions · Construction of Graphs and Transforming Theorem · Limit of a Function · Some Useful Inequalities · Continuity · Properties of Continuous Functions · Infinite Limits · Sequences and Series · Infinite Series Derivative and Differentiability · Derivatives: An Introduction · Derivatives of Some Standard Functions · Special Methods of Differentiation · Successive Derivatives of a Function Applications of Differentiation · Tangents and Normals · Rate Measure · Mean Value Theorems · Maxima-Minima · Convexity, Concavity and Points of Inflection · Cauchy’s Mean Value Theorem and L’Hospital’s Rule Indefinite Integral · Introduction · Examples on Direct Integration Using Standard Integrals · Integration by Substitution · Integration by Parts · Fundamental Classes of Integrable Functions Definite Integral, Areas and Differential Equations · Definite Integral · Areas · Differential Equations Worked-Out Problems Exercises Answers Index

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