Applied Calculus, Brief / Edition 5by Geoffrey C. Berresford, Andrew M. Rockett
Pub. Date: 11/20/2008
Publisher: Cengage Learning
This text uses intriguing real-world applications to engage readers' interest and show them the practical side of calculus. The book's many applications are related to finance, business, and such general-interest topics as learning curves in airplane production, the age of the Dead Sea Scrolls, Apple and Oracle stock prices, the distance traveled by sports cars,… See more details below
This text uses intriguing real-world applications to engage readers' interest and show them the practical side of calculus. The book's many applications are related to finance, business, and such general-interest topics as learning curves in airplane production, the age of the Dead Sea Scrolls, Apple and Oracle stock prices, the distance traveled by sports cars, lives saved by seat belts, and the cost of a congressional victory. The Sixth Edition maintains the hallmark features that have made APPLIED CALCULUS, BRIEF so popular: contemporary and interesting applications; careful and effective use of technology, including graphing calculator and spreadsheet coverage; constant pedagogical reinforcement through section summaries, chapter summaries, annotated examples, and extra practice problems; Just-in-Time algebra review material; and a variety of exercises that allow readers to practice and hone their problem-solving skills.
Table of Contents
1. FUNCTIONS. Real Numbers, Inequalities, and Lines. Exponents. Functions: Linear and Quadratic. Functions: Polynomial, Rational, and Exponential. 2. DERIVATIVES AND THEIR USES. Limits and Continuity. Rates of Change, Slopes, and Derivatives. Some Differentiation Formulas. The Product and Quotient Rules. Higher-Order Derivatives. The Chain Rule and the Generalized Power Rule. Nondifferentiable Functions. 3. FURTHER APPLICATIONS OF DERIVATIVES. Graphing Using the First Derivative. Graphing Using the First and Second Derivatives. Optimization. Further Applications of Optimization. Optimizing Lot Size and Harvest Size. Implicit Differentiation and Related Rates. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Differentiation of Logarithmic and Exponential Functions. Two Applications to Economics: Relative Rates and Elasticity of Demand. 5. INTEGRATION AND ITS APPLICATIONS. Antiderivatives and Indefinite Integrals. Integration Using Logarithmic and Exponential Functions. Definite Integrals and Areas. Further Applications of Definite Integrals: Average Value and Area Between Curves. Two Applications to Economics: Consumers' Surplus and Income Distribution. Integration by Substitution. 6. INTEGRATION TECHNIQUES. Integration by Parts. Integration Using Tables. Improper Integrals. Numerical Integration. Differential Equations. Further Applications of Differential Equations: Three Models of Growth. 7. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Optimizing Functions of Several Variables. Least Squares. Lagrange Multipliers and Constrained Optimization. Total Differentials and Approximate Changes. Multiple Integrals.
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