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This item may be Check for Availability This title in other editionsCalculus, Single Variable: Early Transcendental Functions
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 Contents0 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 Functions1 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 InfinityAsymptotes1.6 Formal Definition of the LimitExploring the Definition of Limit Graphically1.7 Limits and LossofSignificance ErrorsComputer Representation of Real Numbers2 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 Theorem3 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 Sciences4 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 Logarithm5 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 Physics and Engineering5.7 Probability6 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 FractionsBrief Summary of Integration Techniques6.5 Integration Tables and Computer Algebra Systems6.6 Improper IntegralsA Comparison Test7 FirstOrder 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 FirstOrder Differential EquationsPredatorPrey Systems8 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 SeriesParametric 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 Coordinates10 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 SpaceWhat Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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