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Calculus and Its Applications has, for years, been a best-selling text for one simple reason: it anticipates, then meets the needs of today's applied calculus student. Knowing that calculus is a course in which students typically struggle--both with algebra skills and visualizing new calculus concepts--Bittinger and Ellenbogen speak to students in a way they understand, taking great pains to provide clear and careful explanations. Since most students taking this course will go on to careers in the business world, large quantities of real data, especially as they apply to business, are included as well.
Table of Contents
Preface
Diagnostic Test
R. Functions, Graphs, and Models
R.1 Graphs and Equations
R.2 Functions and Models
R.3 Finding Domain and Range
R.4 Slope and Linear Functions
R.5 Nonlinear Funtions and Models
R.6 Mathematical Modeling and Curve Fitting
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Average Price of a Movie Ticket
1. Differentiation
1.1 Limits: A Numerical and Graphical Approach
1.2 Algebraic Limits and Continuity
1.3 Average Rates of Change
1.4 Differentiation Using Limits of Difference Quotients
1.5 Differentiation Techniques: The Power and Sum-Difference Rules
1.6 Differentiation Techniques: The Product and Quotient Rules
1.7 The Chain Rule
1.8 Higher-Order Derivatives
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Path of a Baseball: The Tale of the Tape
2. Applications of Differentiation
2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.3 Graph Sketching: Asymptotes and Rational Functions
2.4 Using Derivatives to Find Absolute Maximum and Minimum Values
2.5 Maximum-Minimum Problems; Business and Economics Applications
2.6 Marginals and Differentials
2.7 Implicit Differentiation and Related Rates
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Maximum Sustainable Harvest
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Applications: Uninhibited and Limited Growth Models
3.4 Applications: Decay
3.5 The Derivatives of ax and logax
3.6 An Economics Application: Elasticity of Demand
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Business: Motion Picture and DVD Revenue
4. Integration
4.1 Antidifferentiation
4.2 Antiderivatives
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Integration Techniques: Tables
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Business: Distribution of Wealth
5. Applications of Integration
5.1 An Economics Application: Consumer Surplus and Producer Surplus
5.2 Applications of the Integration of Growth and Decay Models
5.3 Improper Integrals
5.4 Probability
5.5 Probability: Expected Value; The Normal Distribution
5.6 Volume
5.7 Differential Equations
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda
6. Functions of Several Variables
6.1 Functions of Several Variables
6.2 Partial Derivatives
6.3 Maximum-Minimum Problems
6.4 An Application: The Least-Squares Technique
6.5 Constrained Optimization
6.6 Double Integrals
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Minimizing Employees' Travel Time in a Building
Cumulative Review
Appendix A: Review of Basic Algebra
Appendix B: Regression and Microsoft Excel
Appendix C: The TI MathPrint Operating System
Tables
Answers
Index of Applications
Index
Other Editions for Calculus and Its Applications
Calculus and Its Applications has, for years, been a best-selling text for one simple reason: it anticipates, then meets the needs of today's applied calculus student. Knowing that calculus is a course in which students typically struggle--both with algebra skills and visualizing new calculus concepts--Bittinger and Ellenbogen speak to students in a way they understand, taking great pains to provide clear and careful explanations. Since most students taking this course will go on to careers in the business world, large quantities of real data, especially as they apply to business, are included as well.
Table of Contents
Table of Contents
Preface
Diagnostic Test
R. Functions, Graphs, and Models
R.1 Graphs and Equations
R.2 Functions and Models
R.3 Finding Domain and Range
R.4 Slope and Linear Functions
R.5 Nonlinear Funtions and Models
R.6 Mathematical Modeling and Curve Fitting
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Average Price of a Movie Ticket
1. Differentiation
1.1 Limits: A Numerical and Graphical Approach
1.2 Algebraic Limits and Continuity
1.3 Average Rates of Change
1.4 Differentiation Using Limits of Difference Quotients
1.5 Differentiation Techniques: The Power and Sum-Difference Rules
1.6 Differentiation Techniques: The Product and Quotient Rules
1.7 The Chain Rule
1.8 Higher-Order Derivatives
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Path of a Baseball: The Tale of the Tape
2. Applications of Differentiation
2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.3 Graph Sketching: Asymptotes and Rational Functions
2.4 Using Derivatives to Find Absolute Maximum and Minimum Values
2.5 Maximum-Minimum Problems; Business and Economics Applications
2.6 Marginals and Differentials
2.7 Implicit Differentiation and Related Rates
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Maximum Sustainable Harvest
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Applications: Uninhibited and Limited Growth Models
3.4 Applications: Decay
3.5 The Derivatives of ax and logax
3.6 An Economics Application: Elasticity of Demand
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Business: Motion Picture and DVD Revenue
4. Integration
4.1 Antidifferentiation
4.2 Antiderivatives
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Integration Techniques: Tables
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Business: Distribution of Wealth
5. Applications of Integration
5.1 An Economics Application: Consumer Surplus and Producer Surplus
5.2 Applications of the Integration of Growth and Decay Models
5.3 Improper Integrals
5.4 Probability
5.5 Probability: Expected Value; The Normal Distribution
5.6 Volume
5.7 Differential Equations
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda
6. Functions of Several Variables
6.1 Functions of Several Variables
6.2 Partial Derivatives
6.3 Maximum-Minimum Problems
6.4 An Application: The Least-Squares Technique
6.5 Constrained Optimization
6.6 Double Integrals
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Minimizing Employees' Travel Time in a Building
Cumulative Review
Appendix A: Review of Basic Algebra
Appendix B: Regression and Microsoft Excel
Appendix C: The TI MathPrint Operating System
Tables
Answers
Index of Applications
Index
Other Editions for Calculus and Its Applications