Countless people have relied on Anton to learn the difficult concepts of calculus. The new ninth edition continues the tradition of providing an accessible introduction to the field. It improves on the carefully worked and special problems to increase comprehension. New applied exercises demonstrate the usefulness of mathematics. More summary tables and step-by-step summaries are included to offer additional support when learning the concepts. And Quick Check exercises have been revised to more precisely focus on the most important ideas. This book will help anyone who needs to learn calculus and build a strong mathematical foundation.
0. Before Calculus 0.1 Functions 0.2New Functions from Old 0.3Families of Functions 0.4Inverse Functions 1. Limits and Continuity 1.1Limits (An Intuitive Approach) 1.2Computing Limits 1.3Limits at Infinity; End Behavior of a Function 1.4Limits (Discussed More Rigorously) 1.5Continuity 1.6Continuity of Trigonometric Functions 2. The Derivative 2.1Tangent Lines and Rates of Change 2.2The Derivative Function 2.3Introduction to Techniques of Differentiation 2.4The Product and Quotient Rules 2.5Derivatives of Trigonometric Functions 2.6The Chain Rule 2.7Implicit Differentiation 2.8Related Rates 2.9Local Linear Approximation; Differentials 3. The Derivative in Graphing and Applications 3.1Analysis of Functions I: Increase, Decrease, and Concavity 3.2Analysis of Functions II: Relative Extrema; Graphing Polynomials 3.3Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 3.4Absolute Maxima and Minima 3.5Applied Maximum and Minimum Problems 3.6Rectilinear Motion 3.7Newton's Method 3.8Rolle's Theorem; Mean-Value Theorem 4. Integration 4.1An Overview of the Area Problem 4.2The Indefinite Integral 4.3Integration by Substitution 4.4 The Definition of Area as a Limit; Sigma Notation 4.5The Definite Integral 4.6The Fundamental Theorem of Calculus 4.7Rectilinear Motion Revisited: Using Integration 4.8Average Value of a Function and Its Applications 4.9Evaluating Definite Integrals by Substitution 5. Applications of the Definite Integral in Geometry, Science and Engineering 5.1Area Between Two Curves 5.2Volumes by Slicing; Disks and Washers 5.3Volumes by Cylindrical Shells 5.4Length of a Plane Curve 5.5Area of a Surface Revolution 5.6Work 5.7Moments, Centers of Gravity, and Centroids 5.8Fluid Pressure and Force 6. Exponential, Logarithmic, and Inverse Trigonometric Functions 6.1Exponential and Logarithmic Functions 6.2Derivatives and Integrals Involving Logarithmic Functions 6.3Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 6.4Graphs and Applications Involving Logarithmic and Exponential Functions 6.5L'Hˆopital's Rule; Indeterminate Forms 6.6Logarithmic and Other Functions Defined by Integrals 6.7Derivatives and Integrals Involving Inverse Trigonometric Functions 6.8Hyperbolic Functions and Hanging Cubes Ch 7 Principles of Integral Evaluation 7.1 An Overview of Integration Methods 7.2 Integration by Parts 7.3 Integrating Trigonometric Functions 7.4 Trigonometric Substitutions 7.5 Integrating Rational Functions by Partial Fractions 7.6 Using Computer Algebra Systems and Tables of Integrals 7.7 Numerical Integration; Simpson's Rule 7.8 Improper Integrals Ch 8 Mathematical Modeling with Differential Equations 8.1 Modeling with Differential Equations 8,2 Separation of Variables 8.3 Slope Fields; Euler's Method 8.4 First-Order Differential Equations and Applications Ch 9 Infinite Series 9.1 Sequences 9.2 Monotone Sequences 9.3 Infinite Series 9.4 Convergence Tests 9.5 The Comparison, Ratio, and Root Tests 9.6 Alternating Series; Absolute and Conditional Convergence 9.7 Maclaurin and Taylor Polynomials 9.8 Maclaurin and Taylor Series; Power Series 9.9 Convergence of Taylor Series 9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series Ch 10 Parametric and Polar Curves; Conic Sections 10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 10.2 Polar Coordinates 10.3 Tangent Lines, Arc Length, and Area for Polar Curves 10.4 Conic Sections 10.5 Rotation of Axes
Countless people have relied on Anton to learn the difficult concepts of calculus. The new ninth edition continues the tradition of providing an accessible introduction to the field. It improves on the carefully worked and special problems to increase comprehension. New applied exercises demonstrate the usefulness of mathematics. More summary tables and step-by-step summaries are included to offer additional support when learning the concepts. And Quick Check exercises have been revised to more precisely focus on the most important ideas. This book will help anyone who needs to learn calculus and build a strong mathematical foundation.
Table of Contents
0. Before Calculus 0.1 Functions 0.2New Functions from Old 0.3Families of Functions 0.4Inverse Functions 1. Limits and Continuity 1.1Limits (An Intuitive Approach) 1.2Computing Limits 1.3Limits at Infinity; End Behavior of a Function 1.4Limits (Discussed More Rigorously) 1.5Continuity 1.6Continuity of Trigonometric Functions 2. The Derivative 2.1Tangent Lines and Rates of Change 2.2The Derivative Function 2.3Introduction to Techniques of Differentiation 2.4The Product and Quotient Rules 2.5Derivatives of Trigonometric Functions 2.6The Chain Rule 2.7Implicit Differentiation 2.8Related Rates 2.9Local Linear Approximation; Differentials 3. The Derivative in Graphing and Applications 3.1Analysis of Functions I: Increase, Decrease, and Concavity 3.2Analysis of Functions II: Relative Extrema; Graphing Polynomials 3.3Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 3.4Absolute Maxima and Minima 3.5Applied Maximum and Minimum Problems 3.6Rectilinear Motion 3.7Newton's Method 3.8Rolle's Theorem; Mean-Value Theorem 4. Integration 4.1An Overview of the Area Problem 4.2The Indefinite Integral 4.3Integration by Substitution 4.4 The Definition of Area as a Limit; Sigma Notation 4.5The Definite Integral 4.6The Fundamental Theorem of Calculus 4.7Rectilinear Motion Revisited: Using Integration 4.8Average Value of a Function and Its Applications 4.9Evaluating Definite Integrals by Substitution 5. Applications of the Definite Integral in Geometry, Science and Engineering 5.1Area Between Two Curves 5.2Volumes by Slicing; Disks and Washers 5.3Volumes by Cylindrical Shells 5.4Length of a Plane Curve 5.5Area of a Surface Revolution 5.6Work 5.7Moments, Centers of Gravity, and Centroids 5.8Fluid Pressure and Force 6. Exponential, Logarithmic, and Inverse Trigonometric Functions 6.1Exponential and Logarithmic Functions 6.2Derivatives and Integrals Involving Logarithmic Functions 6.3Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 6.4Graphs and Applications Involving Logarithmic and Exponential Functions 6.5L'Hˆopital's Rule; Indeterminate Forms 6.6Logarithmic and Other Functions Defined by Integrals 6.7Derivatives and Integrals Involving Inverse Trigonometric Functions 6.8Hyperbolic Functions and Hanging Cubes Ch 7 Principles of Integral Evaluation 7.1 An Overview of Integration Methods 7.2 Integration by Parts 7.3 Integrating Trigonometric Functions 7.4 Trigonometric Substitutions 7.5 Integrating Rational Functions by Partial Fractions 7.6 Using Computer Algebra Systems and Tables of Integrals 7.7 Numerical Integration; Simpson's Rule 7.8 Improper Integrals Ch 8 Mathematical Modeling with Differential Equations 8.1 Modeling with Differential Equations 8,2 Separation of Variables 8.3 Slope Fields; Euler's Method 8.4 First-Order Differential Equations and Applications Ch 9 Infinite Series 9.1 Sequences 9.2 Monotone Sequences 9.3 Infinite Series 9.4 Convergence Tests 9.5 The Comparison, Ratio, and Root Tests 9.6 Alternating Series; Absolute and Conditional Convergence 9.7 Maclaurin and Taylor Polynomials 9.8 Maclaurin and Taylor Series; Power Series 9.9 Convergence of Taylor Series 9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series Ch 10 Parametric and Polar Curves; Conic Sections 10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 10.2 Polar Coordinates 10.3 Tangent Lines, Arc Length, and Area for Polar Curves 10.4 Conic Sections 10.5 Rotation of Axes