Wiley s Mathematics for IIT JEE Main and Advanced Calculus Vol 3 Maestro Series Dr. G S N Murti Dr. K P R Sastry

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Wiley s Mathematics for IIT JEE Main and AdvancedCalculus Vol 3 Maestro Series Dr. G S N Murti Dr. K P R Sastry Cover......Page 2 Half Title......Page 4 Title Page......Page 6 Copyright......Page 7 Dedication......Page 8 Acknowledgments......Page 10 Features and Benefits at a Glance......Page 11 About the Cover Picture......Page 12 A. PEDAGOGY......Page 13 B. WORKED-OUT PROBLEMS AND ASSESSMENT – AS PER IIT-JEE PATTERN......Page 16 BOOK FEEDBACK FORM......Page 22 Contents......Page 24 0 Pre-Requisites......Page 26 0.1 Sets......Page 27 0.2 Real Numbers......Page 29 0.3 Bounded Set, Least Upper Bound and Greatest Lower Bound......Page 31 0.4 Completeness Property of R and Archimedes’ Principle......Page 32 0.6 Intervals......Page 34 0.7 Absolute Value of a Real Number......Page 36 1 Functions, Limits, Continuity, Sequences and Series......Page 38 1.1 Functions: Varieties......Page 39 1.2 Functions and Their Inverse......Page 41 1.3 Even and Odd Functions, Periodic Functions......Page 43 1.4 Graphs of Functions......Page 46 1.5 Construction of Graphs and Transforming Theorem......Page 48 1.6 Limit of a Function......Page 51 1.7 Some Useful Inequalities......Page 65 1.8 Continuity......Page 70 1.9 Properties of Continuous Functions......Page 79 1.10 Infinite Limits......Page 83 1.11 Sequences and Series......Page 84 1.12 Infinite Series......Page 94 Worked-Out Problems......Page 99 Exercises......Page 157 Answers......Page 167 2 Derivative and Differentiability......Page 170 2.1 Derivatives: An Introduction......Page 171 2.2 Derivatives of Some Standard Functions......Page 179 2.3 Special Methods of Differentiation......Page 190 2.4 Successive Derivatives of a Function......Page 194 Worked-Out Problems......Page 196 Summary......Page 236 Exercises......Page 239 Answers......Page 245 3 Applications of Differentiation......Page 248 3.1 Tangents and Normals......Page 249 3.2 Rate Measure......Page 254 3.3 Mean Value Theorems......Page 256 3.4 Maxima–Minima......Page 262 3.5 Convexity, Concavity and Points of Inflection......Page 271 3.6 Cauchy’s Mean Value Theorem and L’Hospital’s Rule......Page 273 Worked-Out Problems......Page 278 Summary......Page 360 Exercises......Page 363 Answers......Page 371 4 Indefinite Integral......Page 374 4.1 Introduction......Page 375 4.2 Examples on Direct Integration Using Standard Integrals......Page 378 4.3 Integration by Substitution......Page 385 4.4 Integration by Parts......Page 408 4.5 Fundamental Classes of Integrable Functions......Page 421 Worked-Out Problems......Page 431 Exercises......Page 473 Answers......Page 475 5 Definite Integral, Areas and Differential Equations......Page 478 5.1 Definite Integral......Page 479 5.2 Areas......Page 500 5.3 Differential Equations......Page 505 Worked-Out Problems......Page 517 Exercises......Page 613 Answers......Page 617 Index......Page 620 Back Cover......Page 625