Thomas' calculus : based on the original work by George B. Thomas / Maurice D. Weir, Joel Hass, Frank R. Giordano.

Includes index.

(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.) Preliminaries Real Numbers and the Real LineLines, Circles, and ParabolasFunctions and Their GraphsIdentifying Functions; Mathematical ModelsCombining Functions; Shifting and Scaling GraphsTrigonometric FunctionsGraphing with Calculators and Computers 2. Limits and Derivatives Rates of Change and LimitsCalculating Limits Using the Limit LawsPrecise Definition of a LimitOne-Sided Limits and Limits at InfinityInfinite Limits and Vertical AsymptotesContinuityTangents and Derivatives 3. Differentiation The Derivative as a FunctionDifferentiation RulesThe Derivative as a Rate of ChangeDerivatives of Trigonometric FunctionsThe Chain Rule and Parametric EquationsImplicit DifferentiationRelated RatesLinearization and Differentials 4. Applications of Derivatives Extreme Values of FunctionsThe Mean Value TheoremMonotonic Functions and the First Derivative TestConcavity and Curve SketchingApplied Optimization ProblemsIndeterminate Forms and L'Hopital's RuleNewton's MethodAntiderivatives 5. Integration Estimating with Finite SumsSigma Notation and Limits of Finite SumsThe Definite IntegralThe Fundamental Theorem of CalculusIndefinite Integrals and the Substitution RuleSubstitution and Area Between Curves 6. Applications of Definite Integrals Volumes 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 Forces 7. Transcendental Functions Inverse Functions and their DerivativesNatural LogarithmsThe Exponential Functionax and loga xExponential Growth and DecayRelative Rates of GrowthInverse Trigonometric FunctionsHyperbolic Functions 8. Techniques of Integration Basic Integration FormulasIntegration by PartsIntegration of Rational Functions by Partial FractionsTrigonometric IntegralsTrigonometric SubstitutionsIntegral Tables and Computer Algebra SystemsNumerical IntegrationImproper Integrals 9. Further Applications of Integration Slope Fields and Separable Differential EquationsFirst-Order Linear Differential EquationsEuler's MethodGraphical Solutions of Autonomous EquationsApplications of First-Order Differential Equations 10. Conic Sections and Polar Coordinates Conic Sections and Quadratic Equations Classifying Conic Sections by EccentricityQuadratic Equations and RotationsConics and Parametric Equations; The CycloidPolar Coordinates Graphing in Polar CoordinatesArea and Lengths in Polar CoordinatesConic Sections in Polar Coordinates 11. Infinite Sequences and Series SequencesInfinite 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 Series 12. Vectors and the Geometry of Space Three-Dimensional Coordinate SystemsVectorsThe Dot ProductThe Cross ProductLines and Planes in SpaceCylinders and Quadric Surfaces 13. Vector-Valued Functions and Motion in Space Vector FunctionsModeling Projectile MotionArc Length and the Unit Tangent Vector TCurvature and the Unit Normal Vector NTorsion and the Unit Binormal Vector BPlanetary Motion and Satellites 14. Partial Derivatives Functions of Several VariablesLimits and Continuity in Higher DimensionsPartial DerivativesThe Chain RuleDirectional Derivatives and Gradient VectorsTangent Planes and DifferentialsExtreme Values and Saddle PointsLagrange Multipliers*Partial Derivatives with Constrained VariablesTaylor's Formula for Two Variables 15. Multiple Integrals Double IntegralsAreas, Moments and Centers of Mass*Double Integrals in Polar FormTriple Integrals in Rectangular CoordinatesMasses and Moments in Three DimensionsTriple Integrals in Cylindrical and Spherical CoordinatesSubstitutions in Multiple Integrals 16. Integration in Vector Fields Line IntegralsVector Fields, Work, Circulation, and FluxPath Independence, Potential Functions, and Conservative FieldsGreen's Theorem in the PlaneSurface Area and Surface IntegralsParametrized SurfacesStokes' TheoremThe Divergence Theorem and a Unified Theory Appendices Mathematical InductionProofs of Limit TheoremsCommonly Occurring Limits Theory 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