Overview

In the newly revised Twelfth Edition of Calculus, an expert team of mathematicians delivers a rigorous and intuitive exploration of calculus, introducing polynomials, rational functions, exponentials, logarithms, and trigonometric functions late in the text. Using the Rule of Four, the authors present mathematical concepts from verbal, algebraic, visual, and numerical points of view. The book includes numerous exercises, applications, and examples that help readers learn and retain the concepts discussed within.

Full Product Details

Author:   Howard Anton (Drexel University) ,  Irl C. Bivens (Davidson College) ,  Stephen Davis (Davidson College)
Publisher:   John Wiley & Sons Inc
Imprint:   John Wiley & Sons Inc
Edition:   12th Revised edition
Dimensions:   Width: 21.30cm , Height: 4.30cm , Length: 27.70cm
Weight:   2.200kg
ISBN:  

9781119778127

ISBN 10:   1119778123
Pages:   1152
Publication Date:   02 November 2021
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Loose-leaf
Publisher's Status:   Active
Availability:   Available To Order  
We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately.

Table of Contents

Preface vii Supplements ix Acknowledgments xi The Roots of Calculus xv 1 Limits and Continuity 1 1.1 Limits (An Intuitive Approach) 1 1.2 Computing Limits 13 1.3 Limits at Infinity; End Behavior of a Function 21 1.4 Limits (Discussed More Rigorously) 30 1.5 Continuity 39 1.6 Continuity of Trigonometric Functions 50 2 The Derivative 77 2.1 Tangent Lines and Rates of Change 77 2.2 The Derivative Function 87 2.3 Introduction to Techniques of Differentiation 98 2.4 The Product and Quotient Rules 105 2.5 Derivatives of Trigonometric Functions 110 2.6 The Chain Rule 114 2.7 Implicit Differentiation 124 2.8 Related Rates 142 2.9 Local Linear Approximation; Differentials 149 3 The Derivative in Graphing and Applications 169 3.1 Analysis of Functions I: Increase, Decrease, and Concavity 169 3.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 180 3.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 189 3.4 Absolute Maxima and Minima 200 3.5 Applied Maximum and Minimum Problems 208 3.6 Rectilinear Motion 222 3.7 Newton's Method 230 3.8 Rolle's Theorem; Mean-Value Theorem 235 4 Integration 249 4.1 An Overview of the Area Problem 249 4.2 The Indefinite Integral 254 4.3 Integration by Substitution 264 4.4 The Definition of Area as a Limit; Sigma Notation 271 4.5 The Definite Integral 281 4.6 The Fundamental Theorem of Calculus 290 4.7 Rectilinear Motion Revisited Using Integration 302 4.8 Average Value of a Function and its Applications 310 4.9 Evaluating Definite Integrals by Substitution 315 5 Applications of the Definite Integral in Geometry, Science, and Engineering 336 5.1 Area Between Two Curves 336 5.2 Volumes by Slicing; Disks and Washers 344 5.3 Volumes by Cylindrical Shells 354 5.4 Length of a Plane Curve 360 5.5 Area of a Surface of Revolution 365 5.6 Work 370 5.7 Moments, Centers of Gravity, and Centroids 378 5.8 Fluid Pressure and Force 387 6 Exponential, Logarithmic, and Inverse Trigonometric Functions 336 6.1 Exponential and Logarithmic Functions 336 6.2 Derivatives and Integrals Involving Logarithmic Functions 347 6.3 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 353 6.4 Graphs and Applications Involving Logarithmic and Exponential Functions 360 6.5 L'Hopital's Rule; Indeterminate Forms 367 6.6 Logarithmic and Other Functions Defined by Integrals 376 6.7 Derivatives and Integrals Involving Inverse Trigonometric Functions 387 6.8 Hyperbolic Functions and Hanging Cables 398 7 Principles of Integral Evaluation 406 7.1 An Overview of Integration Methods 406 7.2 Integration by Parts 409 7.3 Integrating Trigonometric Functions 417 7.4 Trigonometric Substitutions 424 7.5 Integrating Rational Functions by Partial Fractions 430 7.6 Using Computer Algebra Systems and Tables of Integrals 437 7.7 Numerical Integration; Simpson's Rule 446 7.8 Improper Integrals 458 8 Mathematical Modeling with Differential Equations 471 8.1 Modeling with Differential Equations 471 8.2 Separation of Variables 477 8.3 Slope Fields; Euler's Method 488 8.4 First-Order Differential Equations and Applications 494 9 Infinite Series 504 9.1 Sequences 504 9.2 Monotone Sequences 513 9.3 Infinite Series 520 9.4 Convergence Tests 528 9.5 The Comparison, Ratio, and Root Tests 534 9.6 Alternating Series; Absolute and Conditional Convergence 539 9.7 Maclaurin and Taylor Polynomials 549 9.8 Maclaurin and Taylor Series; Power Series 559 9.9 Convergence of Taylor Series 567 9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 575 10 Parametric and Polar Curves; Conic Sections 588 10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 588 10.2 Polar Coordinates 600 10.3 Tangent Lines, Arc Length, and Area for Polar Curves 613 10.4 Conic Sections 622 10.5 Rotation of Axes; Second-Degree Equations 639 10.6 Conic Sections in Polar Coordinates 644 11 Three-dimensional Space; Vector 11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 657 11.2 Vectors 663 11.3 Dot Product; Projections 673 11.4 Cross Product 682 11.5 Parametric Equations of Lines 692 11.6 Planes in 3-Space 698 11.7 Quadric Surfaces 705 11.7 Cylindrical and Spherical Coordinates 715 12 Vector-Valued Functions 723 12.1 Introduction to Vector-Valued Functions 723 12.2 Calculus of Vector-Valued Functions 729 12.3 Change of Parameter; Arc Length 738 12.4 Unit Tangent, Normal, and Binormal Vectors 746 12.5 Curvature 751 12.6 Motion Along a Curve 759 12.7 Kepler's Laws of Planetary Motion 771 13 Partial Derivatives 781 13.1 Functions of Two or More Variables 781 13.2 Limits and Continuity 791 13.3 Partial Derivatives 800 13.4 Differentiability, Differentials, and Local Linearity 812 13.5 The Chain Rule 820 13.6 Directional Derivatives and Gradients 830 13.7 Tangent Planes and Normal Vectors 840 13.8 Maxima and Minima of Functions of Two Variables 845 13.9 Lagrange Multipliers 856 14 Multiple Integrals 925 14.1 Double Integrals 925 14.2 Double Integrals Over Nonrectangular Regions 932 14.3 Double Integrals in Polar Coordinates 941 14.4 Surface Area; Parametric Surfaces 948 14.5 Triple Integrals 961 14.6 Triple Integrals in Cylindrical and Spherical Coordinates 968 14.7 Change of Variables in Multiple Integrals; Jacobians 977 14.8 Centers of Gravity Using Multiple Integrals 989 15 Topics in Vector Calculus 1001 15.1 Vector Fields 1001 15.2 Line Integrals 1010 15.3 Independence of Path; Conservative Vector Fields 1025 15.4 Green's Theorem 1035 15.5 Surface Integrals 1042 15.6 Applications of Surface Integrals; Flux 1049 15.7 The Divergence Theorem 1058 15.8 Stokes' Theorem 1067 Appendix A A1 Appendix B 00 Appendix C 00 Appendix D 00 Appendix E 00 Answers 00 Index I1

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions