Calculus (6th Edition)

2 "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, Sixth 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!" -Amazon.com Front Cover......Page 1 Title Page......Page 2 Copyright......Page 3 Contents......Page 4 Preface......Page 12 To The Student......Page 24 Diagnostic Tests......Page 25 A Preview Of Calculus......Page 31 1 FUNCTIONS AND MODELS......Page 39 1.1 Four Ways To Represent A Function......Page 40 1.2 Mathematical Models: A Catalog of Essential Functions......Page 53 1.3 New Functions From Old Functions......Page 66 1.4 Graphing Calculators and Computers......Page 75 Review......Page 81 Principles of Problem Solving......Page 83 2 LIMITS......Page 89 2.1 The Tangent and Velocity Problems......Page 90 2.2 The Limit of a Function......Page 95 2.3 Calculating Limits Using the Limit Laws......Page 106 2.4 The Precise Definition of a Limit......Page 116 2.5 Continuity......Page 126 Review......Page 137 Problems Plus......Page 139 3 DERIVATIVES......Page 141 3.1 Derivatives and Rates of Change......Page 142 3.2 The Derivative as a Function......Page 152 3.3 Differentiation Formulas......Page 164 3.4 Derivatives of Trigonometric Functions......Page 177 3.5 The Chain Rule......Page 184 3.6 Implicit Differentiation......Page 193 3.7 Rates of Change In The Natural And Social Sciences......Page 199 3.8 Related Rates......Page 211 3.9 Linear Approximations and Differentials......Page 218 Laboratory Project: Taylor Polynomials......Page 224 Review......Page 225 Problems Plus......Page 229 4 APPLICATIONS OF DIFFERENTIATION......Page 233 4.1 Maximum and Minimum Values......Page 234 Applied Project: The Calculus of Rainbows......Page 242 4.2 The Mean Value Theorem......Page 243 4.3 How Derivatives Affect the Shape of a Graph......Page 249 4.4 Limits At Infinity; Horizontal Asymptotes......Page 259 4.5 Summary Of Curve Sketching......Page 272 4.6 Graphing With Calculus And Calculators......Page 279 4.7 Optimization Problems......Page 285 Applied Project: The Shape Of A Can......Page 297 4.8 Newton’s Method......Page 298 4.9 Antiderivatives......Page 303 Review......Page 310 Problems Plus......Page 314 5 INTEGRALS......Page 317 5.1 Areas and Distances......Page 318 5.2 The Definite Integral......Page 329 Discovery Project: Area Functions......Page 341 5.3 The Fundamental Theorem Of Calculus......Page 342 5.4 Indefinite Integrals and the Net Change Theorem......Page 353 Writing Project: Newton, Leibniz, and the Invention of Calculus......Page 361 5.5 The Substitution Rule......Page 362 Review......Page 369 Problems Plus......Page 373 6 APPLICATIONS OF INTEGRATION......Page 375 6.1 Areas Between Curves......Page 376 6.2 Volumes......Page 383 6.3 Volumes by Cylindrical Shells......Page 394 6.4 Work......Page 399 6.5 Average Value Of A Function......Page 403 Review......Page 407 Problems Plus......Page 409 7 INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS......Page 413 7.1 Inverse Functions......Page 414 7.2 Exponential Functions and Their Derivatives......Page 421 7.3 Logarithmic Functions......Page 434 7.4 Derivatives of Logarithmic Functions......Page 440 7.2* The Natural Logarithmic Function......Page 450 7.3* The Natural Exponential Function......Page 459 7.4* General Logarithmic and Exponential Functions......Page 467 7.5 Exponential Growth and Decay......Page 476 7.6 Inverse Trigonometric Functions......Page 483 7.7 Hyperbolic Functions......Page 492 7.8 Indeterminate Forms and L’Hospital’s Rule......Page 499 Writing Project: The Origins Of L’hospital’s Rule......Page 510 Review......Page 511 Problems Plus......Page 515 8 TECHNIQUES OF INTEGRATION......Page 517 8.1 Integration by Parts......Page 518 8.2 Trigonometric Integrals......Page 525 8.3 Trigonometric Substitution......Page 532 8.4 Integration of Rational Functions by Partial Fractions......Page 538 8.5 Strategy for Integration......Page 548 8.6 Integration Using Tables and Computer Algebra Systems......Page 554 Discovery Project: Patterns in Integrals......Page 559 8.7 Approximate Integration......Page 560 8.8 Improper Integrals......Page 573 Review......Page 583 Problems Plus......Page 586 9 FURTHER APPLICATIONS OF INTEGRATION......Page 589 9.1 Arc Length......Page 590 9.2 Area of A Surface of Revolution......Page 597 Discovery Project: Rotating on a Slant......Page 603 9.3 Applications to Physics and Engineering......Page 604 9.4 Applications to Economics and Biology......Page 615 9.5 Probability......Page 620 Review......Page 627 Problems Plus......Page 629 10 DIFFERENTIAL EQUATIONS......Page 631 10.1 Modeling With Differential Equations......Page 632 10.2 Direction Fields and Euler’s Method......Page 637 10.3 Separable Equations......Page 645 Applied Project: How Fast Does a Tank Drain?......Page 653 Applied Project: Which Is Faster, Going Up or Coming Down?......Page 655 10.4 Models for Population Growth......Page 656 Applied Project: Calculus and Baseball......Page 666 10.5 Linear Equations......Page 667 10.6 Predator-prey Systems......Page 673 Review......Page 679 Problems Plus......Page 683 11 PARAMETRIC EQUATIONS AND POLAR COORDINATES......Page 685 11.1 Curves Defined by Parametric Equations......Page 686 Laboratory Project: Running Circles Around Circles......Page 694 11.2 Calculus With Parametric Curves......Page 695 11.3 Polar Coordinates......Page 704 11.4 Areas and Lengths in Polar Coordinates......Page 715 11.5 Conic Sections......Page 719 11.6 Conic Sections in Polar Coordinates......Page 727 Review......Page 734 Problems Plus......Page 737 12 INFINITE SEQUENCES AND SERIES......Page 739 12.1 Sequences......Page 740 12.2 Series......Page 752 12.3 The Integral Test and Estimates of Sums......Page 762 12.4 The Comparison Tests......Page 770 12.5 Alternating Series......Page 775 12.6 Absolute Convergence and The Ratio and Root Tests......Page 779 12.7 Strategy for Testing Series......Page 786 12.8 Power Series......Page 788 12.9 Representations of Functions as Power Series......Page 793 12.10 Taylor and Maclaurin Series......Page 799 Writing Project: How Newton Discovered The Binomial Series......Page 813 12.11 Applications of Taylor Polynomials......Page 814 Applied Project: Radiation From The Stars......Page 822 Review......Page 823 Problems Plus......Page 826 13 VECTORS AND THE GEOMETRY OF SPACE......Page 829 13.1 Three-Dimensional Coordinate Systems......Page 830 13.2 Vectors......Page 835 13.3 The Dot Product......Page 844 13.4 The Cross Product......Page 851 13.5 Equations of Lines and Planes......Page 859 13.6 Cylinders and Quadric Surfaces......Page 869 Review......Page 877 Problems Plus......Page 880 14 VECTOR FUNCTIONS......Page 881 14.1 Vector Functions and Space Curves......Page 882 14.2 Derivatives and Integrals of Vector Functions......Page 889 14.3 Arc Length and Curvature......Page 895 14.4 Motion in Space: Velocity and Acceleration......Page 903 Applied Project: Kepler’s Laws......Page 913 Review......Page 914 Problems Plus......Page 917 15 PARTIAL DERIVATIVES......Page 919 15.1 Functions of Several Variables......Page 920 15.2 Limits and Continuity......Page 935 15.3 Partial Derivatives......Page 943 15.4 Tangent Planes and Linear Approximations......Page 957 15.5 The Chain Rule......Page 966 15.6 Directional Derivatives and the Gradient Vector......Page 975 15.7 Maximum and Minimum Values......Page 987 Discovery Project: Quadratic Approximations and Critical Points......Page 998 15.8 Lagrange Multipliers......Page 999 Applied Project: Rocket Science......Page 1006 Applied Project: Hydro-turbine Optimization......Page 1008 Review......Page 1009 Problems Plus......Page 1013 16 MULTIPLE INTEGRALS......Page 1015 16.1 Double Integrals over Rectangles......Page 1016 16.2 Iterated Integrals......Page 1024 16.3 Double Integrals over General Regions......Page 1030 16.4 Double Integrals in Polar Coordinates......Page 1039 16.5 Applications of Double Integrals......Page 1045 16.6 Triple Integrals......Page 1055 16.7 Triple Integrals In Cylindrical Coordinates......Page 1065 16.8 Triple Integrals in Spherical Coordinates......Page 1070 16.9 Change of Variables In Multiple Integrals......Page 1077 Review......Page 1086 Problems Plus......Page 1089 17 VECTOR CALCULUS......Page 1091 17.1 Vector Fields......Page 1092 17.2 Line Integrals......Page 1099 17.3 The Fundamental Theorem for Line Integrals......Page 1111 17.4 Green’s Theorem......Page 1120 17.5 Curl and Divergence......Page 1126 17.6 Parametric Surfaces and Their Areas......Page 1135 17.7 Surface Integrals......Page 1146 17.8 Stokes’ Theorem......Page 1157 Writing Project: Three Men and Two Theorems......Page 1163 17.9 The Divergence Theorem......Page 1164 17.10 Summary......Page 1170 Review......Page 1171 Problems Plus......Page 1174 18 SECOND-ORDER DIFFERENTIAL EQUATIONS......Page 1175 18.1 Second-Order Linear Equations......Page 1176 18.2 Nonhomogeneous Linear Equations......Page 1182 18.3 Applications of Second-Order Differential Equations......Page 1190 18.4 Series Solutions......Page 1198 Review......Page 1202 APPENDIXES......Page 1204 A: Numbers, Inequalities, and Absolute Values......Page 1205 B: Coordinate Geometry and Lines......Page 1213 C: Graphs of Second-degree Equations......Page 1219 D: Trigonometry......Page 1227 E: Sigma Notation......Page 1237 F: Proofs of Theorems......Page 1242 G: Complex Numbers......Page 1251 H: Answers To Odd-numbered Exercises......Page 1260 INDEX......Page 1328 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.

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, Seventh 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!

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The latest edition of Stewart's (McMaster University) college textbook emphasizes conceptual understanding while retaining the traditional fundamentals of calculus. Annotation c. Book News, Inc., Portland, OR (booknews.com)