Calculus : early transcendentals

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: EARLY TRANCENDENTALS, 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! Appropriate For The Traditional 2 Or 3-term College Calculus Course, This Textbook Presents The Fundamentals Of Calculus. Topics Include, But Are Not Limited To: A Review Of Polynomials, Trigonometric, Exponential, And Logarithmic Functions, Followed By Discussions Of Limits, Derivatives, Applications Of Differential Calculus To Real-world Problem Areas, An Overview Of Integration, Basic Techniques For Integration, A Variety Of Applications Of Integration, And An Introduction To (systems Of) Differential Equations. Preface -- To The Student -- Diagnostic Tests -- A Preview Of Calculus -- 1. Functions And Models -- 1.1. Four Ways To Represent A Function -- 1.2. Mathematical Models : A Catalog Of Essential Functions -- 1.3. New Functions From Old Functions -- 1.4. Graphing Calculators And Computers -- 1.5. Exponential Functions -- 1.6. Inverse Functions And Logarithms -- Review -- Principles Of Problem Solving -- 2. Limits And Derivatives -- 2.1. The Tangent And Velocity Problems -- 2.2. The Limit Of A Function -- 2.3. Calculating Limits Using The Limit Laws -- 2.4. The Precise Definition Of A Limit -- 2.5. Continuity -- 2.6. Limits At Infinity ; Horizontal Asymptotes -- 2.7. Derivatives And Rates Of Change -- Writing Project : Early Methods For Finding Tangents -- 2.8. The Derivative As A Function -- Review -- Problems Plus -- 3. Differentiation Rules -- 3.1. Derivatives Of Polynomials And Exponential Functions -- Applied Project : Building A Better Roller Coaster -- 3.2. The Product And Quotient Rules -- 3.3. Derivatives Of Trigonometric Functions -- 3.4. The Chain Rule -- Applied Project : Where Should A Pilot Start Descent? -- 3.5. Implicit Differentiation -- 3.6. Derivatives Of Logarithmic Functions -- 3.7. Rates Of Change In The Natural And Social Sciences -- 3.8. Exponential Growth And Decay -- 3.9. Related Rates -- 3.10. Linear Approximations And Differentials -- Laboratory Project : Taylor Polynomials -- 3.11. Hyperbolic Functions -- Review -- Problems Plus -- 4. Applications Of Differentiation -- 4.1. Maximum And Minimum Values -- Applied Project : The Calculus Of Rainbows -- 4.2. The Mean Value Theorem -- 4.3. How Derivatives Affect The Shape Of A Graph -- 4.4. Indeterminate Forms And L'hospital's Rule -- Writing Project : The Origins Of L'hospital's Rule -- 4.5. Summary Of Curve Sketching -- 4.6. Graphing With Calculus And Calculators -- 4.7. Optimization Problems -- Applied Project : The Shape Of A Can -- 4.8. Newton's Method -- 4.9. Antiderivatives -- Review -- Problems Plus -- 5. Integrals -- 5.1. Areas And Distances -- 5.2. The Definite Integral -- Discovery Project : Area Functions -- 5.3. The Fundamental Theorem Of Calculus -- 5.4. Indefinite Integrals And The Net Change Theorem -- Writing Project : Newton, Leibniz, And The Invention Of Calculus -- 5.5. The Substitution Rule -- Review -- Problems Plus -- 6. Integrals -- 6.1. Areas Between Curves -- 6.2. Volumes -- 6.3. Volumes By Cylindrical Shells -- 6.4. Work -- 6.5. Average Value Of A Function -- Applied Projects : Where To Sit At The Movies -- Review -- Problems Plus -- 7. Techniques Of Integration -- 7.1. Integration By Parts -- 7.2. Trigonometric Integrals -- 7.3. Trigonometric Substitution -- 7.4. Integration Of Rational Functions By Partial Fractions -- 7.5. Strategy For Integration -- 7.6. Integration Using Tables And Computer Algebra Systems -- Discovery Project : Patterns In Integrals -- 7.7. Approximate Integration -- 7.8. Improper Integrals -- Review -- Problems Plus -- 8. Further Applications Of Integration -- 8.1. Arc Length -- Discovery Project : Arc Length Contest -- 8.2. Area Of A Surface Of Revolution -- Discovery Project : Rotating On A Slant -- 8.3. Applications To Physics And Engineering -- Discovery Project : Complementary Coffee Cups -- 8.4. Applications To Economics And Biology -- 8.5. Probability -- Review -- Problems Plus -- 9. Differential Equations -- 9.1. Modeling With Differential Equations -- 9.2. Direction Fields And Euler's Method -- 9.3. Separable Equations -- Applied Project : How Fast Does A Tank Drain? -- Applied Project : Which Is Faster, Going Up Or Coming Down? -- 9.4. Models For Population Growth -- Applied Project : Calculus And Baseball -- 9.5. Linear Equations -- 9.6. Predator-prey Systems -- Review -- Problems Plus -- 10. Parametric Equations And Polar Coordinates -- 10.1. Curves Defined By Parametric Equations -- Laboratory Project : Running Circles Around Circles -- 10.2. Calculus With Parametric Curves -- Laboratory Project : Bézier Curves -- 10.3. Polar Coordinates -- 10.4. Areas And Lengths In Polar Coordinates -- 10.5. Conic Sections -- 10.6. Conic Sections In Polar Coordinates -- Review -- Problems Plus -- 11. Infinite Sequences And Series -- 11.1. Sequences -- Laboratory Project : Logistic Sequences -- 11.2. Series -- 11.3. The Integral Test And Estimates Of Sums -- 11.4. The Comparison Tests -- 11.5. Alternating Series -- 11.6. Absolute Convergence And The Ratio And Root Tests -- 11.7. Strategy For Testing Series -- 11.8. Power Series -- 11.9. Representations Of Functions As Power Series -- 11.10. Taylor And Maclaurin Series -- Laboratory Project : An Elusive Limit -- Writing Project : How Newton Discovered The Binomial Series -- 11.11. Applications Of Taylor Polynomials -- Applied Project : Radiation From The Stars -- Review -- Problems Plus -- 12. Vectors And Geometry Of Space -- 12.1. Three-dimensional Coordinate Systems -- 12.2. Vectors -- 12.3. The Dot Product -- 12.4. The Cross Product -- Discovery Project : The Geometry Of A Tetrahedrom -- 12.5. Equations Of Lines And Planes -- Laboratory Project : Putting 3d In Perspective -- 12.6. Cylinders And Quadric Surfaces -- Review -- Problems Plus -- 13. Vector Functions -- 13.1. Vector Functions And Space Curves -- 13.2. Derivatives And Integrals Of Vector Functions -- 13.3. Arc Length And Curvature -- 13.4. Motion In Space : Velocity And Acceleration -- Applied Project : Kepler's Laws -- Review -- Problems Plus -- 14. Partial Derivatives -- 14.1. Functions Of Several Variables -- 14.2. Limits And Continuity -- 14.3. Partial Derivatives -- 14.4. Tangent Planes And Linear Approximations -- 14.5. The Chain Rule -- 14.6. Directional Derivatives And The Gradient Vector -- 14.7. Maximum And Minimum Values -- Applied Project : Designing A Dumpster -- Discovery Project : Quadratic Approximation And Critical Points -- 14.8. Lagrange Multipliers -- Applied Project : Rocket Science -- Applied Project : Hydro-turbine Optimization -- Review -- Problems Plus -- 15. Multiple Integrals -- 15.1. Double Integrals Over Rectangles -- 15.2. Iterated Integrals -- 15.3. Double Integrals Over General Regions -- 15.4. Double Integrals In Polar Coordinates -- 15.5. Applications Of Double Integrals -- 15.6. Triple Integrals -- Discovery Project : Volumes Of Hyperspheres -- 15.7. Triple Integrals In Cylindrical Coordinates -- Discovery Project : The Intersection Of Three Cylinders -- 15.8. Triple Integrals In Spherical Coordinates -- Applied Project : Roller Derby -- 15.9. Change Of Variables In Multiple Integrals -- Review -- Problems Plus -- 16. Vector Calculus -- 16.1. Vector Fields -- 16.2. Line Integrals -- 16.3. The Fundamental Theorem For Line Integrals -- 16.4. Green's Theorem -- 16.5. Curl And Divergence -- 16.6. Parametric Surfaces And Their Areas -- 16.7. Surface Integrals -- 16.8. Stokes' Theorem -- Writing Project : Three Men And Two Theorems -- 16.9. The Divergence Theorem -- 16.10. Summary -- Review -- Problems Plus -- 17. Second-order Differential Equations -- 17.1. Second-order Linear Equations -- 17.2. Nonhomogeneous Linear Equations -- 17.3. Applications Of Second-order Differential Equations -- 17.4. Series Solutions -- Review -- Appendixes -- A. Numbers, Inequalities, And Absolute Values -- B. Coordinate Geometry And Lines -- C. Graphs Of Second-degree Equations -- D. Trigonometry -- E. Sigma Notation -- F. Proofs Of Theorems -- G. The Logarithm Defined As An Integral -- H. Complex Numbers -- I. Answers To Odd-numbered Exercises. James Stewart. Includes Index. Front matter ......Page 1 Table of contents ......Page 3 Preface ......Page 11 To the student ......Page 23 Diagnostic tests ......Page 24 Preview of calculus ......Page 30 1 - Functions and models ......Page 38 2 - Limits and derivatives ......Page 110 3 - Differentiaton rules ......Page 200 4 - Applications of differentiation ......Page 298 5 - Integrals ......Page 382 6 - Applications of integration ......Page 442 7 - Techniques of integration ......Page 480 8 - Further applications of integration ......Page 552 9 - Differential equations ......Page 594 10 - Parametric equations and polar coords ......Page 648 11 - Infinite sequences and series ......Page 702 12 - Vectors and the geometry of space ......Page 792 13 - Vector functions ......Page 844 14 - Partial derivatives ......Page 882 15 - Multiple integrals ......Page 978 16 - Vector calculus ......Page 1054 17 - Second-order differential equations ......Page 1138 Appendixes ......Page 1167 Answers to odd-numbered exercises ......Page 1231 Index ......Page 1297 calculus Front matter 1 Table of contents 3 Preface 11 To the student 23 Diagnostic tests 24 Preview of calculus 30 1 - Functions and models 38 2 - Limits and derivatives 110 3 - Differentiaton rules 200 4 - Applications of differentiation 298 5 - Integrals 382 6 - Applications of integration 442 7 - Techniques of integration 480 8 - Further applications of integration 552 9 - Differential equations 594 10 - Parametric equations and polar coords 648 11 - Infinite sequences and series 702 12 - Vectors and the geometry of space 792 13 - Vector functions 844 14 - Partial derivatives 882 15 - Multiple integrals 978 16 - Vector calculus 1054 17 - Second-order differential equations 1138 Appendixes 1167 Answers to odd-numbered exercises 1231 Index 1297