Calculus with applications

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Langue : Anglais

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This book is for the one-term calculus course taken by students in business, economics, management, and the social, biological and environmental sciences. A prerequisite of intermediate algebra is assumed. In courses where college algebra is the prerequisite, much of Chapter 1 may be omitted. For students that need additional work in algebra, an algebra review is provided in Appendix A. Since the students who use this book aspire to become users of mathematics rather than makers of mathematics, the text includes few mathematical proofs. The author introduces a deducible statement through a concrete situation that either illustrates the statement or involves steps that parallel those in a general proof. Concepts are motivated through examples of particular interest to the student, rather than examples whose attraction is primarily mathematical. The focus is on problem solving, and the author has taken great care in writing the exercise sets so the student can practice these skills. Exercise sets include problems that ask the student to discuss, write, explore, and use technology. Many sections include graphing calculator problems, and a few of these sections contain subsections that serve as a basis for the problems. These problems are clearly identified with an icon. In addition, Calculus with Applications integrates nine basic computer programs. The sections where these programs appear also include problems that take advantage of the computer. This material may be omitted without disturbing the continuity of the text.
CHAPTER 1: Functions and Limits. Functions. Finding Formulas for Functions. Linear Functions. Quadratic Functions. Limits at Infinity. Limits as x c and Continuity. Important Terms. Review Problems. CHAPTER 2: Differentiation. Slopes of Tangents. The Derivative. Rules for Computing Derivatives. Approximating Change. More Rules for Computing Derivatives. Optimization on Closed Intervals. More on Optimization. More on Approximating Change. Important Terms. Review Problems. CHAPTER 3: More on Differentiation. Instantaneous Rates. The Second Derivative and Curve Sketching. More on the Second Derivative. Two Useful Rational Functions. More on Rational Functions. Percentage Rate of Change. Newton's Method for Approximating Zeros. Important Terms. Review Problems. CHAPTER 4: Exponential and Logarithmic Functions. Compound Interest. Exponential Functions. The Natural Logarithmic Function. Differentiation of ln u(x). Differentiation of e u(x). Two Models for Bounded Growth. Important Terms. Review Problems. CHAPTER 5: Integration. Antidifferentiation. The Definite Integral. Area and Definite Integrals. Integration by Substitution. Integration by Parts. Riemann Sums. Important Terms. Review Problems. CHAPTER 6: More on Integration. Simpson's Rule. Consumers' and Producers' Surpluses. Probability. Expected Value. Differential Equations for Exponential Change. Differential Equations for Bounded Change. Important Terms. Review Problems. CHAPTER 7: Differentiation of Functions of More than One Variable. Functions of More than One Variable. Partial Derivatives. Optimization. The Second Derivative Test. Curve Fitting. Constrained Optimization. The Method of Lagrange Multipliers. Important Terms. Review Problems. Appendix A Algebra Review. Real Numbers. Exponents and Radicals. Polynomial Expressions Rational Expressions. Appendix B Integration by Tables.