Calculus, Loose-leaf Version

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, 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 Limits......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: The Tangent and Velocity Problems......Page 77 1.5: The Limit of a Function......Page 82 1.6: Calculating Limits Using the Limit Laws......Page 94 1.7: The Precise Definition of a Limit......Page 104 1.8: Continuity......Page 114 1: Review......Page 126 Principles of Problem Solving......Page 130 Ch 2: Derivatives......Page 137 2.1: Derivatives and Rates of Change......Page 138 2.2: The Derivative as a Function......Page 149 2.3: Differentiation Formulas......Page 162 2.4: Derivatives of Trigonometric Functions......Page 176 2.5: The Chain Rule......Page 184 2.6: Implicit Differentiation......Page 193 2.7: Rates of Change in the Natural and Social Sciences......Page 201 2.8: Related Rates......Page 213 2.9: Linear Approximations and Differentials......Page 220 2: Review......Page 227 Problems Plus......Page 232 Ch 3: Applications of Differentiation......Page 235 3.1: Maximum and Minimum Values......Page 236 3.2: The Mean Value Theorem......Page 247 3.3: How Derivatives Affect the Shape of a Graph......Page 253 3.4: Limits at Infinity; Horizontal Asymptotes......Page 263 3.5: Summary of Curve Sketching......Page 276 3.6: Graphing with Calculus and Calculators......Page 283 3.7: Optimization Problems......Page 290 3.8: Newton's Method......Page 304 3.9: Antiderivatives......Page 310 3: Review......Page 317 Problems Plus......Page 321 Ch 4: Integrals......Page 325 4.1: Areas and Distances......Page 326 4.2: The Definite Integral......Page 338 4.3: The Fundamental Theorem of Calculus......Page 352 4.4: Indefinite Integrals and the Net Change Theorem......Page 362 4.5: The Substitution Rule......Page 372 4: Review......Page 380 Problems Plus......Page 384 Ch 5: Applications of Integration......Page 387 5.1: Areas between Curves......Page 388 5.2: Volumes......Page 398 5.3: Volumes by Cylindrical Shells......Page 409 5.4: Work......Page 415 5.5: Average Value of a Function......Page 421 5: Review......Page 425 Problems Plus......Page 427 Ch 6: Inverse Functions......Page 431 6.1: Inverse Functions......Page 432 6.2: Exponential Functions and Their Derivatives......Page 440 6.3: Logarithmic Functions......Page 453 6.4: Derivatives of Logarithmic Functions......Page 460 6.5: Exponential Growth and Decay......Page 498 6.6: Inverse Trigonometric Functions......Page 506 6.7: Hyperbolic Functions......Page 516 6.8: Indeterminate Forms and l'Hospital's Rule......Page 523 6: Review......Page 535 Problems Plus......Page 540 Ch 7: Techniques of Integration......Page 543 7.1: Integration by Parts......Page 544 7.2: Trigonometric Integrals......Page 551 7.3: Trigonometric Substitution......Page 558 7.4: Integration of Rational Functions by Partial Fractions......Page 565 7.5: Strategy for Integration......Page 575 7.6: Integration Using Tables and Computer Algebra Systems......Page 580 7.7: Approximate Integration......Page 586 7.8: Improper Integrals......Page 599 7: Review......Page 609 Problems Plus......Page 612 Ch 8: Further Applications of Integration......Page 615 8.1: Arc Length......Page 616 8.2: Area of a Surface of Revolution......Page 623 8.3: Applications to Physics and Engineering......Page 630 8.4: Applications to Economics and Biology......Page 641 8.5: Probability......Page 645 8: Review......Page 653 Problems Plus......Page 655 Ch 9: Differential Equations......Page 657 9.1: Modeling with Differential Equations......Page 658 9.2: Direction Fields and Euler's Method......Page 663 9.3: Separable Equations......Page 671 9.4: Models for Population Growth......Page 682 9.5: Linear Equations......Page 692 9.6: Predator-Prey Systems......Page 699 9: Review......Page 706 Problems Plus......Page 709 Ch 10: Parametric Equations and Polar Coordinates......Page 711 10.1: Curves Defined by Parametric Equations......Page 712 10.2: Calculus with Parametric Curves......Page 721 10.3: Polar Coordinates......Page 730 10.4: Areas and Lengths in Polar Coordinates......Page 741 10.5: Conic Sections......Page 746 10.6: Conic Sections in Polar Coordinates......Page 754 10: Review......Page 761 Problems Plus......Page 764 Ch 11: Infinite Sequences and Series......Page 765 11.1: Sequences......Page 766 11.2: Series......Page 779 11.3: The Integral Test and Estimates of Sums......Page 791 11.4: The Comparison Tests......Page 799 11.5: Alternating Series......Page 804 11.6: Absolute Convergence and the Ratio and Root Tests......Page 809 11.7: Strategy for Testing Series......Page 816 11.8: Power Series......Page 818 11.9: Representations of Functions as Power Series......Page 824 11.10: Taylor and Maclaurin Series......Page 831 11.11: Applications of Taylor Polynomials......Page 846 11: Review......Page 856 Problems Plus......Page 859 Ch 12: Vectors and the Geometry of Space......Page 863 12.1: Three-Dimensional Coordinate Systems......Page 864 12.2: Vectors......Page 870 12.3: The Dot Product......Page 879 12.4: The Cross Product......Page 886 12.5: Equations of Lines and Planes......Page 895 12.6: Cylinders and Quadric Surfaces......Page 906 12: Review......Page 913 Problems Plus......Page 916 Ch 13: Vector Functions......Page 919 13.1: Vector Functions and Space Curves......Page 920 13.2: Derivatives and Integrals of Vector Functions......Page 927 13.3: Arc Length and Curvature......Page 933 13.4: Motion in Space: Velocity and Acceleration......Page 942 13: Review......Page 953 Problems Plus......Page 956 Ch 14: Partial Derivatives......Page 959 14.1: Functions of Several Variables......Page 960 14.2: Limits and Continuity......Page 975 14.3: Partial Derivatives......Page 983 14.4: Tangent Planes and Linear Approximations......Page 999 14.5: The Chain Rule......Page 1009 14.6: Directional Derivatives and the Gradient Vector......Page 1018 14.7: Maximum and Minimum Values......Page 1031 14.8: Lagrange Multipliers......Page 1043 14: Review......Page 1053 Problems Plus......Page 1057 Ch 15: Multiple Integrals......Page 1059 15.1: Double Integrals over Rectangles......Page 1060 15.2: Double Integrals over General Regions......Page 1073 15.3: Double Integrals in Polar Coordinates......Page 1082 15.4: Applications of Double Integrals......Page 1088 15.5: Surface Area......Page 1098 15.6: Triple Integrals......Page 1101 15.7: Triple Integrals in Cylindrical Coordinates......Page 1112 15.8: Triple Integrals in Spherical Coordinates......Page 1117 15.9: Change of Variables in Multiple Integrals......Page 1124 15: Review......Page 1133 Problems Plus......Page 1137 Ch 16: Vector Calculus......Page 1139 16.1: Vector Fields......Page 1140 16.2: Line Integrals......Page 1147 16.3: The Fundamental Theorem for Line Integrals......Page 1159 16.4: Green's Theorem......Page 1168 16.5: Curl and Divergence......Page 1175 16.6: Parametric Surfaces and Their Areas......Page 1183 16.7: Surface Integrals......Page 1194 16.8: Stokes' Theorem......Page 1206 16.9: The Divergence Theorem......Page 1213 16.10: Summary......Page 1219 16: Review......Page 1220 Problems Plus......Page 1223 Ch 17: Second-Order Differential Equations......Page 1225 17.1: Second-Order Linear Equations......Page 1226 17.2: Nonhomogeneous Linear Equations......Page 1232 17.3: Applications of Second-Order Differential Equations......Page 1240 17.4: Series Solutions......Page 1248 17: Review......Page 1253 Appendixes......Page 1255 A: Numbers, Inequalities, and Absolute Values......Page 1256 B: Coordinate Geometry and Lines......Page 1264 C: Graphs of Second-Degree Equations......Page 1270 D: Trigonometry......Page 1278 E: Sigma Notation......Page 1288 F: Proofs of Theorems......Page 1293 G: Complex Numbers......Page 1302 H: Answers to Odd-Numbered Exercises......Page 1311 Index......Page 1385 Reference......Page 1407 Concept Check Answers......Page 1417 James Stewart's Calculus Texts Are Widely Renowned For Their Mathematical Precision And Accuracy, Clarity Of Exposition, And Outstanding Examples And Problem Sets. Millions Of Students Worldwide Have Explored Calculus Through Stewart's Trademark Style, While Instructors Have Turned To His Approach Time And Time Again. In The Eighth Edition Of Calculus, Stewart Continues To Set The Standard For The Course While Adding Carefully Revised Content. The Patient Explanations, Superb Exercises, Focus On Problem Solving, And Carefully Graded Problem Sets That Have Made Stewart's Texts Best-sellers Continue To Provide A Strong Foundation For The Eighth Edition. From The Most Unprepared Student To The Most Mathematically Gifted, Stewart's Writing And Presentation Serve To Enhance Understanding And Build Confidence.--publisher's Website. Functions And Limits -- Derivatives -- Applications Of Differentiation -- Integrals -- Applications Of Integration -- Inverse Functions -- Techniques Of Integration -- Further Applications Of Integration -- Differential Equations -- Parametric Equations And Polar Coordinates -- Infinite Sequences And Series -- Vectors And The Geometry Of Space -- Vector Functions -- Partial Derivatives -- Multiple Integrals -- Vector Calculus -- Second-order Differential Equations. James Stewart, Mcmaster University And University Of Toronto. Includes Bibliographical References And Index. James Stewart’s Calculus Texts Are Widely Renowned For Their Mathematical Precision And Accuracy, Clarity Of Exposition, And Outstanding Examples And Problem Sets. Millions Of Students Worldwide Have Explored Calculus Through Stewart’s Trademark Style, While Instructors Have Turned To His Approach Time And Time Again. In The Eighth Edition Of Calculus, Stewart Continues To Set The Standard For The Course While Adding Carefully Revised Content. The Patient Explanations, Superb Exercises, Focus On Problem Solving, And Carefully Graded Problem Sets That Have Made Stewart’s Texts Best-sellers Continue To Provide A Strong Foundation For The Eighth Edition. From The Most Unprepared Student To The Most Mathematically Gifted, Stewart’s Writing And Presentation Serve To Enhance Understanding And Build Confidence. Important Notice: Media Content Referenced Within The Product Description Or The Product Text May Not Be Available In The Ebook Version.