Wiley s Mathematics for IIT JEE Main and Advanced Calculus 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