About the Book

The new edition of Calculus continues to bring together the best of both new and traditional curricula in an effort to meet the needs of even more instructors teaching calculus. The author team's extensive experience teaching from both traditional and innovative books and their expertise in developing innovative problems put them in an unique position to make this new curriculum meaningful for those going into mathematics and those going into the sciences and engineering. This new text exhibits the same strengths from earlier editions including an emphasis on modeling and a flexible approach to technology.

About the Author

Howard Anton he joined the Mathematics Department at Drexel University, where he taught full time until 1983. Since that time he has been an adjunct professor at Drexel and has devoted the majority of his time to textbook writing and activities for mathematical associations. Dr. Anton was president of the EPADEL Section of the Mathematical Association of America (MAA), Served on the board of Governors of that organization, and guided the creation of the Student Chapters of the MAA. He has published numerous research papers in functional analysis, approximation theory and topology, as well as pedagogical papers.

Table of Contents:
Before Calculus 0.1 Functions 0.2 New Functions from Old 0.3 Families of Functions 0.4 Inverse Functions Limits and Continuity 1.1 Limits (An Intuitive Approach) 1.2 Computing Limits 62 1.3 Limits at Infinity; End Behavior of a Function 1.4 Limits (Discussed More Rigorously) 1.5 Continuity 1.6 Continuity of Trigonometric Functions The Derivative 2.1 Tangent Lines and Rates of Change 2.2 The Derivative Function 2.3 Introduction to Techniques of Differentiation 2.4 The Product and Quotient Rules 2.5 Derivatives of Trigonometric Functions 2.6 The Chain Rule 2.7 Implicit Differentiation 2.8 Related Rates 2.9 Local Linear Approximation; Differentials The Derivative in Graphing and Applications 3.1 Analysis of Functions I: Increase, Decrease and Concavity 3.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 3.3 Analysis of Functions III: Rational Functions, Cusps and Vertical Tangents 3.4 Absolute Maxima and Minima 3.5 Applied Maximum and Minimum Problems 3.6 Rectilinear Motion 3.7 Newton's Method 3.8 Rolle's Theorem; Mean-Value Theorem Integration 4.1 An Overview of the Area Problem 4.2 The Indefinite Integral 4.3 Integration by Substitution 4.4 The Definition of Area as a Limit; Sigma Notation 4.5 The Definite Integral 4.6 The Fundamental Theorem of Calculus 4.7 Rectilinear Motion Revisited Using Integration 4.8 Average Value of a Function and its Applications 4.9 Evaluating Definite Integrals by Substitution Applications of The Definite Integral in Geometry, Science and Engineering 5.1 Area Between Two Curves 5.2 Volumes by Slicing; Disks and Washers 5.3 Volumes by Cylindrical Shells 5.4 Length of a Plane Curve 5.5 Area of a Surface of Revolution 5.6 Work 5.7 Moments, Centers of Gravity and Centroids 5.8 Fluid Pressure and Force Exponential, Logarithmic and Inverse Trigonometric Functions 6.1 Exponential and Logarithmic Functions 6.2 Derivatives and Integrals Involving Logarithmic Functions 6.3 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 6.4 Graphs and Applications Involving Logarithmic and Exponential Functions 6.5 L'Hôpital's Rule; Indeterminate Forms 6.6 Logarithmic and Other Functions Defined by Integrals 6.7 Derivatives and Integrals Involving Inverse Trigonometric Functions 6.8 Hyperbolic Functions and Hanging Cables 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 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 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 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; Second-Degree Equations 10.6 Conic Sections in Polar Coordinates Three-Dimensional Space; Vectors 11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 11.2 Vectors 11.3 Dot Product; Projections 11.4 Cross Product 11.5 Parametric Equations of Lines 11.6 Planes in 3-Space 11.7 Quadric Surfaces 11.8 Cylindrical and Spherical Coordinates Vector-Valued Functions 12.1 Introduction to Vector-Valued Functions 12.2 Calculus of Vector-Valued Functions 12.3 Change of Parameter; Arc Length 12.4 Unit Tangent, Normal and Binormal Vectors 12.5 Curvature 12.6 Motion Along a Curve 12.7 Kepler's Laws of Planetary Motion Partial Derivatives 13.1 Functions of Two or More Variables 13.2 Limits and Continuity 13.3 Partial Derivatives 13.4 Differentiability, Differentials and Local Linearity 13.5 The Chain Rule 13.6 Directional Derivatives and Gradients 13.7 Tangent Planes and Normal Vectors 13.8 Maxima and Minima of Functions of Two Variables 13.9 Lagrange Multipliers Multiple Integrals 14.1 Double Integrals 14.2 Double Integrals over Nonrectangular Regions 14.3 Double Integrals in Polar Coordinates 14.4 Surface Area; Parametric Surfaces 14.5 Triple Integrals 14.6 Triple Integrals in Cylindrical and Spherical Coordinates 14.7 Change of Variables in Multiple Integrals; Jacobians 14.8 Centers of Gravity using Multiple Integrals Topics In Vector Calculus 15.1 Vector Fields 15.2 Line Integrals 15.3 Independence of Path; Conservative Vector Fields 15.4 Green's Theorem 15.5 Surface Integrals 15.6 Applications of Surface Integrals; Flux 15.7 The Divergence Theorem 15.8 Stokes' Theorem A Appendices A Graphing Functions Using Calculators and Computer Algebra Systems B Trigonometry Review C Solving Polynomial Equations D Selected Proofs Answers To Odd-Numbered Exercises Index I Web Appendices (Online Only) E Real Numbers, Intervals and Inequalities F Absolute Value G Coordinate Planes, Lines and Linear Functions H Distance, Circles and Quadratic Equations I Early Parametric Equations Option J Mathematical Models K The Discriminant L Second-Order Linear Homogeneous Differential Equations Web Projects: Expanding The Calculus Horizon (Online Only) Blammo The Human Cannonball Comet Collision Hurricane Modeling Iteration and Dynamical Systems Railroad Design Robotics