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The hallmark of this popular text for the two-semester applied or business calculus course is its ability to engage students with a wealth of intriguing real-world applications.
Retaining the strengths of its first edition, Applied Calculus, 2/e, features updated optional graphing calculator coverage. In addition, project and essay questions previously found at the end of each chapter are now incorporated into the section exercise sets.
Preliminary Contents
Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises.
1. Functions
1.1 Real Numbers, Inequalities, and Lines
1.2 Exponents
1.3 Functions
1.4 Functions, Continued
2. Derivatives and Their Uses
2.1 Limits and Continuity
2.2 Slopes, Rates of Change, and Derivatives
2.3 Some Differentiation Formulas
2.4 The Product and Quotient Rules
2.5 Higher-Order Derivatives
2.6 The Chain Rule and the Generalized Power Rule
2.7 Nondifferentiable Functions
3. Further Applications of The Derivative
3.1 Graphing Using the First Derivative
3.2 Graphing Using the First and Second Derivatives
3.3 Optimization
3.4 Further Applications of Optimization
3.5 Optimizing Lost Size and harvest Size
3.6 Implicit Differentiation and Related Rates
Cumulative Review for Chapters 1-3
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Differentiation of Logarithmic and Exponential Functions
4.4 Two Applications to Economics: Relative Rates and Elasticity of Demand
5. Integration and Its Applications
5.1 Antiderivatives
5.2 Integration Using Logarithmic and Exponential Functions
5.3 Definite Integrals and Areas
5.4 Further Applications of Definite Integrals: Average Value and Area Between Curves
5.5 Two Applications to Economics: Consumers' Surplus and Income Distribution
5.6 Integration by Substitution
6. Integration Techniques
6.1 Integration by Parts
6.2 Integration Using Tables
6.3 Improper Integrals
6.4 Numerical Integration
7. Calculus of Several Variables
7.1 Functions of Several Variables
7.2 Partial Derivatives
7.3 Optimizing Functions of Several Variables
7.4 Least Squares
7.5 Lagrange Multipliers and Constrained optimization
7.6 Total Differentials and Approximate Changes
7.7 Multiple Integrals
Cumulative Review for Chapters 1-7
8. Trigonometric Functions
8.1 Angles, Triangles, and Radian Measure
8.2 Sine and Cosine Functions
8.3 Derivatives of Sine and Cosine Functions
8.4 Integrals of Sine and Cosine Functions
8.5 Other Trigonometric Functions
9. Differential Equations
9.1 Separation of Variables
9.2 Further Applications of Differential Equations: Three Models of Growth
9.3 First-Order Differential Equations
9.4 Approximate Solutions of Differential Equations: Euler's Method
10. Sequences and Series
10.1 Geometric Series
10.2 Taylor Polynomials
10.3 Taylor Series
10.4 Newton's Method
11. Probability
11.1 Discrete Probability
11.2 Continuous Probability
11.3 Uniform and Exponential Random Variables
11.4 Normal Random Variables
Cumulative Review for Chapters 1-11
Appendix Normal Probabilities from Tables
Solutions to Practice Problems
Answers to Selected Exercises
Index
Geoffrey C. Berresford and Andrew M. Rockett
ISBN13: 978-0395978177The hallmark of this popular text for the two-semester applied or business calculus course is its ability to engage students with a wealth of intriguing real-world applications.
Retaining the strengths of its first edition, Applied Calculus, 2/e, features updated optional graphing calculator coverage. In addition, project and essay questions previously found at the end of each chapter are now incorporated into the section exercise sets.
Table of Contents
Preliminary Contents
Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises.
1. Functions
1.1 Real Numbers, Inequalities, and Lines
1.2 Exponents
1.3 Functions
1.4 Functions, Continued
2. Derivatives and Their Uses
2.1 Limits and Continuity
2.2 Slopes, Rates of Change, and Derivatives
2.3 Some Differentiation Formulas
2.4 The Product and Quotient Rules
2.5 Higher-Order Derivatives
2.6 The Chain Rule and the Generalized Power Rule
2.7 Nondifferentiable Functions
3. Further Applications of The Derivative
3.1 Graphing Using the First Derivative
3.2 Graphing Using the First and Second Derivatives
3.3 Optimization
3.4 Further Applications of Optimization
3.5 Optimizing Lost Size and harvest Size
3.6 Implicit Differentiation and Related Rates
Cumulative Review for Chapters 1-3
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Differentiation of Logarithmic and Exponential Functions
4.4 Two Applications to Economics: Relative Rates and Elasticity of Demand
5. Integration and Its Applications
5.1 Antiderivatives
5.2 Integration Using Logarithmic and Exponential Functions
5.3 Definite Integrals and Areas
5.4 Further Applications of Definite Integrals: Average Value and Area Between Curves
5.5 Two Applications to Economics: Consumers' Surplus and Income Distribution
5.6 Integration by Substitution
6. Integration Techniques
6.1 Integration by Parts
6.2 Integration Using Tables
6.3 Improper Integrals
6.4 Numerical Integration
7. Calculus of Several Variables
7.1 Functions of Several Variables
7.2 Partial Derivatives
7.3 Optimizing Functions of Several Variables
7.4 Least Squares
7.5 Lagrange Multipliers and Constrained optimization
7.6 Total Differentials and Approximate Changes
7.7 Multiple Integrals
Cumulative Review for Chapters 1-7
8. Trigonometric Functions
8.1 Angles, Triangles, and Radian Measure
8.2 Sine and Cosine Functions
8.3 Derivatives of Sine and Cosine Functions
8.4 Integrals of Sine and Cosine Functions
8.5 Other Trigonometric Functions
9. Differential Equations
9.1 Separation of Variables
9.2 Further Applications of Differential Equations: Three Models of Growth
9.3 First-Order Differential Equations
9.4 Approximate Solutions of Differential Equations: Euler's Method
10. Sequences and Series
10.1 Geometric Series
10.2 Taylor Polynomials
10.3 Taylor Series
10.4 Newton's Method
11. Probability
11.1 Discrete Probability
11.2 Continuous Probability
11.3 Uniform and Exponential Random Variables
11.4 Normal Random Variables
Cumulative Review for Chapters 1-11
Appendix Normal Probabilities from Tables
Solutions to Practice Problems
Answers to Selected Exercises
Index