Mathematics for IIT-JEE: Calculus (Volume - 3)

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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 strategist a given problem and tactically solve it. Key Features Eminent Authorship Clear, Concise, and Inviting Writing Style, Tone and Layout Optimum Balance of Theory and Applications Excellent Pedagogy Theorems and Corollaries (with proofs) Solved Examples Examples Quick Look Try It Out Worked Out Problems Summary Exercises Answers Worked-Out Problems and End-Of-Chapter Material as per IIT-JEE Assessment Pattern Single Correct Choice Type Multiple Correct Choice Type Matrix-Match Type Comprehension-Type Assertion-Reasoning Type Integer Answer Type

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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. In addition to being a great teacher, Dr. Murti is also considered a master trainer and mentor by a huge community of Mathematics teachers who prepare students for engineering entrance examinations. 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. Table of Contents 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 Worked-Out Problems Exercises Answers Derivative and Differentiability Derivatives: An Introduction Derivatives of Some Standard Functions Special Methods of Differentiation Successive Derivatives of a Function Worked-Out Problems Summary Exercises Answers 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 Worked-Out Problems Summary Exercises Answers Indefinite Integral Introduction Examples on Direct Integration Using Standard Integrals Integration by Substitution Integration by Parts Fundamental Classes of Integrable Functions Worked-Out Problems Exercises Answers Definite Integral, Areas and Differential Equations Definite Integral Areas Differential Equations Worked-Out Problems Exercises Answers Index