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This item may be Check for Availability This title in other editionsCalculus: Late Transcendental Functions
Synopses & ReviewsPublisher Comments:Smith/Minton: Mathematically Precise. StudentFriendly. Superior Technology. Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors approach which combines the most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, realitybased applications that appeal to students interests and demonstrate the elegance of math in the world around us. New features include: • Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises • New exploratory exercises in every section that challenge students to make connections to previous introduced material. • New commentaries (“Beyond Formulas”) that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, “Today in Mathematics,” stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus. • Exceptional Media Resources: Within MathZone, instructors and students have access to a series of unique Conceptual Videos that help students understand key Calculus concepts proven to be most difficult to comprehend, 248 Interactive Applets that help students master concepts and procedures and functions, 1600 algorithms , and 113 eProfessors.
Table of ContentsChapter 0: Preliminaries0.1 The Real Numbers and the Cartesian Plane0.2 Lines and Functions0.3 Graphing Calculators and Computer Algebra Systems0.4 Trigonometric Functions0.5 Transformations of FunctionsChapter 1: Limits and Continuity1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve1.2 The Concept of Limit1.3 Computation of Limits1.4 Continuity and its ConsequencesThe Method of Bisections1.5 Limits Involving InfinityAsysmptotes1.6 The Formal Definition of the Limit1.7 Limits and LossofSignificance ErrorsComputer Representation or Real NumbersChaper 2: Differentiation2.1 Tangent Lines and Velocity2.2 The DerivativeAlternative Derivative NotationsNumerical Differentiation2.3 Computation of Derivatives: The Power RuleHigher Order DerivativesAcceleration2.4 The Product and Quotient Rules2.5 The Chain Rule2.6 Derivatives of the Trigonometric Functions2.7 Implicit Differentiation2.8 The Mean Value TheoremChapter 3: Applications of Differentiation3.1 Linear Approximations and Newton's Method3.2 Maximum and Minimum Values3.3 Increasing and Decreasing Functions3.4 Concavity and the Second Derivative Test3.5Overview of Curve Sketching3.6Optimization3.8Related Rates3.8Rates of Change in Economics and the SciencesChapter 4: Integration4.1 Antiderivatives4.2 Sums and Sigma NotationPrinciple of Mathematical Induction4.3 Area under a Curve4.4 The Definite IntegralAverage Value of a Function4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical IntegrationError bounds for Numerical IntegrationChapter 5: Applications of the Definite Integral5.1 Area Between Curves5.2 Volume: Slicing, Disks, and Washers5.3 Volumes by Cylindrical Shells5.4 Arc Length and Srface Area5.5 Projectile Motion5.6 Applications of Integration to Physics and EngineeringChapter 6: Exponentials, Logarithms and other Transcendental Functions6.1 The Natural Logarithm6.2 Inverse Functions6.3 Exponentials6.4 The Inverse Trigonometric Functions6.5 The Calculus of the Inverse Trigonometric Functions6.6 The Hyperbolic FunctionChapter 7: FirstOrder Differential Equations7.1 Modeling with Differential EquationsGrowth and Decay ProblemsCompound Interest7.2 Separable Differential EquationsLogistic Growth7.3 Direction Fields and Euler's Method7.4 Systems of FirstOrder Differential EquationsPredatorPrey Systems7.6 Indeterminate Forms and L'Hopital's RuleImproper IntegralsA Comparison Test7.8 ProbabilityChapter 8: FirstOrder Differential Equations8.1 modeling with Differential EquationsGrowth and Decay ProblemsCompound Interest8.2 Separable Differential EquationsLogistic Growth8.3 Direction Fields and Euler's MethodSystems of First Order EquationsChapter 9: Infinite Series9.1 Sequences of Real Numbers9.2 Infinite Series9.3 The Integral Test and Comparison Tests9.4 Alternating SeriesEstimating the Sum of an Alternating Series9.5 Absolute Convergence and the Ratio TestThe Root TestSummary of Convergence Test9.6 Power Series9.7 Taylor SeriesRepresentations of Functions as SeriesProof of Taylor's Theorem9.8 Applications of Taylor SeriesThe Binomial Series9.9 Fourier SeriesChapter 10: Parametric Equations and Polar Coordinates10.1 Plane Curves and Parametric Equations10.2 Calculus and Parametric Equations10.3 Arc Length and Surface Area in Parametric Equations10.4 Polar Coordinates10.5 Calculus and Polar Coordinates10.6 Conic Sections10.7 Conic Sections in Polar CoordinatesChapter 11: Vectors and the Geometry of Space11.1 Vectors in the Plane11.2 Vectors in Space11.3 The Dot ProductComponents and Projections11.4 The Cross Product11.5 Lines and Planes in Space11.6 Surfaces in SpaceChapter 12: VectorValued Functions12.1 VectorValued Functions12.2 The Calculus VectorValued Functions12.3 Motion in Space12.4 Curvature12.5 Tangent and Normal VectorsComponents of Acceleration, Kepler's Laws11.6 Parametric SurfacesChapter 13: Functions of Several Variables and Partial Differentiation13.1 Functions of Several Variables13.2 Limits and Continuity13.3 Partial Derivatives13.4 Tangent Planes and Linear ApproximationsIncrements and Differentials13.5 The Chain RuleImplicit Differentiation13.6 The Gradient and Directional Derivatives13.7 Extrema of Functions of Several Variables13.8 Constrained Optimization and Lagrange MultipliersChapter 14: Multiple Integrals14.1 Double Integrals14.2 Area, Volume, and Center of Mass14.3 Double Integrals in Polar Coordinates14.4 Surface Area14.5 Triple IntegralsMass and Center of Mass14.6 Cylindrical Coordinates14.7 Spherical Coordinates14.8 Change of Variables in Multiple IntegralsChapter 15: Vector Calculus15.1 Vector Fields15.2 Line Integrals15.3 Independence of Path and Conservative Vector Fields15.4 Green's Theorem15.5 Curl and Divergence15.6 Surface Integrals15.7 The Divergence Theorem15.8 Stokes' Theorem15.9 Applications of Vector CalculusChapter 16: SecondOrder Differential Equations16.1 SecondOrder Equations with Constant Coefficients16.2 Nonhomogeneous Equations: Undetermined Coefficients16.3 Applications of SecondOrder Differential Equations16.4 Power Series Solutions of Differential EquationsAppendix A: Proofs of Selected TheoremsAppendix B: Answers to OddNumbered ExercisesWhat Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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