- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Calculus hasn't changed, but your students have. Many of today's students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas' Calculus Early Transcendentals, Part One, Media Upgrade, Eleventh Edition responds to the needs of today's students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course. Thomas' Calculus Early Transcendentals, Part One, Media Upgrade, Eleventh Edition is now available with an enhanced MyMathLab (TM) course-the ultimate homework, tutorial and study solution for today's students. The enhanced MyMathLab (TM) course includes a rich and flexible set of course materials and features innovative Java (TM) Applets, Group Projects, and new MathXL (R) exercises. This text is also available with WebAssign (R) and WeBWorK (R).
Contents
1. FunctionsFunctions and Their GraphsIdentifying Functions; Mathematical ModelsCombining Functions; Shifting and Scaling GraphsGraphing with Calculators and ComputersExponential FunctionsInverse Functions and Logarithms2. Limits and ContinuityRates of Change and LimitsCalculating Limits Using the Limit LawsPrecise Definition of a LimitOne-Sided Limits and Limits at InfinityInfinite Limits and Vertical AsymptotesContinuityTangents and Derivatives3. DifferentiationThe Derivative as a FunctionDifferentiation Rules for Polynomials, Exponentials, Products and QuotientsThe Derivative as a Rate of ChangeDerivatives of Trigonometric FunctionsThe Chain Rule and Parametric EquationsImplicit DifferentiationDerivatives of Inverse Functions and LogarithmsInverse Trigonometric FunctionsRelated RatesLinearization and Differentials4. Applications of DerivativesExtreme Values of FunctionsThe Mean Value TheoremMonotonic Functions and the First Derivative TestConcavity and Curve SketchingApplied Optimization ProblemsIndeterminate Forms and L'Hopital's RuleNewton's MethodAntiderivatives5. IntegrationEstimating with Finite SumsSigma Notation and Limits of Finite SumsThe Definite IntegralThe Fundamental Theorem of CalculusIndefinite Integrals and the Substitution RuleSubstitution and Area Between Curves6. Applications of Definite IntegralsVolumes by Slicing and Rotation About an AxisVolumes by Cylindrical ShellsLengths of Plane CurvesMoments and Centers of MassAreas of Surfaces of Revolution and The Theorems of PappusWorkFluid Pressures and Forces7. Integrals and Transcendental FunctionsThe Logarithm Defined as an IntegralExponential Growth and DecayRelative Rates of GrowthHyperbolic Functions8. Techniques of IntegrationBasic Integration FormulasIntegration by PartsIntegration of Rational Functions by Partial FractionsTrigonometric IntegralsTrigonometric SubstitutionsIntegral Tables and Computer Algebra SystemsNumerical IntegrationImproper Integrals9. Further Applications of IntegrationSlope Fields and Separable Differential EquationsFirst-Order Linear Differential EquationsEuler's MethodGraphical Solutions of Autonomous EquationsApplications of First-Order Differential Equations10. Conic Sections and Polar CoordinatesConic Sections and Quadratic EquationsClassifying Conic Sections by EccentricityQuadratic Equations and RotationsConics and Parametric Equations; The CycloidPolar CoordinatesGraphing in Polar CoordinatesArea and Lengths in Polar CoordinatesConic Sections in Polar Coordinates11. Infinite Sequences and SeriesSequencesInfinite SeriesThe Integral TestComparison TestsThe Ratio and Root TestsAlternating Series, Absolute and Conditional ConvergencePower SeriesTaylor and Maclaurin SeriesConvergence of Taylor Series; Error EstimatesApplications of Power SeriesFourier SeriesAppendices.Mathematical InductionProofs of Limit TheoremsCommonly Occurring LimitsTheory of the Real NumbersComplex NumbersThe Distributive Law for Vector Cross ProductsDeterminants and Cramer's RuleThe Mixed Derivative Theorem and the Increment TheoremThe Area of a Parallelogram's Projection on a Plane
