Calculus: Early Transcendentals

Cover\nContents\nPreface\nA Tribute to James Stewart\nAbout the Authors\nTechnology in the Ninth Edition\nTo the Student\nDiagnostic Tests\n	A: Diagnostic Test: Algebra\n	B: Diagnostic Test: Analytic Geometry\n	C: Diagnostic Test: Functions\n	D: Diagnostic Test: Trigonometry\nA Preview of Calculus\n	What Is Calculus?\n	The Area Problem\n	The Tangent Problem\n	A Relationship between the Area and Tangent Problems\n	Summary\nChapter 1: Functions and Models\n	1.1 Four Ways to Represent a Function\n	1.2 Mathematical Models: A Catalog of Essential Functions\n	1.3 New Functions from Old Functions\n	1.4 Exponential Functions\n	1.5 Inverse Functions and Logarithms\n	1 Review\n	Principles of Problem Solving\nChapter 2: Limits and Derivatives\n	2.1 The Tangent and Velocity Problems\n	2.2 The Limit of a Function\n	2.3 Calculating Limits Using the Limit Laws\n	2.4 The Precise Definition of a Limit\n	2.5 Continuity\n	2.6 Limits at Infinity; Horizontal Asymptotes\n	2.7 Derivatives and Rates of Change\n	2.8 The Derivative as a Function\n	2 Review\n	Problems Plus\nChapter 3: Differentiation Rules\n	3.1 Derivatives of Polynomials and Exponential Functions\n	3.2 The Product and Quotient Rules\n	3.3 Derivatives of Trigonometric Functions\n	3.4 The Chain Rule\n	3.5 Implicit Differentiation\n	3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions\n	3.7 Rates of Change in the Natural and Social Sciences\n	3.8 Exponential Growth and Decay\n	3.9 Related Rates\n	3.10 Linear Approximations and Differentials\n	3.11 Hyperbolic Functions\n	3 Review\n	Problems Plus\nChapter 4: Applications of Differentiation\n	4.1 Maximum and Minimum Values\n	4.2 The Mean Value Theorem\n	4.3 What Derivatives Tell Us about the Shape of a Graph\n	4.4 Indeterminate Forms and l\'Hospital\'s Rule\n	4.5 Summary of Curve Sketching\n	4.6 Graphing with Calculus and Technology\n	4.7 Optimization Problems\n	4.8 Newton\'s Method\n	4.9 Antiderivatives\n	4 Review\n	Problems Plus\nChapter 5: Integrals\n	5.1 The Area and Distance Problems\n	5.2 The Definite Integral\n	5.3 The Fundamental Theorem of Calculus\n	5.4 Indefinite Integrals and the Net Change Theorem\n	5.5 The Substitution Rule\n	5 Review\n	Problems Plus\nChapter 6: Applications of Integration\n	6.1 Areas between Curves\n	6.2 Volumes\n	6.3 Volumes by Cylindrical Shells\n	6.4 Work\n	6.5 Average Value of a Function\n	6 Review\n	Problems Plus\nChapter 7: Techniques of Integration\n	7.1 Integration by Parts\n	7.2 Trigonometric Integrals\n	7.3 Trigonometric Substitution\n	7.4 Integration of Rational Functions by Partial Fractions\n	7.5 Strategy for Integration\n	7.6 Integration Using Tables and Technology\n	7.7 Approximate Integration\n	7.8 Improper Integrals\n	7 Review\n	Problems Plus\nChapter 8: Further Applications of Integration\n	8.1 Arc Length\n	8.2 Area of a Surface of Revolution\n	8.3 Applications to Physics and Engineering\n	8.4 Applications to Economics and Biology\n	8.5 Probability\n	8 Review\n	Problems Plus\nChapter 9: Differential Equations\n	9.1 Modeling with Differential Equations\n	9.2 Direction Fields and Euler\'s Method\n	9.3 Separable Equations\n	9.4 Models for Population Growth\n	9.5 Linear Equations\n	9.6 Predator-Prey Systems\n	9 Review\n	Problems Plus\nChapter 10: Parametric Equations and Polar Coordinates\n	10.1 Curves Defined by Parametric Equations\n	10.2 Calculus with Parametric Curves\n	10.3 Polar Coordinates\n	10.4 Calculus in Polar Coordinates\n	10.5 Conic Sections\n	10.6 Conic Sections in Polar Coordinates\n	10 Review\n	Problems Plus\nChapter 11: Sequences, Series, and Power Series\n	11.1 Sequences\n	11.2 Series\n	11.3 The Integral Test and Estimates of Sums\n	11.4 The Comparison Tests\n	11.5 Alternating Series and Absolute Convergence\n	11.6 The Ratio and Root Tests\n	11.7 Strategy for Testing Series\n	11.8 Power Series\n	11.9 Representations of Functions as Power Series\n	11.10 Taylor and Maclaurin Series\n	11.11 Applications of Taylor Polynomials\n	11 Review\n	Problems Plus\nChapter 12: Vectors and the Geometry of Space\n	12.1 Three-Dimensional Coordinate Systems\n	12.2 Vectors\n	12.3 The Dot Product\n	12.4 The Cross Product\n	12.5 Equations of Lines and Planes\n	12.6 Cylinders and Quadric Surfaces\n	12 Review\n	Problems Plus\nChapter 13: Vector Functions\n	13.1 Vector Functions and Space Curves\n	13.2 Derivatives and Integrals of Vector Functions\n	13.3 Arc Length and Curvature\n	13.4 Motion in Space: Velocity and Acceleration\n	13 Review\n	Problems Plus\nChapter 14: Partial Derivatives\n	14.1 Functions of Several Variables\n	14.2 Limits and Continuity\n	14.3 Partial Derivatives\n	14.4 Tangent Planes and Linear Approximations\n	14.5 The Chain Rule\n	14.6 Directional Derivatives and the Gradient Vector\n	14.7 Maximum and Minimum Values\n	14.8 Lagrange Multipliers\n	14 Review\n	Problems Plus\nChapter 15: Multiple Integrals\n	15.1 Double Integrals over Rectangles\n	15.2 Double Integrals over General Regions\n	15.3 Double Integrals in Polar Coordinates\n	15.4 Applications of Double Integrals\n	15.5 Surface Area\n	15.6 Triple Integrals\n	15.7 Triple Integrals in Cylindrical Coordinates\n	15.8 Triple Integrals in Spherical Coordinates\n	15.9 Change of Variables in Multiple Integrals\n	15 Review\n	Problems Plus\nChapter 16: Vector Calculus\n	16.1 Vector Fields\n	16.2 Line Integrals\n	16.3 The Fundamental Theorem for Line Integrals\n	16.4 Green\'s Theorem\n	16.5 Curl and Divergence\n	16.6 Parametric Surfaces and Their Areas\n	16.7 Surface Integrals\n	16.8 Stokes\' Theorem\n	16.9 The Divergence Theorem\n	16.10 Summary\n	16 Review\n	Problems Plus\nAppendixes\n	Appendix A: Numbers, Inequalities, and Absolute Values\n	Appendix B: Coordinate Geometry and Lines\n	Appendix C: Graphs of Second-Degree Equations\n	Appendix D: Trigonometry\n	Appendix E: Sigma Notation\n	Appendix F: Proofs of Theorems\n	Appendix G: The Logarithm Defined as an Integral\n	Appendix H: Answers to Odd-Numbered Exercises\nIndex