# Wiley's Mathematics for JEE (Main & Advanced): Calculus, Vol 3

ISBN: 9788126569069

644 pages

## Description

This book has been written by a pioneer teacher associated with IIT-JEE coaching, Dr. G.S.N. Murti, along with Dr. U.M. Swamy who had an illustrious career as a renowned mathematician. The topics covered in this book – 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.

Chapter 0: 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

Chapter 1: 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

Chapter 2: Derivative and Differentiability

- Derivatives: An Introduction
- Derivatives of Some Standard Functions
- Special Methods of Differentiation
- Successive Derivatives of a Function

Chapter 3: 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

Chapter 4: Indefinite Integral

- Introduction
- Examples on Direct Integration Using Standard Integrals
- Integration by Substitution
- Integration by Parts
- Fundamental Classes of Integrable Functions

Chapter 5: Definite Integral, Areas and Differential Equations

- Definite Integral
- Areas
- Differential Equations

Worked-Out Problems

Exercises

Answers

Appendix A: Additional Practice Problems

Index