## Details

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.

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

For students preparing for Engineering Entrance Examinations

Dr. G.S.N. Murti: An eminent mathematician, accomplished author and a dedicated teacher, Dr. G.S.N. Murti brings vast knowledge and experience to teaching the fundamental concepts of pure Mathematics. Dr. Murti has taught Mathematics at degree level for 27 years before moving onto coach prospective IIT-JEE candidates. Over the last 25 years, his name has become synonymous with the best quality IIT-JEE coaching in Mathematics.

Dr. K.P.R. Sastry: Dr. K.P.R. Sastry is an illustrious Mathematician with 50 years of teaching and research experience who served at various levels in the Department of Mathematics at Andhra University. He was also the Director at Dr. L.B. College for Post Graduate Courses, Visakhapatnam. Dr. Sastry is acclaimed as a distinguished teacher in the teaching community.