Calculus with Applications, Tenth Edition (also available in a Brief Version containing Chapters 1–9) by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to get involved with the material, such as “Your Turn” exercises and “Apply It” vignettes that encourage active participation. The MyMathLab® course for the text provides additional learning resources for students, such as video tutorials, algebra help, step-by-step examples, and graphing calculator help. The course also features many more assignable exercises than the previous edition. Features + Benefits
A wide variety of applications reference real data from articles in newspapers, journals, and websites. Examples with recent data help students learn how the mathematics is applied to their field of study, immediately addressing the question “why are we learning this?”
Apply It opens most sections with a provocative, real-world oriented question that is addressed in the exposition and exercises.
Applied exercises are grouped by type of application and highlighted for easy identification.
Extended Applications appear at the end of all chapters to stimulate student interest and foster in-depth learning. Directions forGroup Projects in the Extended Applications provide an opportunity for cooperative learning.
Index of Applications provides instructors and students with an overview of the types of applications throughout the book.
NEW! Application exercises within MyMathLab are now labeled by type of application.
Assessment and remediation features appear at key points to ensure that students keep up with the material, and provide plenty of pointers to help those who fall behind.
NEW! “Your Turn” exercises following selected examples provide students with an easy way to stop and check their understanding of the skill or concept being presented. Answers are provided at the end of the section’s exercises.
NEW! The Prerequisite Skills Diagnostic Test, just prior to Chapter R, gives students and instructors an opportunity to assess students’ skills on topics that are critical to success in this course. Answers reference specific review material in the text for targeted remediation.
Algebra Reference chapter appears at the beginning of the text, allowing students to brush up on their algebra skills.
“For Review” boxes in the margin provide immediate review, or refer students back to appropriate sections as needed.
Chapter Summaries include important concepts, rules, and formulas, helping students review what they have learned.
Caution boxes warn students of common errors/misconceptions and Note boxes offer additional useful information. Both are highlighted for easy reference.
Diverse exercise sets show how math is used in students’ major courses of study—business, life science, and social sciences.
Connection Exercises, denoted with an icon, integrate topics/concepts from different sections.
Writing Exercises, denoted with an icon, provide students with an opportunity to write about important mathematical ideas.
Technology Exercises, denoted with an icon, explore concepts using a graphing calculator or spreadsheet.
Concept Check exercises in the Chapter reviews help students verify their understanding of important topics.
NEW! Reference Tables for Exercises appear in the back of the book, next to the answers to odd-numbered exercises. These tables correlate homework exercises to a helpful example in the text.
Technology coverage keeps your classroom and students up-to-date with the latest software and technology options available on the market.
NEW! The updated design makes it easier to identify technology coverage so instructors can more easily highlight (or skip) the material.
Excel®Spreadsheets are included in examples and exercises where appropriate, allowing students to work problems that closely relate to real-life and business situations.
Graphing Calculator discussions are included in many examples, but are not essential for understanding the text. Figures depicting graphing calculator screens now feature the new TI MathPrint™ operating system.
MyMathLab® provides a complete online course designed to increase student achievement. The course contains over 4,100 assignable exercises with help features that can be customized to the needs of your course. It also features video tutorials, algebra diagnostic and remediation, and more.
R. Algebra Reference
R.1 Polynomials
R.2 Factoring
R.3 Rational Expressions
R.4 Equations
R.5 Inequalities
R.6 Exponents
R.7 Radicals
1. Linear Functions
1.1 Slopes and Equations of Lines
1.2 Linear Functions and Applications
1.3 The Least Squares Line
Chapter 1 Review
Extended Application: Using Extrapolation to Predict Life Expectancy
2. Nonlinear Functions
2.1 Properties of Functions
2.2 Quadratic Functions; Translation and Reflection
2.3 Polynomial and Rational Functions
2.4 Exponential Functions
2.5 Logarithmic Functions
2.6 Applications: Growth and Decay; Mathematics of Finance
Chapter 2 Review
Extended Application: Characteristics of the Monkeyface Prickleback
3. The Derivative
3.1 Limits
3.2 Continuity
3.3 Rates of Change
3.4 Definition of the Derivative
3.5 Graphical Differentiation
Chapter 3 Review
Extended Application: A Model for Drugs Administered Intravenously
4. Calculating the Derivative
4.1 Techniques for Finding Derivatives
4.2 Derivatives of Products and Quotients
4.3 The Chain Rule
4.4 Derivatives of Exponential Functions
4.5 Derivatives of Logarithmic Functions
Chapter 4 Review
Extended Application: Electrical Potential and Electric Field
5. Graphs and the Derivative
5.1 Increasing and Decreasing Functions
5.2 Relative Extrema
5.3 Higher Derivatives, Concavity, and the Second Derivative Test
5.4 Curve Sketching
Chapter 5 Review
Extended Application: A Drug Concentration Model for Orally Administered Medications
6. Applications of the Derivative
6.1 Absolute Extrema
6.2 Applications of Extrema
6.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand
6.4 Implicit Differentiation
6.5 Related Rates
6.6 Differentials: Linear Approximation
Chapter 6 Review
Extended Application: A Total Cost Model for a Training Program
7. Integration
7.1 Antiderivatives
7.2 Substitution
7.3 Area and the Definite Integral
7.4 The Fundamental Theorem of Calculus
7.5 The Area Between Two Curves
7.6 Numerical Integration
Chapter 7 Review
Extended Application: Estimating Depletion Dates for Minerals
8. Further Techniques and Applications of Integration
8.1 Integration by Parts
8.2 Volume and Average Value
8.3 Continuous Money Flow
8.4 Improper Integrals
Chapter 8 Review
Extended Application: Estimating Learning Curves in Manufacturing with Integrals
9. Multivariable Calculus
9.1 Functions of Several Variables
9.2 Partial Derivatives
9.3 Maxima and Minima
9.4 Lagrange Multipliers
9.5 Total Differentials and Approximations
9.6 Double Integrals
Chapter 9 Review
Extended Application: Using Multivariable Fitting to Create a Response Surface Design
10. Differential Equations
10.1 Solutions of Elementary and Separable Differential Equations
10.2 Linear First-Order Differential Equations
10.3 Euler's Method
10.4 Applications of Differential Equations
Chapter 10 Review
Extended Application: Pollution of the Great Lakes
11. Probability and Calculus
11.1 Continuous Probability Models
11.2 Expected Value and Variance of Continuous Random Variables
11.3 Special Probability Density Functions
Chapter 11 Review
Extended Application: Exponential Waiting Times
12. Sequences and Series
12.1 Geometric Sequences
12.2 Annuities: An Application of Sequences
12.3 Taylor Polynomials at 0
12.4 Infinite Series
12.5 Taylor Series
12.6 Newton's Method
12.7 L'Hôpital's Rule
Chapter 12 Review
Extended Application: Living Assistance and Subsidized Housing
A wide variety of applications reference real data from articles in newspapers, journals, and websites. Examples with recent data help students learn how the mathematics is applied to their field of study, immediately addressing the question “why are we learning this?”
Apply It opens most sections with a provocative, real-world oriented question that is addressed in the exposition and exercises.
Applied exercises are grouped by type of application and highlighted for easy identification.
Extended Applications appear at the end of all chapters to stimulate student interest and foster in-depth learning. Directions forGroup Projects in the Extended Applications provide an opportunity for cooperative learning.
Index of Applications provides instructors and students with an overview of the types of applications throughout the book.
NEW! Application exercises within MyMathLab are now labeled by type of application.
Assessment and remediation features appear at key points to ensure that students keep up with the material, and provide plenty of pointers to help those who fall behind.
NEW! “Your Turn” exercises following selected examples provide students with an easy way to stop and check their understanding of the skill or concept being presented. Answers are provided at the end of the section’s exercises.
NEW! The Prerequisite Skills Diagnostic Test, just prior to Chapter R, gives students and instructors an opportunity to assess students’ skills on topics that are critical to success in this course. Answers reference specific review material in the text for targeted remediation.
Algebra Reference chapter appears at the beginning of the text, allowing students to brush up on their algebra skills.
“For Review” boxes in the margin provide immediate review, or refer students back to appropriate sections as needed.
Chapter Summaries include important concepts, rules, and formulas, helping students review what they have learned.
Caution boxes warn students of common errors/misconceptions and Note boxes offer additional useful information. Both are highlighted for easy reference.
Diverse exercise sets show how math is used in students’ major courses of study—business, life science, and social sciences.
Connection Exercises, denoted with an icon, integrate topics/concepts from different sections.
Writing Exercises, denoted with an icon, provide students with an opportunity to write about important mathematical ideas.
Technology Exercises, denoted with an icon, explore concepts using a graphing calculator or spreadsheet.
Concept Check exercises in the Chapter reviews help students verify their understanding of important topics.
NEW! Reference Tables for Exercises appear in the back of the book, next to the answers to odd-numbered exercises. These tables correlate homework exercises to a helpful example in the text.
Technology coverage keeps your classroom and students up-to-date with the latest software and technology options available on the market.
NEW! The updated design makes it easier to identify technology coverage so instructors can more easily highlight (or skip) the material.
Excel®Spreadsheets are included in examples and exercises where appropriate, allowing students to work problems that closely relate to real-life and business situations.
Graphing Calculator discussions are included in many examples, but are not essential for understanding the text. Figures depicting graphing calculator screens now feature the new TI MathPrint™ operating system.
MyMathLab® provides a complete online course designed to increase student achievement. The course contains over 4,100 assignable exercises with help features that can be customized to the needs of your course. It also features video tutorials, algebra diagnostic and remediation, and more.
R. Algebra Reference
R.1 Polynomials
R.2 Factoring
R.3 Rational Expressions
R.4 Equations
R.5 Inequalities
R.6 Exponents
R.7 Radicals
1. Linear Functions
1.1 Slopes and Equations of Lines
1.2 Linear Functions and Applications
1.3 The Least Squares Line
Chapter 1 Review
Extended Application: Using Extrapolation to Predict Life Expectancy
2. Nonlinear Functions
2.1 Properties of Functions
2.2 Quadratic Functions; Translation and Reflection
2.3 Polynomial and Rational Functions
2.4 Exponential Functions
2.5 Logarithmic Functions
2.6 Applications: Growth and Decay; Mathematics of Finance
Chapter 2 Review
Extended Application: Characteristics of the Monkeyface Prickleback
3. The Derivative
3.1 Limits
3.2 Continuity
3.3 Rates of Change
3.4 Definition of the Derivative
3.5 Graphical Differentiation
Chapter 3 Review
Extended Application: A Model for Drugs Administered Intravenously
4. Calculating the Derivative
4.1 Techniques for Finding Derivatives
4.2 Derivatives of Products and Quotients
4.3 The Chain Rule
4.4 Derivatives of Exponential Functions
4.5 Derivatives of Logarithmic Functions
Chapter 4 Review
Extended Application: Electrical Potential and Electric Field
5. Graphs and the Derivative
5.1 Increasing and Decreasing Functions
5.2 Relative Extrema
5.3 Higher Derivatives, Concavity, and the Second Derivative Test
5.4 Curve Sketching
Chapter 5 Review
Extended Application: A Drug Concentration Model for Orally Administered Medications
6. Applications of the Derivative
6.1 Absolute Extrema
6.2 Applications of Extrema
6.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand
6.4 Implicit Differentiation
6.5 Related Rates
6.6 Differentials: Linear Approximation
Chapter 6 Review
Extended Application: A Total Cost Model for a Training Program
7. Integration
7.1 Antiderivatives
7.2 Substitution
7.3 Area and the Definite Integral
7.4 The Fundamental Theorem of Calculus
7.5 The Area Between Two Curves
7.6 Numerical Integration
Chapter 7 Review
Extended Application: Estimating Depletion Dates for Minerals
8. Further Techniques and Applications of Integration
8.1 Integration by Parts
8.2 Volume and Average Value
8.3 Continuous Money Flow
8.4 Improper Integrals
Chapter 8 Review
Extended Application: Estimating Learning Curves in Manufacturing with Integrals
9. Multivariable Calculus
9.1 Functions of Several Variables
9.2 Partial Derivatives
9.3 Maxima and Minima
9.4 Lagrange Multipliers
9.5 Total Differentials and Approximations
9.6 Double Integrals
Chapter 9 Review
Extended Application: Using Multivariable Fitting to Create a Response Surface Design
10. Differential Equations
10.1 Solutions of Elementary and Separable Differential Equations
10.2 Linear First-Order Differential Equations
10.3 Euler's Method
10.4 Applications of Differential Equations
Chapter 10 Review
Extended Application: Pollution of the Great Lakes
11. Probability and Calculus
11.1 Continuous Probability Models
11.2 Expected Value and Variance of Continuous Random Variables
11.3 Special Probability Density Functions
Chapter 11 Review
Extended Application: Exponential Waiting Times
12. Sequences and Series
12.1 Geometric Sequences
12.2 Annuities: An Application of Sequences
12.3 Taylor Polynomials at 0
12.4 Infinite Series
12.5 Taylor Series
12.6 Newton's Method
12.7 L'Hôpital's Rule
Chapter 12 Review
Extended Application: Living Assistance and Subsidized Housing