Calculus of One Variable

¿PrefaceTo the Instructor1 Preliminaries 1.1 Sets of Real Numbers 1.2 Absolute Value and Inequalities 1.3 The Cartesian Plane 1.4 Lines 1.5 Equations of a Straight Line 1.6 Functions 1.7 Operations with Functions 1.8 Shifting the Graphs of Functions (Optional) Review Exercises for Chapter One2 Limits And Derivatives 2.1 Introduction to the Derivative 2.2 The Calculation of Limits 2.3 The Limit Theorems 2.4 Infinite Limits and Limits at Infinity 2.5 Tangent Lines and Derivatives 2.6 The Derivative as a Rate of Change 2.7 Continuity 2.8 The Theory of Limits (Optional) Review Exercises for Chapter Two3 More About Derivatives 3.1 Some Differentiation Formulas 3.2 The Product and Quotient Rules 3.3 The Derivative of Composite Functions: The Chain Rule 3.4 The Derivative of a Power Function 3.5 The Derivatives of the Trigonometric Functions 3.6 Implicit Differentiation 3.7 Higher-Order Derivatives 3.8 Approximation and Differentials Review Exercises for Chapter Three4 Applications Of The Derivative 4.1 Related Rates of Change 4.2 The Mean Value Theorem 4.3 Elementary Curve Sketching I: Increasing and Decreasing Functions and the First Derivative Test 4.4 Elementary Curve Sketching II: Concavity and the Second Derivative Test 4.5 The Theory of Maxima and Minima 4.6 Maxima and Minima: Applications 4.7 Some Applications in Economics (Optional) 4.8 Newton's Method for Solving Equations Review Exercises for Chapter Four5 The Integral 5.1 Introduction 5.2 Antiderivatives 5.3 The S Notation 5.4 Approximations to Area 5.5 The Definite Integral 5.6 The Fundamental Theorem of Calculus 5.7 Integration by Substitution 5.8 The Area Between Two Curves 5.9 Work, Power, and Energy (Optional) 5.10 Additional Integration Theory (Optional) Review Exercises for Chapter Five6 Exponentials And Logarithms 6.1 Inverse Functions 6.2 The Exponential and Logarithmic Functions I 6.3 The Derivatives and Integrals of logax and ax 6.4 The Exponential and Logarithmic Functions II 6.5 Differentiation and Integration of More General Exponential and Logarithmic Functions 6.6 Differential Equations of Exponential Growth and Decay 6.7 Applications in Economics (Optional) 6.8 A Model for Epidemics (Optional) Review Exercises for Chapter Six7 More On Trigonometric Functions And The Hyperbolic Functions 7.1 Integration of Trigonometric Functions 7.2 The Inverse Trigonometric Functions 7.3 Periodic Motion (Optional) 7.4 The Hyperbolic Functions 7.5 The Inverse Hyperbolic Functions (Optional) Review Exercises for Chapter Seven8 Techniques Of Integration 8.1 Review of the Basic Formulas of Integration 8.2 Integration by Parts 8.3 Integrals of Certain Trigonometric Functions 8.4 The Idea Behind Integration by Substitution 8.5 Integrals Involving va2 - x2, va2 + x2, and vx2 - a2: Trigonometric Substitutions 8.6 The Integration of Rational Functions I: Linear and Quadratic Denominators 8.7 The Integration of Rational Functions II: The Method of Partial Fractions 8.8 Other Substitutions 8.9 Using the Integral Tables 8.10 Numerical Integration Review Exercises for Chapter Eight9 Further Applications Of The Definite Integral 9.1 Volumes 9.2 Arc Length 9.3 Surface Area 9.4 Center of Mass and the First Moment 9.5 The Centroid of a Plane Region 9.6 Moments of Inertia and Kinetic Energy (Optional) 9.7 Fluid Pressure (Optional) Review Exercises for Chapter Nine10 Topics In Analytic Geometry 10.1 The Ellipse and Translation of Axes 10.2 The Parabola 10.3 The Hyperbola 10.4 Second-Degree Equations and Rotation of Axes Review Exercises for Chapter Ten11 Polar Coordinates 11.1 The Polar Coordinate System 11.