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Informationen zum Autor Satunino L. Salas is the author of various Wiley calculus textbooks. Garret Etgen is a professor of mathematics and the University of Houston. Klappentext Wiley is proud to publish a new revision of this successful classic text known for its elegant writing style, precision and perfect balance of theory and applications. This Tenth Edition offers students an even clearer understanding of calculus and insight into mathematics. It includes a wealth of rich problem sets which makes calculus relevant for students. Salas/Hille/Etgen is recognized for its mathematical integrity, accuracy, and clarity. Zusammenfassung For ten editions! readers have turned to Salas to learn the difficult concepts of calculus without sacrificing rigor. The book consistently provides clear calculus content to help them master these concepts and understand its relevance to the real world. Inhaltsverzeichnis Chapter 1. Precalculus Review . 1 1.1 What is Calculus? 1 1.2 Review of Elementary Mathematics.3 1.3 Review of Inequalities.11 1.4 Coordinate Plane; Analytic Geometry.17 1.5 Functions.24 1.6 The Elementary Functions.32 1.7 Combinations of Functions.41 1.8 A Note on Mathematical Proof; Mathematical Induction.47 Chapter 2. Limits and Continuity.53 2.1 The Limit Process (An Intuitive Introduction).53 2.2 Definition of Limit.64 2.3 Some Limit Theorems.73 2.4 Continuity.82 2.5 The Pinching Theorem; Trigonometric Limits.91 2.6 Two Basic Theorems.97 Project 2.6 The Bisection Method for Finding the Roots of f ( x ) = 0 102 Chapter 3. The Derivative; The Process of Differentiation.105 3.1 The Derivative.105 3.2 Some Differentiation Formulas.115 3.3 The d/dx Notation; Derivatives of Higher Order.124 3.4 The Derivative as a Rate of Change.130 3.5 The Chain Rule.133 3.6 Differentiating the Trigonometric Functions.142 3.7 Implicit Differentiation; Rational Powers.147 Chapter 4. The Mean-Value Theorem; Applications of the First and Second Derivatives.154 4.1 The Mean-Value Theorem.154 4.2 Increasing and Decreasing Functions.160 4.3 Local Extreme Values.167 4.4 Endpoint Extreme Values; Absolute Extreme Values.174 4.5 Some Max-Min Problems.182 Project 4.5 Flight Paths of Birds 190 4.6 Concavity and Points of Inflection.190 4.7 Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps.195 4.8 Some Curve Sketching.201 4.9 Velocity and Acceleration; Speed.209 Project 4.9A Angular Velocity; Uniform Circular Motion 217 Project 4.9B Energy of a Falling Body (Near the Surface of the Earth) 217 4.10 Related Rates of Change Per Unit Time.218 4.11 Differentials.223 Project 4.11 Marginal Cost, Marginal Revenue, Marginal Profit 228 4.12 Newton-Raphson Approximations.229 Chapter 5. Integration.234 5.1 An Area Problem; A Speed-Distance Problem.234 5.2 The Definite Integral of a Continuous Function.234 5.3 The Function f (x) = Integral from a to x of f (t) dt .246 5.4The Fundamental Theorem of Integral Calculus.254 5.5 Some Area Problems.260 Project 5.5 Integrability; Integrating Discontinuous Functions 266 5.6 Indefinite Integrals.268 5.7 Working Back from the Chain Rule; the u -Substitution.274 5.8 Additional Properties of the Definite Integral.281 5.9 Mean-Value Theorems for Integrals; Average Value of a Function.285 Chapter 6. Some Applications of the Integral.292 6.1 More on Area.292 6.2 Volume by Parallel Cross-Sections; Discs and Washers.296 6.3 Volume by the Shell Method.306 6.4 The Centroid of a Re...
