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This text for the one semester applied or business calculus course uses intriguing real-world applications to engage students' interest and show them the practical side of calculus. Many applications are financial or business related, but many applications in this text cover general-interest topics as well, including the growing population of Africa, the composition of the Supreme Court, water shortage, the fastest pitch in baseball, and pollution and the depletion of natural resources. The Fifth Edition maintains the hallmark features that have made Brief Applied Calculus so popular: contemporary and interesting applications; careful and effective use of technology, including integrated calculator coverage that is optional; constant pedagogical reinforcement through section summaries, chapter summaries, carefully annotated examples, and extra practice problems; and a variety of exercises and assignment options including exercise sets, projects, and essays.
Preface.
A User's Guide to Features.
Integrating Excel.
Graphing Calculator Terminology.
1. FUNCTIONS.
Real Numbers, Inequalities, and Lines.
Exponents.
Functions.
Functions, Continued.
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 and Second Derivatives.
Optimization.
Further Applications of Optimization.
Optimizing Lot Size and Harvest Size.
Implicit Differentiation and Related Rules.
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 AND DIFFERENTIAL EQUATIONS.
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.
Cumulative Review for Chapters 1-7.
Answers to Selected Exercises.
Index.
Geoffrey C. Berresford and Andrew M. Rockett
ISBN13: 978-0547169774This text for the one semester applied or business calculus course uses intriguing real-world applications to engage students' interest and show them the practical side of calculus. Many applications are financial or business related, but many applications in this text cover general-interest topics as well, including the growing population of Africa, the composition of the Supreme Court, water shortage, the fastest pitch in baseball, and pollution and the depletion of natural resources. The Fifth Edition maintains the hallmark features that have made Brief Applied Calculus so popular: contemporary and interesting applications; careful and effective use of technology, including integrated calculator coverage that is optional; constant pedagogical reinforcement through section summaries, chapter summaries, carefully annotated examples, and extra practice problems; and a variety of exercises and assignment options including exercise sets, projects, and essays.
Table of Contents
Preface.
A User's Guide to Features.
Integrating Excel.
Graphing Calculator Terminology.
1. FUNCTIONS.
Real Numbers, Inequalities, and Lines.
Exponents.
Functions.
Functions, Continued.
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 and Second Derivatives.
Optimization.
Further Applications of Optimization.
Optimizing Lot Size and Harvest Size.
Implicit Differentiation and Related Rules.
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 AND DIFFERENTIAL EQUATIONS.
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.
Cumulative Review for Chapters 1-7.
Answers to Selected Exercises.
Index.