LEADER 06795nam 2200529 450 001 9910153251703321 005 20230807214229.0 010 $a1-292-06253-3 035 $a(CKB)3710000000380592 035 $a(MiAaPQ)EBC5186437 035 $a(MiAaPQ)EBC5176311 035 $a(MiAaPQ)EBC5833020 035 $a(MiAaPQ)EBC5137415 035 $a(MiAaPQ)EBC5482997 035 $a(MiAaPQ)EBC6399323 035 $a(Au-PeEL)EBL5137415 035 $a(CaONFJC)MIL942795 035 $a(OCoLC)1024285026 035 $a(EXLCZ)993710000000380592 100 $a20210326d2015 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aCalculus /$fWilliam Briggs [and three others] 205 $aSecond, Global edition. 210 1$aHarlow, England :$cPearson,$d[2015] 210 4$dİ2015 215 $a1 online resource (1,326 pages) $cillustrations 300 $aIncludes index. 311 $a1-292-06232-0 327 $aCover -- Title -- Copyright -- Contents -- Preface -- Credits -- 1 Functions -- 1.1 Review of Functions -- 1.2 Representing Functions -- 1.3 Trigonometric Functions -- Review Exercises -- 2 Limits -- 2.1 The Idea of Limits -- 2.2 Definitions of Limits -- 2.3 Techniques for Computing Limits -- 2.4 Infinite Limits -- 2.5 Limits at Infinity -- 2.6 Continuity -- 2.7 Precise Definitions of Limits -- Review Exercises -- 3 Derivatives -- 3.1 Introducing the Derivative -- 3.2 Working with Derivatives -- 3.3 Rules of Differentiation -- 3.4 The Product and Quotient Rules -- 3.5 Derivatives of Trigonometric Functions -- 3.6 Derivatives as Rates of Change -- 3.7 The Chain Rule -- 3.8 Implicit Differentiation -- 3.9 Related Rates -- Review Exercises -- 4 Applications of the Derivative -- 4.1 Maxima and Minima -- 4.2 What Derivatives Tell Us -- 4.3 Graphing Functions -- 4.4 Optimization Problems -- 4.5 Linear Approximation and Differentials -- 4.6 Mean Value Theorem -- 4.7 L'Ho?pital's Rule -- 4.8 Newton's Method -- 4.9 Antiderivatives -- Review Exercises -- 5 Integration -- 5.1 Approximating Areas under Curves -- 5.2 Definite Integrals -- 5.3 Fundamental Theorem of Calculus -- 5.4 Working with Integrals -- 5.5 Substitution Rule -- Review Exercises -- 6 Applications of Integration -- 6.1 Velocity and Net Change -- 6.2 Regions Between Curves -- 6.3 Volume by Slicing -- 6.4 Volume by Shells -- 6.5 Length of Curves -- 6.6 Surface Area -- 6.7 Physical Applications -- Review Exercises -- 7 Logarithmic and Exponential Functions -- 7.1 Inverse Functions -- 7.2 The Natural Logarithmic and Exponential Functions -- 7.3 Logarithmic and Exponential Functions with Other Bases -- 7.4 Exponential Models -- 7.5 Inverse Trigonometric Functions -- 7.6 L'Ho?pital's Rule and Growth Rates of Functions -- 7.7 Hyperbolic Functions -- Review Exercises -- 8 Integration Techniques. 327 $a8.1 Basic Approaches -- 8.2 Integration by Parts -- 8.3 Trigonometric Integrals -- 8.4 Trigonometric Substitutions -- 8.5 Partial Fractions -- 8.6 Other Integration Strategies -- 8.7 Numerical Integration -- 8.8 Improper Integrals -- 8.9 Introduction to Differential Equations -- Review Exercises -- 9 Sequences and Infinite Series -- 9.1 An Overview -- 9.2 Sequences -- 9.3 Infinite Series -- 9.4 The Divergence and Integral Tests -- 9.5 The Ratio, Root, and Comparison Tests -- 9.6 Alternating Series -- Review Exercises -- 10 Power Series -- 10.1 Approximating Functions with Polynomials -- 10.2 Properties of Power Series -- 10.3 Taylor Series -- 10.4 Working with Taylor Series -- Review Exercises -- 11 Parametric and Polar Curves -- 11.1 Parametric Equations -- 11.2 Polar Coordinates -- 11.3 Calculus in Polar Coordinates -- 11.4 Conic Sections -- Review Exercises -- 12 Vectors and Vector-Valued Functions -- 12.1 Vectors in the Plane -- 12.2 Vectors in Three Dimensions -- 12.3 Dot Products -- 12.4 Cross Products -- 12.5 Lines and Curves in Space -- 12.6 Calculus of Vector-Valued Functions -- 12.7 Motion in Space -- 12.8 Length of Curves -- 12.9 Curvature and Normal Vectors -- Review Exercises -- 13 Functions of Several Variables -- 13.1 Planes and Surfaces -- 13.2 Graphs and Level Curves -- 13.3 Limits and Continuity -- 13.4 Partial Derivatives -- 13.5 The Chain Rule -- 13.6 Directional Derivatives and the Gradient -- 13.7 Tangent Planes and Linear Approximation -- 13.8 Maximum/Minimum Problems -- 13.9 Lagrange Multipliers -- Review Exercises -- 14 Multiple Integration -- 14.1 Double Integrals over Rectangular Regions -- 14.2 Double Integrals over General Regions -- 14.3 Double Integrals in Polar Coordinates -- 14.4 Triple Integrals -- 14.5 Triple Integrals in Cylindrical and Spherical Coordinates -- 14.6 Integrals for Mass Calculations. 327 $a14.7 Change of Variables in Multiple Integrals -- Review Exercises -- 15 Vector Calculus -- 15.1 Vector Fields -- 15.2 Line Integrals -- 15.3 Conservative Vector Fields -- 15.4 Green's Theorem -- 15.5 Divergence and Curl -- 15.6 Surface Integrals -- 15.7 Stokes' Theorem -- 15.8 Divergence Theorem -- Review Exercises -- A Appendix Algebra Review -- B Appendix Proofs of Selected Theorems -- Answers -- Index -- Table of Integrals. 330 $aFor a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors.   This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows. The groundbreaking eBook contains over 650 Interactive Figures that can be manipulated to shed light on key concepts.   This text offers a superior teaching and learning experience. Here's how: Reflects how students use a textbook-they start with the exercises and flip back for help if they need it.   Organization and presentation of content facilitates learning of key concepts, skills, and applications. 606 $aCalculus$vTextbooks 615 0$aCalculus 676 $a515 700 $aBriggs$b William L.$0104342 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910153251703321 996 $aCalculus$93408491 997 $aUNINA