Calculus and its applications

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Contents

Front Cover; Calculus and its Applications; Copyright Page; PREFACE; Table of Contents;
CHAPTER I. FUNDAMENTAL IDEAS; 1.1 The Concept of Function; 1.2 Exercises; 1.3 Introduction to the Limit Concept; 1.4 Exercises; 1.5 Intuitive Definition of Limit; 1.6 Exercises; 1.7 A Precising Definition of Limit; 1.8 Exercises; 1.9 Limits Involving Infinity; 1.10 Operations on Limits; 1.11 Exercises; 1.12 Continuity; 1.13 Exercises; 1.14 An Interpretation of Ratio; 1.15 Average Rate of Change; 1.16Exercises; 1.17 Use of Limits in Defining The Slope of a Curve ata Point; 1.18 Exercises

1.19 Generalized Instantaneous Rate of Change1.20 Exercises; 1.21 Units of Instantaneous Rates; CHAPTER II. DERIVATIVE; 2.1 Differentiation of Algebraic Functions by Formula; 2.2 Exercises; 2.3 Proof of Differentiation Rules I
VIII; 2.4 Proof of Formula IX; 2.5 Proof of Formula X; 2.6 Exercises; CHAPTER III. DIFFERENTIATION AND APPLICATIONS; 3.1 The Use of Derivatives in Sketching Graphs of Algebraic Functions; 3.2 Exercises; 3.3 The Use of Derivatives in Examining Functions for ExtremeValues; 3.4 Exercises; 3.5 Differentiation of Implicit Functions; 3.6 Exercises; 3.7 Time Rates

3.8 Exercises
CHAPTER IV. HIGHER ORDER DERIVATIVES; 4.1 Derivatives of Higher Order; 4.2 Exercises; 4.3 The Use of the Second Derivative in Curve Sketching; 4.4Exercises; 4.5The Second Derivative in Linear Motion; 4.6Exercises;
CHAPTER V. DIFFERENTIATION OF THE TRIGONOMETRIC FUNCTIONS; 5.1 Derivatives of sin v and cos v; 5.2Exercises; 5.3 The FunctionsArcsin x and Arccos x and Their Derivatives; 5.4 Differentiation Formulas for the SixInverse Trigonometric Fractions; 5.5 Exercises;
CHAPTER VI. EXPONENTIAL AND LOGARITHMIC FUNCTIONS; 6.1 Laws of Exponents; 6.2 The Exponential Function

6.3 The Logarithmic Function6.4 Laws of Logarithms; 6.5 TheNumber; 6.6 The Derivative oflog; 6.7 The Derivativeof; 6.8 Exercises;
CHAPTER VII. DIFFERENTIALS AND PARAMETRIC EQUATIONS; 7.1 Differentials; 7.2 Exercises; 7.3 Parametric Equations and Curvature; 7.4 Exercises; 7.5 Derivative of Arc Length; 7.6 Curvature; 7.7 Circle of Curvature; 7.8 Exercises; 7.9 Tangents to Polar Curves; 7.10 Exercises;
CHAPTER VIII. VECTORS; 8.1 Introduction; 8.2 Definitions of Vector and Scalar Quantities; 8.3 Geometrical Representation of Vectors; 8.4 Components; 8.5 Differentiation of Vectors; 8.6 Exercises

CHAPTER IX. ANTI-DIFFERENTIATION9.1 Integration, The Inverse of Differentiation; 9.2 Constant of Integration; 9.3 Exercises; 9.4 Rules and Formulas for Integration; 9.5 Exercises; 9.6 Rules for Integration; 9.7 Integration by Standard Formulas; 9.8 Exercises; CHAPTER X. SEPARABLE DIFFERENTIAL EQUATIONS; 10.1 Introduction; 10.2 Solving Differential Equations; 10.3 Integrating Both Sides
10.4 Applications to Geometry; 10.5 Exercises; 10.6 Applications to Physical Problems; 10.7 Exercises on Motion; 10.8 Exercises on Physical Problems; CHAPTER XI. DEFINITE INTEGRAL; 11.1 Introduction

Summary

Calculus and Its Applications.

Publication date: 1963
Series: A Pergamon Press book
ISBN: 9781483168128 (electronic bk.); 1483168123 (electronic bk.); 1483195600; 9781483195605