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Mathematics for IIT JEE Main and Advanced Calculus Vol-3 by GSN Murti, KPR Sastry



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Mathematics for IIT JEE Main and Advanced Calculus by Dr. GSN Murti , Senior Mathematics Faculty at Narayana IIT Academy, Spark Batch, AC Campus, Visakhapatnam, AP, India and Dr. KPR Sastry , Professor of Mathematics, Department of Mathematics, Andhra University, India.

Mathematics for IIT JEE Main and Advanced Calculus by GSN Murti, KPR Sastry cover the following topics.

  • 0 Pre-Requisites
    0.1 Sets
    0.2 Real Numbers
    0.3 Bounded Set, Least Upper Bound and Greatest Lower Bound
    0.4 Completeness Property of  and Archimedes’ Principle
    0.5 Rational Numbers, Irrational Numbers and Density Property of Rational Numbers
    0.6 Intervals
    0.7 Absolute Value of a Real Number

  • 1. Functions, Limits, Continuity, Sequences and Series
    1.1 Functions: Varieties
    1.2 Functions and Their Inverse
    1.3 Even and Odd Functions, Periodic Functions
    1.4 Graphs of Functions
    1.5 Construction of Graphs and Transforming Theorem
    1.6 Limit of a Function
    1.7 Some Useful Inequalities
    1.8 Continuity
    1.9 Properties of Continuous Functions
    1.10 Infinite Limits
    1.11 Sequences and Series
    1.12 Infinite Series
    Worked-Out Problems
    Exercises
    Answers

  • 2. Derivative and Differentiability
    2.1 Derivatives: An Introduction
    2.2 Derivatives of Some Standard Functions
    2.3 Special Methods of Differentiation
    2.4 Successive Derivatives of a Function
    Worked-Out Problems
    Summary
    Exercises
    Answers

  • 3. Applications of Differentiation
    3.1 Tangents and Normals
    3.2 Rate Measure
    3.3 Mean Value Theorems
    3.4 Maxima–Minima
    3.5 Convexity, Concavity and Points of Inflection
    3.6 Cauchy’s Mean Value Theorem and L’Hospital’s Rule
    Worked-Out Problems
    Summary
    Exercises
    Answers

  • 4. Indefinite Integral
    4.1 Introduction
    4.2 Examples on Direct Integration Using Standard Integrals
    4.3 Integration by Substitution
    4.4 Integration by Parts
    4.5 Fundamental Classes of Integrable Functions
    Worked-Out Problems
    Exercises
    Answers

  • 5. Definite Integral, Areas and Differential Equations
    5.1 Definite Integral
    5.2 Areas
    5.3 Differential Equations
    Worked-Out Problems
    Exercises
    Answers
    Index

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