Single Variable Calculus Early Transcendentals Version / Edition 6by C. Henry Edwards, David Penney
Pub. Date: 02/28/2002
Publisher: Prentice Hall
A mainstream calculus book with the most flexible and open approach to new ideas and calculator/computer technology. Solid coverage of the calculus of early transcendental functions is now fully integrated in Chapters 1 through 6. A new Chapter 8 on differential equations appears immediately after the chapter on techniques of integration. It includes both direction fields and Euler's method, together with the more symbolic elementary methods and applications for both first- and second-order equations. The CD-ROM accompanying the book contains a functional array of fully integrated learning resources linked to individual sections of the book. The user can view any desired book section in PDF format.
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Table of Contents1. Functions, Graphs, and Models.
Functions and Mathematical Modeling. Graphs of Equationsand Functions. Polynomials and Algebraic Functions. TranscendentalFunctions. Preview: What Is Calculus?
2. Prelude to Calculus.
Tangent Lines and Slope Predictors. The Limit Concept. MoreAbout Limits. The Concept of Continuity.
3. The Derivative.
The Derivative and Rates of Change. Basic DifferentiationRules. The Chain Rule. Derivatives of Algebraic Functions. Maximaand Minima of Functions on Closed Intervals. Applied OptimizationProblems. Derivatives of Trigonometric Functions. Exponential andLogarithmic Functions. Implicit Differentiation and Related Rates.Successive Approximations and Newton's Method.
4. Additional Applications of the Derivative.
Introduction. Increments, Differentials, and Linear Approximation.Increasing and Decreasing Functions and the Mean Value Theorem. TheFirst Derivative Test and Applications. Simple Curve Sketching. HigherDerivatives and Concavity. Curve Sketching and Asymptotes. IndeterminateForms and L'Hôpitals' Rule. More Indeterminate Forms.
5. The Integral.
Introduction. Antiderivatives and Initial Value Problems.Elementary Area Computations. Riemann Sums and the Integral. Evaluationof Integrals. The Fundamental Theorem of Calculus. Integration bySubstitution. Areas of Plane Regions. Numerical Integration.
6. Applications of the Integral.
Riemann Sum Approximations. Volumes by the Method of CrossSections. Volumes by the Method of Cylindrical Shells. Arc Lengthand Surface Area of Revolution. Force and Work. Centroids of PlaneRegions and Curves. The NaturalLogarithm as an Integral. Inverse TrigonometricFunctions. Hyperbolic Functions.
7. Techniques of Integration.
Introduction. Integral Tables and Simple Substitutions.Integration by Parts. Trigonometric Integrals. Rational Functionsand Partial Fractions. Trigonometric Substitutions. Integrals InvolvingQuadratic Polynomials. Improper Integrals.
8. Differential Equations.
Simple Equations and Models. Slope Fields and Euler's Method.Separable Equations and Applications. Linear Equations and Applications.Population Models. Linear Second-Order Equations. Mechanical Vibrations.
9. Polar Coordinates and Parametric Curves.
Analytic Geometry and the Conic Sections. Polar Coordinates.Area Computations in Polar Coordinates. Parametric Curves. IntegralComputations with Parametric Curves. Conic Sections and Applications.
10. Infinite Series.
Introduction. Infinite Sequences. Infinite Series and Convergence.Taylor Series and Taylor Polynomials. The Integral Test. ComparisonTests for Positive-Term Series. Alternating Series and Absolute Convergence.Power Series. Power Series Computations. Series Solutions of DifferentialEquations.
A. Real Numbers and Inequalities. B. The Coordinate Plane and Straight Lines. C. Review of Trigonometry. D. Proofs of the Limit Laws. E. The Completeness of the Real Number System. F. Existence of the Integral. G. Approximations and Riemann Sums. H. L'Hôpital's Rule and Cauchy's Mean Value Theorem. I. Proof of Taylor's Formula. J. Conic Sections as Sections of a Cone. K. Proof of the Linear Approximation Theorem. L. Units of Measurement and Conversion Factors. M. Formulas from Algebra, Geometry, and Trigonometry. N. The Greek Alphabet.
Answers to Odd-Numbered Problems.
References for Further Study.
Table of Integrals.
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