Calculus: One and Several Variables,10ed, An Indian Adaptation

Chapter 1: Limits and Continuity  

1.1 The Limit Process (An Intuitive Introduction)

1.2 Definition of Limit

1.3 Some Limit Theorems

1.4 Continuity

1.5 The Pinching Theorem; Trigonometric Limits

1.6 Two Basic Theorems

Chapter 2: The Derivative; The Process of Differentiation

2.1 The Derivative

2.2 Some Differentiation Formulas

2.3 The d/dx Notation; Derivatives of Higher Order

2.4 The Derivative as a Rate of Change

2.5 The Chain Rule

2.6 Differentiating the Trigonometric Functions

2.7 Implicit Differentiation; Rational Powers

Chapter 3: The Mean-Value Theorem; Applications of the First and Second Derivatives

3.1 The Mean-Value Theorem

3.2 Increasing and Decreasing Functions

3.3 Local Extreme Values

3.4 Endpoint Extreme Values; Absolute Extreme Values

3.5 Some Max-Min Problems

3.6 Concavity and Points of Inflection

3.7 Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps

3.8 Some Curve Sketching

3.9 Velocity and Acceleration; Speed

3.10 Related Rates of Change Per Unit Time

3.11 Differentials

3.12 Newton-Raphson Approximations

Chapter 4: Integration

4.1 An Area Problem; A Speed-Distance Problem

4.2 The Definite Integral of a Continuous Function

4.3 The Function f(x) =