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This item may be Check for Availability Calculus: Early Transcendental Functions: Multivariableby Robert Smith
Synopses & ReviewsPublisher Comments: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 best elements of reform with the most reliable aspects of mainstream calculus teaching, resulting in a motivating, challenging book. Smith/Minton also provide exceptional, realitybased applications that appeal to students interests and demonstrate the elegance of math in the world around us. New features include: • A new organization placing all transcendental functions early in the book and consolidating the introduction to L'Hôpital's Rule in a single section. • More concisely written explanations in every chapter. • Many new exercises (for a total of 7,000 throughout the book) that require additional rigor not found in the 2nd Edition. • New exploratory exercises in every section that challenge students to synthesize key concepts to solve intriguing projects. • New commentaries (“Beyond Formulas”) that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, “Today in Mathematics,” that 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.
Table of ContentsChapter 0: Preliminaries0.1 Polynomials and Rational Functions0.2 Graphing Calculators and Computer Algebra Systems0.3 Inverse Functions0.4 Trigonometric and Inverse Trigonometric Functions0.5 Exponential and Logarithmic FunctionsHyperbolic FunctionsFitting a Curve to Data0.6 Transformations of FunctionsChapter 1: Limits and Continuity1.1 A First Look at Calculus1.2 The Concept of Limit1.3 Computation of Limits1.4 Continuity and its ConsequencesThe Method of Bisections1.5 Limits Involving InfinityAsymptotes1.6 Formal Definition of the LimitExploring the Definition of Limit Graphically1.7 Limits and LossofSignificance ErrorsComputer Representation of Real NumbersChapter 2: Differentiation2.1 Tangent Lines and Velocity2.2 The DerivativeNumerical 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 Derivatives of the Exponential and Logarithmic Functions2.8 Implicit Differentiation and Inverse Trigonometric Functions2.9 The Mean Value TheoremChapter 3: Applications of Differentiation3.1 Linear Approximations and Newtons Method3.2 Indeterminate Forms and LHopitals Rule3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity and the Second Derivative Test3.6 Overview of Curve Sketching3.7 Optimization3.8 Related Rates3.9 Rates of Change in Economics and the SciencesChapter 4: Integration4.1 Antiderivatives4.2 Sums and Sigma NotationPrinciple of Mathematical Induction4.3 Area4.4 The Definite IntegralAverage Value of a Function4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical IntegrationError Bounds for Numerical Integration4.8 The Natural Logarithm as an IntegralThe Exponential Function as the Inverse of the Natural LogarithmChapter 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 Surface Area5.5 Projectile Motion5.6 Applications of Integration to Economics and the Sciences5.7 ProbabilityChapter 6: Integration Techniques6.1 Review of Formulas and Techniques6.2 Integration by Parts6.3 Trigonometric Techniques of IntegrationIntegrals Involving Powers of Trigonometric FunctionsTrigonometric Substitution6.4 Integration of Rational Functions Using Partial FractionsGeneral Strategies for Integration Techniques6.5 Integration Tables and Computer Algebra Systems6.6 Improper IntegralsA Comparison TestChapter 7: First Order Differential Equations7.1 Growth and Decay ProblemsCompound InterestModeling with Differential Equations7.2 Separable Differential EquationsLogistic Growth7.3 Direction Fields and Euler's Method7.4 Systems of First Order Differential EquationsPredatorPrey SystemsChapter 8: Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating SeriesEstimating the Sum of an Alternating Series8.5 Absolute Convergence and the Ratio TestThe Root TestSummary of Convergence Tests8.6 Power Series8.7 Taylor SeriesRepresentations of Functions as SeriesProof of Taylors Theorem8.8 Applications of Taylor SeriesThe Binomial Series8.9 Fourier SeriesChapter 9: Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar CoordinatesChapter 10: Vectors and the Geometry of Space10.1 Vectors in the Plane10.2 Vectors in Space10.3 The Dot ProductComponents and Projections10.4 The Cross Product10.5 Lines and Planes in Space10.6 Surfaces in SpaceChapter 11: VectorValued Functions11.1 VectorValued Functions11.2 The Calculus of VectorValued Functions11.3 Motion in Space11.4 Curvature11.5 Tangent and Normal VectorsTangential and Normal Components of AccelerationKeplers Laws11.6 Parametric SurfacesChapter 12: Functions of Several Variables and Differentiation12.1 Functions of Several Variables12.2 Limits and Continuity12.3 Partial Derivatives12.4 Tangent Planes and Linear ApproximationsIncrements and Differentials12.5 The Chain Rule12.6 The Gradient and Directional Derivatives12.7 Extrema of Functions of Several Variables12.8 Constrained Optimization and Lagrange MultipliersChapter 13: Multiple Integrals13.1 Double Integrals13.2 Area, Volume, and Center of Mass13.3 Double Integrals in Polar Coordinates13.4 Surface Area13.5 Triple IntegralsMass and Center of Mass13.6 Cylindrical Coordinates13.7 Spherical Coordinates13.8 Change of Variables in Multiple IntegralsChapter 14: Vector Calculus14.1 Vector Fields14.2 Line Integrals14.3 Independence of Path and Conservative Vector Fields14.4 Green's Theorem14.5 Curl and Divergence14.6 Surface Integrals14.7 The Divergence Theorem14.8 Stokes' Theorem14.9 Applications of Vector CalculusChapter 15: Second Order Differential Equations15.1 SecondOrder Equations with Constant Coefficients15.2 Nonhomogeneous Equations: Undetermined Coefficients15.3 Applications of Second Order Equations15.4 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
Related SubjectsScience and Mathematics » Mathematics » Calculus » General Textbooks » General 

