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Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition introduces calculus in real-world contexts and provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, the life sciences, and the social sciences. This EXPANDED EDITION includes four additional chapters on Differential Equations, Infinite Series and Taylor Approximations, Probability, and Trigonometric Functions. The new Ninth Edition builds on the straightforward writing style, practical applications from a variety of disciplines, clear step-by-step problem solving techniques, and comprehensive exercise sets that have been hallmarks of Hoffmann/Bradley's success through the years.
Calculator Introduction
1. Functions, Graphs, and Limits
1.1 Functions
1.2 The Graph of a Function
1.3 Linear Functions
1.4 Functional Models
1.5 Limits
1.6 One-Sided Limits and Continuity
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 1
Review Problems
Explore! Update
Think About It
2. Differentiation: Basic Concepts
2.1 The Derivative
2.2 Techniques of Differentiation
2.3 Product and Quotient Rules; Higher Order Derivatives
2.4 The Chain Rule
2.5 Marginal Analysis and Approximations Using Increments
2.6 Implicit Differentiation and Related Rates
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 2
Review Problems
Explore! Update
Think About It
3. Additional Applications of the Derivative
3.1 Increasing and Decreasing Functions; Relative Extrema
3.2 Concavity and Points of Inflection
3.3 Curve Sketching
3.4 Optimization
3.5 Additional Applied Optimization
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 3
Review Problems
Explore! Update
Think About It
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Differentiation of Logarithmic and Exponential Functions
4.4 Additional Exponential Models
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 4
Review Problems
Explore! Update
Think About It
5. Integration
5.1 Antidifferentiation: The Indefinite Integral
5.2 Integration by Substitution
5.3 The Definite Integral and the Fundamental Theorem of Calculus
5.4 Applying Definite Integration: Area Between Curves and Average Value
5.5 Additional Applications to Business and Economics
5.6 Additional Applications to the Life and Social Sciences
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 5
Review Problems
Explore! Update
Think About It
6. Additional Topics in Integration
6.1 Integration by Parts; Integral Tables
6.2 Improper Integrals
6.3 Numerical Integration
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 6
Review Problems
Explore! Update
Think About It
7. Calculus of Several Variables
7.1 Functions of Several Variables
7.2 Partial Derivatives
7.3 Optimizing Functions of Two Variables
7.4 The Method of Least-Squares
7.5 Constrained Optimization: The Method of Lagrange Multipliers
7.6 Double Integrals
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 7
Review Problems
Explore! Update
Think About It
8. Differential Equations
8.1 Introduction to Differential Equations
8.2 First-Order Linear Differential Equations
8.3 Additional Applications of Differential Equations
8.4 Approximate Solutions of Differential Equations
8.5 Difference Equations
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 8
Review Problems
Explore! Update
Think About It
9. Infinite Series and Taylor Series Approximations
9.1 Infinite Series; Geometric Series
9.2 Tests for Convergence
9.3 Functions as Power Series; Taylor Series
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 9
Review Problems
Explore! Update
Think About It
10. Probability and Calculus
10.1 Discrete Random Variables
10.2 Continuous Random Variables
10.3 Expected Value and Variance of Continuous Random Variables
10.4 Normal and Poisson Probability Distributions
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 10
Review Problems
Explore! Update
Think About It
11. Trigonometric Functions
11.1 The Trigonometric Functions
11.2 Differentiation and Integration of Trigonometric Functions
11.3 Additional Applications Involving Trigonometric Functions
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 11
Review Problems
Explore! Update
Think About It
Appendix A: Algebra Review
A.1 A Brief Review of Algebra
A.2 Factoring Polynomials and Solving Systems of Equations
A.3 Evaluating Limits with L'Hôpital's Rule
Appendix Summary
Important Terms, Symbols, and Formulas
Review Problems
Think About It
Tables
I Powers of e
II The Natural Logarithm (Base e)
III Trigonometric Functions
Text Solutions
Answers to Odd-Numbered Problems, Chapter Checkup Problems, and Chapter Review Problems
Index
Laurence D. Hoffmann and Gerald L. Bradley
ISBN13: 978-0073309262Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition introduces calculus in real-world contexts and provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, the life sciences, and the social sciences. This EXPANDED EDITION includes four additional chapters on Differential Equations, Infinite Series and Taylor Approximations, Probability, and Trigonometric Functions. The new Ninth Edition builds on the straightforward writing style, practical applications from a variety of disciplines, clear step-by-step problem solving techniques, and comprehensive exercise sets that have been hallmarks of Hoffmann/Bradley's success through the years.
Table of Contents
Calculator Introduction
1. Functions, Graphs, and Limits
1.1 Functions
1.2 The Graph of a Function
1.3 Linear Functions
1.4 Functional Models
1.5 Limits
1.6 One-Sided Limits and Continuity
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 1
Review Problems
Explore! Update
Think About It
2. Differentiation: Basic Concepts
2.1 The Derivative
2.2 Techniques of Differentiation
2.3 Product and Quotient Rules; Higher Order Derivatives
2.4 The Chain Rule
2.5 Marginal Analysis and Approximations Using Increments
2.6 Implicit Differentiation and Related Rates
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 2
Review Problems
Explore! Update
Think About It
3. Additional Applications of the Derivative
3.1 Increasing and Decreasing Functions; Relative Extrema
3.2 Concavity and Points of Inflection
3.3 Curve Sketching
3.4 Optimization
3.5 Additional Applied Optimization
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 3
Review Problems
Explore! Update
Think About It
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Differentiation of Logarithmic and Exponential Functions
4.4 Additional Exponential Models
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 4
Review Problems
Explore! Update
Think About It
5. Integration
5.1 Antidifferentiation: The Indefinite Integral
5.2 Integration by Substitution
5.3 The Definite Integral and the Fundamental Theorem of Calculus
5.4 Applying Definite Integration: Area Between Curves and Average Value
5.5 Additional Applications to Business and Economics
5.6 Additional Applications to the Life and Social Sciences
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 5
Review Problems
Explore! Update
Think About It
6. Additional Topics in Integration
6.1 Integration by Parts; Integral Tables
6.2 Improper Integrals
6.3 Numerical Integration
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 6
Review Problems
Explore! Update
Think About It
7. Calculus of Several Variables
7.1 Functions of Several Variables
7.2 Partial Derivatives
7.3 Optimizing Functions of Two Variables
7.4 The Method of Least-Squares
7.5 Constrained Optimization: The Method of Lagrange Multipliers
7.6 Double Integrals
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 7
Review Problems
Explore! Update
Think About It
8. Differential Equations
8.1 Introduction to Differential Equations
8.2 First-Order Linear Differential Equations
8.3 Additional Applications of Differential Equations
8.4 Approximate Solutions of Differential Equations
8.5 Difference Equations
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 8
Review Problems
Explore! Update
Think About It
9. Infinite Series and Taylor Series Approximations
9.1 Infinite Series; Geometric Series
9.2 Tests for Convergence
9.3 Functions as Power Series; Taylor Series
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 9
Review Problems
Explore! Update
Think About It
10. Probability and Calculus
10.1 Discrete Random Variables
10.2 Continuous Random Variables
10.3 Expected Value and Variance of Continuous Random Variables
10.4 Normal and Poisson Probability Distributions
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 10
Review Problems
Explore! Update
Think About It
11. Trigonometric Functions
11.1 The Trigonometric Functions
11.2 Differentiation and Integration of Trigonometric Functions
11.3 Additional Applications Involving Trigonometric Functions
Chapter Summary
Important Terms, Symbols, and Formulas
Checkup for Chapter 11
Review Problems
Explore! Update
Think About It
Appendix A: Algebra Review
A.1 A Brief Review of Algebra
A.2 Factoring Polynomials and Solving Systems of Equations
A.3 Evaluating Limits with L'Hôpital's Rule
Appendix Summary
Important Terms, Symbols, and Formulas
Review Problems
Think About It
Tables
I Powers of e
II The Natural Logarithm (Base e)
III Trigonometric Functions
Text Solutions
Answers to Odd-Numbered Problems, Chapter Checkup Problems, and Chapter Review Problems
Index