Calculus: Early Transcendentals

Description

Success in your calculus course starts here! James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANSCENDENTALS, Eighth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course. Contents......Page 5 Preface......Page 13 To the Student......Page 25 Calculators, Computers, and Other Graphing Devices......Page 26 Diagnostic Tests......Page 28 A Preview of Calculus......Page 33 Ch 1: Functions and Models......Page 41 1.1: Four Ways to Represent a Function......Page 42 1.2: Mathematical Models: A Catalog of Essential Functions......Page 55 1.3: New Functions from Old Functions......Page 68 1.4: Exponential Functions......Page 77 1.5: Inverse Functions and Logarithms......Page 87 Review......Page 100 Principles of Problem Solving......Page 103 Ch 2: Limits and Derivatives......Page 109 2.1: The Tangent and Velocity Problems......Page 110 2.2: The Limit of a Function......Page 115 2.3: Calculating Limits Using the Limit Laws......Page 127 2.4: The Precise Definition of a Limit......Page 136 2.5: Continuity......Page 146 2.6: Limits at Infinity; Horizontal Asymptotes......Page 158 2.7: Derivatives and Rates of Change......Page 172 2.8: The Derivative as a Function......Page 184 Review......Page 197 Problems Plus......Page 201 Ch 3: Differentiation Rules......Page 203 3.1: Derivatives of Polynomials and Exponential Functions......Page 204 3.2: The Product and Quotient Rules......Page 215 3.3: Derivatives of Trigonometric Functions......Page 222 3.4: The Chain Rule......Page 229 3.5: Implicit Differentiation......Page 240 3.6: Derivatives of Logarithmic Functions......Page 250 3.7: Rates of Change in the Natural and Social Sciences......Page 256 3.8: Exponential Growth and Decay......Page 269 3.9: Related Rates......Page 277 3.10: Linear Approximations and Differentials......Page 283 3.11: Hyperbolic Functions......Page 291 Review......Page 298 Problems Plus......Page 302 Ch 4: Applications of Differentiation......Page 307 4.1: Maximum and Minimum Values......Page 308 4.2: The Mean Value Theorem......Page 319 4.3: How Derivatives Affect the Shape of a Graph......Page 325 4.4: Indeterminate Forms and L'Hospital's Rule......Page 336 4.5: Summary of Curve Sketching......Page 347 4.6: Graphing with Calculus and Calculators......Page 355 4.7: Optimization Problems......Page 362 4.8: Newton's Method......Page 377 4.9: Antiderivatives......Page 382 Review......Page 390 Problems Plus......Page 395 Ch 5: Integrals......Page 397 5.1: Areas and Distances......Page 398 5.2: The Definite Integral......Page 410 5.3: The Fundamental Theorem of Calculus......Page 424 5.4: Indefinite Integrals and the Net Change Theorem......Page 434 5.5: The Substitution Rule......Page 444 Review......Page 453 Problems Plus......Page 457 Ch 6: Applications of Integration......Page 459 6.1: Areas between Curves......Page 460 6.2: Volumes......Page 470 6.3: Volumes by Cylindrical Shells......Page 481 6.4: Work......Page 487 6.5: Average Value of a Function......Page 493 Review......Page 498 Problems Plus......Page 500 Ch 7: Techniques of Integration......Page 503 7.1: Integration by Parts......Page 504 7.2: Trigonometric Integrals......Page 511 7.3: Trigonometric Substitution......Page 518 7.4: Integration of Rational Functions by Partial Fractions......Page 525 7.5: Strategy for Integration......Page 535 7.6: Integration Using Tables and Computer Algebra Systems......Page 540 7.7: Approximate Integration......Page 546 7.8: Improper Integrals......Page 559 Review......Page 569 Problems Plus......Page 572 Ch 8: Further Applications of Integration......Page 575 8.1: Arc Length......Page 576 8.2: Area of a Surface of Revolution......Page 583 8.3: Applications to Physics and Engineering......Page 590 8.4: Applications to Economics and Biology......Page 601 8.5: Probability......Page 605 Review......Page 613 Problems Plus......Page 615 Ch 9: Differential Equations......Page 617 9.1: Modeling with Differential Equations......Page 618 9.2: Direction Fields and Euler's Method......Page 623 9.3: Separable Equations......Page 631 9.4: Models for Population Growth......Page 642 9.5: Linear Equations......Page 652 9.6: Predator-Prey Systems......Page 659 Review......Page 666 Problems Plus......Page 669 Ch 10: Parametric Equations and Polar Coordinates......Page 671 10.1: Curves Defined by Parametric Equations......Page 672 10.2: Calculus with Parametric Curves......Page 681 10.3: Polar Coordinates......Page 690 10.4: Areas and Lengths in Polar Coordinates......Page 701 10.5: Conic Sections......Page 706 10.6: Conic Sections in Polar Coordinates......Page 714 Review......Page 721 Problems Plus......Page 724 Ch 11: Infinite Sequences and Series......Page 725 11.1: Sequences......Page 726 11.2: Series......Page 739 11.3: The Integral Test and Estimates of Sums......Page 751 11.4: The Comparison Tests......Page 759 11.5: Alternating Series......Page 764 11.6: Absolute Convergence and the Ratio and Root Tests......Page 769 11.7: Strategy for Testing Series......Page 776 11.8: Power Series......Page 778 11.9: Representations of Functions as Power Series......Page 784 11.10: Taylor and Maclaurin Series......Page 791 11.11: Applications of Taylor Polynomials......Page 806 Review......Page 816 Problems Plus......Page 819 Ch 12: Vectors and the Geometry of Space......Page 823 12.1: Three-Dimensional Coordinate Systems......Page 824 12.2: Vectors......Page 830 12.3: The Dot Product......Page 839 12.4: The Cross Product......Page 846 12.5: Equations of Lines and Planes......Page 855 12.6: Cylinders and Quadric Surfaces......Page 866 Review......Page 873 Problems Plus......Page 876 Ch 13: Vector Functions......Page 879 13.1: Vector Functions and Space Curves......Page 880 13.2: Derivatives and Integrals of Vector Functions......Page 887 13.3: Arc Length and Curvature......Page 893 13.4: Motion in Space: Velocity and Acceleration......Page 902 Review......Page 913 Problems Plus......Page 916 Ch 14: Partial Derivatives......Page 919 14.1: Functions of Several Variables......Page 920 14.2: Limits and Continuity......Page 935 14.3: Partial Derivatives......Page 943 14.4: Tangent Planes and Linear Approximations......Page 959 14.5: The Chain Rule......Page 969 14.6: Directional Derivatives and the Gradient Vector......Page 978 14.7: Maximum and Minimum Values......Page 991 14.8: Lagrange Multipliers......Page 1003 Review......Page 1013 Problems Plus......Page 1017 Ch 15: Multiple Integrals......Page 1019 15.1: Double Integrals over Rectangles......Page 1020 15.2: Double Integrals over General Regions......Page 1033 15.3: Double Integrals in Polar Coordinates......Page 1042 15.4: Applications of Double Integrals......Page 1048 15.5: Surface Area......Page 1058 15.6: Triple Integrals......Page 1061 15.7: Triple Integrals in Cylindrical Coordinates......Page 1072 15.8: Triple Integrals in Spherical Coordinates......Page 1077 15.9: Change of Variables in Multiple Integrals......Page 1084 Review......Page 1093 Problems Plus......Page 1097 Ch 16: Vector Calculus......Page 1099 16.1: Vector Fields......Page 1100 16.2: Line Integrals......Page 1107 16.3: The Fundamental Theorem for Line Integrals......Page 1119 16.4: Green's Theorem......Page 1128 16.5: Curl and Divergence......Page 1135 16.6: Parametric Surfaces and Their Areas......Page 1143 16.7: Surface Integrals......Page 1154 16.8: Stokes' Theorem......Page 1166 16.9: The Divergence Theorem......Page 1173 16.10: Summary......Page 1179 Review......Page 1180 Problems Plus......Page 1183 Ch 17: Second-Order Differential Equations......Page 1185 17.1: Second-Order Linear Equations......Page 1186 17.2: Nonhomogeneous Linear Equations......Page 1192 17.3: Applications of Second-Order Differential Equations......Page 1200 17.4: Series Solutions......Page 1208 Review......Page 1213 Appendixes......Page 1215 Appendix A: Numbers, Inequalities, and Absolute Values......Page 1216 Appendix B: Coordinate Geometry and Lines......Page 1224 Appendix C: Graphs of Second-Degree Equations......Page 1230 Appendix D: Trigonometry......Page 1238 Appendix E: Sigma Notation......Page 1248 Appendix F: Proofs of Theorems......Page 1253 Appendix G: The Logarithm Defined as an Integral......Page 1264 Appendix H: Complex Numbers......Page 1271 Appendix I: Answers to Odd-Numbered Exercises......Page 1279 Index......Page 1353 Concept Check Answers......Page 1371