Calculus and Its Applications
2nd Edition
Published on 8. January 2019
Book
Hardback
960 pages
978-0-13-509168-5 (ISBN)
Description
For two-semester courses in Applied Calculus.
Anticipating and meeting student needs
Calculus and Its Applications remains a best-selling text because of its intuitive approach that anticipates student needs, and a writing style that pairs clear explanations with carefully crafted figures to help students visualize concepts. Key enhancements in the 2nd Edition include the earlier introduction of logarithmic and exponential functions to help students master these important functions and their applications.
The text's accompanying MyLab (TM) Math course also has been revised substantially, as new co-author Gene Kramer (University of Cincinnati, Blue Ash) revisited every homework question and learning aid to improve content clarity and accuracy. These and all other aspects of the new edition are designed to motivate and help students more readily understand and apply principles of calculus.
The title of this text was formerly Calculus and Its Applications, Expanded Version.
Also available with MyLab Math
MyLab (TM) Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student.
Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.
If you would like to purchase both the physical text and MyLab Math, search for:
013530802X / 9780135308028 Calculus and Its Applications plus MyLab Math with Pearson eText - Title-Specific Access Card Package
Package consists of:
0135091683 / 9780135091685 Calculus and Its Applications
0135218233 / 9780135218235 MyLab Math with Pearson eText - Standalone Access Card - for Calculus and Its Applications
Anticipating and meeting student needs
Calculus and Its Applications remains a best-selling text because of its intuitive approach that anticipates student needs, and a writing style that pairs clear explanations with carefully crafted figures to help students visualize concepts. Key enhancements in the 2nd Edition include the earlier introduction of logarithmic and exponential functions to help students master these important functions and their applications.
The text's accompanying MyLab (TM) Math course also has been revised substantially, as new co-author Gene Kramer (University of Cincinnati, Blue Ash) revisited every homework question and learning aid to improve content clarity and accuracy. These and all other aspects of the new edition are designed to motivate and help students more readily understand and apply principles of calculus.
The title of this text was formerly Calculus and Its Applications, Expanded Version.
Also available with MyLab Math
MyLab (TM) Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student.
Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.
If you would like to purchase both the physical text and MyLab Math, search for:
013530802X / 9780135308028 Calculus and Its Applications plus MyLab Math with Pearson eText - Title-Specific Access Card Package
Package consists of:
0135091683 / 9780135091685 Calculus and Its Applications
0135218233 / 9780135218235 MyLab Math with Pearson eText - Standalone Access Card - for Calculus and Its Applications
More details
Edition
2nd edition
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
College/higher education
Dimensions
Height: 277 mm
Width: 217 mm
Thickness: 40 mm
Weight
2074 gr
ISBN-13
978-0-13-509168-5 (9780135091685)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
About our authors Marvin Bittinger has been teaching math at the university level for more than 38 years. Since 1968, he has been employed at Indiana University - Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 250 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has 2 grown and married sons, Lowell and Chris, and 4 granddaughters.
David Ellenbogen has taught math at the college level for over 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has also taught at St. Michael's College and the University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a Vermont state delegate. He has been a member of the Mathematical Association of America since 1979, has authored dozens of publications on topics ranging from prealgebra to calculus, and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from the University of Massachusetts at Amherst, and a certificate of graduate study in Ecological Economics from the University of Vermont. Professor Ellenbogen has a deep love for the environment and the outdoors, and serves on the boards of 3 nonprofit organizations in his home state of Vermont. In his spare time, he enjoys playing jazz piano, hiking, biking, and skiing. He has 2 sons, Monroe and Zack.
Scott Surgent received his B.S. and M.S. degrees in mathematics from the University of California - Riverside, and has taught mathematics at Arizona State University in Tempe, Arizona since 1994. He is an avid sports fan and has authored books on hockey, baseball, and hiking. Scott enjoys hiking and climbing the mountains of the western United States. He was active in search and rescue, including 6 years as an Emergency Medical Technician with the Central Arizona Mountain Rescue Association (Maricopa County Sheriff's Office) from 1998 until 2004. Scott and his wife Beth live in Scottsdale, Arizona.
Gene Kramer received his PhD from the University of Cincinnati, where he researched the well-posedness of initial-boundary value problems for nonlinear wave equations. He is currently a professor of mathematics at the University of Cincinnati Blue Ash College. He is active in scholarship of teaching and learning research and is a member of the Academy of the Fellows for Teaching and Learning at the University of Cincinnati. He is a co-founder and an editor for The Journal for Research and Practice in College Teaching and serves as a Peer Reviewer for the Higher Learning Commission.
David Ellenbogen has taught math at the college level for over 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has also taught at St. Michael's College and the University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a Vermont state delegate. He has been a member of the Mathematical Association of America since 1979, has authored dozens of publications on topics ranging from prealgebra to calculus, and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from the University of Massachusetts at Amherst, and a certificate of graduate study in Ecological Economics from the University of Vermont. Professor Ellenbogen has a deep love for the environment and the outdoors, and serves on the boards of 3 nonprofit organizations in his home state of Vermont. In his spare time, he enjoys playing jazz piano, hiking, biking, and skiing. He has 2 sons, Monroe and Zack.
Scott Surgent received his B.S. and M.S. degrees in mathematics from the University of California - Riverside, and has taught mathematics at Arizona State University in Tempe, Arizona since 1994. He is an avid sports fan and has authored books on hockey, baseball, and hiking. Scott enjoys hiking and climbing the mountains of the western United States. He was active in search and rescue, including 6 years as an Emergency Medical Technician with the Central Arizona Mountain Rescue Association (Maricopa County Sheriff's Office) from 1998 until 2004. Scott and his wife Beth live in Scottsdale, Arizona.
Gene Kramer received his PhD from the University of Cincinnati, where he researched the well-posedness of initial-boundary value problems for nonlinear wave equations. He is currently a professor of mathematics at the University of Cincinnati Blue Ash College. He is active in scholarship of teaching and learning research and is a member of the Academy of the Fellows for Teaching and Learning at the University of Cincinnati. He is a co-founder and an editor for The Journal for Research and Practice in College Teaching and serves as a Peer Reviewer for the Higher Learning Commission.
Content
Prerequisite Skills 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 Functions and Models
R.6 Exponential and Logarithmic Functions
R.7 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 and Difference Quotients
1.5 Leibniz Notation and the Power and Sum-Difference Rules
1.6 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. Exponential and Logarithmic Functions
2.1 Exponential and Logarithmic Functions of the Natural Base, e
2.2 Derivatives of Exponential (Base-e) Functions
2.3 Derivatives of Natural Logarithmic Functions
2.4 Applications: Uninhibited and Limited Growth Models
2.5 Applications: Exponential Decay
2.6 The Derivatives of ax and loga x
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: The Business of Motion Picture Revenue and DVD Release
3. Applications of Differentiation
3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
3.3 Graph Sketching: Asymptotes and Rational Functions
3.4 Optimization: Finding Absolute Maximum and Minimum Values
3.5 Optimization: Business, Economics, and General Applications
3.6 Marginals, Differentials, and Linearization
3.7 Elasticity of Demand
3.8 Implicit Differentiation and Logarithmic Differentiation
3.9 Related Rates
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Maximum Sustainable Harvest
4. Integration
4.1 Antidifferentiation
4.2 Antiderivatives as Areas
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Numerical Integration
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Business and Economics: Distribution of Wealth
5. Applications of Integration
5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss
5.2 Integrating 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 Volumes of Containers
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: Lagrange Multipliers and the Extreme-Value Theorem
6.6 Double Integrals
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Minimizing Employees' Travel Time in a Building
7. Trigonometric Functions
7.1 Basics of Trigonometry
7.2 Derivatives of Trigonometric Functions
7.3 Integration of Trigonometric Functions
7.4 Inverse Trigonometric Functions and Applications
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
8. Differential Equations
8.1 Direction Fields, Autonomic Forms, and Population Models
8.2 Applications: Inhibited Growth Models
8.3 First-Order Linear Differential Equations
8.4 Higher-Order Differential Equations and a Trigonometry Connection
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
9. Sequences and Series
9.1 Arithmetic Sequences and Series
9.2 Geometric Sequences and Series
9.3 Simple and Compound Interest
9.4 Annuities and Amortization
9.5 Power Series and Linearization
9.6 Taylor Series and a Trigonometry Connection
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
10. Probability Distributions
10.1 A Review of Sets
10.2 Theoretical Probability
10.3 Discrete Probability Distributions
10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
11. Systems and Matrices (online only)
11.1 Systems of Linear Equations
11.2 Gaussian Elimination
11.3 Matrices and Row Operations
11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples
11.5 Matrix Multiplication, Multiplicative Identities, and Inverses
11.6 Determinants and Cramer's Rule
11.7 Systems of Linear Inequalities and Linear Programming
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
12. Combinatorics and Probability (online only)
12.1 Compound Events and Odds
12.2 Combinatorics: The Multiplication Principle and Factorial Notation
12.3 Permutations and Distinguishable Arrangements
12.4 Combinations and the Binomial Theorem
12.5 Conditional Probability and the Hypergeometric Probability Distribution Model
12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model
12.7 Bayes Theorem
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
Cumulative Review
Appendices
A. Review of Basic Algebra
B. Indeterminate Forms and l'Hopital's Rule
C. Regression and Microsoft Excel
D. Areas for a Standard Normal Distribution
E. Using Tables of Integration Formulas
Answers Index of Applications Index
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 Functions and Models
R.6 Exponential and Logarithmic Functions
R.7 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 and Difference Quotients
1.5 Leibniz Notation and the Power and Sum-Difference Rules
1.6 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. Exponential and Logarithmic Functions
2.1 Exponential and Logarithmic Functions of the Natural Base, e
2.2 Derivatives of Exponential (Base-e) Functions
2.3 Derivatives of Natural Logarithmic Functions
2.4 Applications: Uninhibited and Limited Growth Models
2.5 Applications: Exponential Decay
2.6 The Derivatives of ax and loga x
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: The Business of Motion Picture Revenue and DVD Release
3. Applications of Differentiation
3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
3.3 Graph Sketching: Asymptotes and Rational Functions
3.4 Optimization: Finding Absolute Maximum and Minimum Values
3.5 Optimization: Business, Economics, and General Applications
3.6 Marginals, Differentials, and Linearization
3.7 Elasticity of Demand
3.8 Implicit Differentiation and Logarithmic Differentiation
3.9 Related Rates
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Maximum Sustainable Harvest
4. Integration
4.1 Antidifferentiation
4.2 Antiderivatives as Areas
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Numerical Integration
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Business and Economics: Distribution of Wealth
5. Applications of Integration
5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss
5.2 Integrating 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 Volumes of Containers
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: Lagrange Multipliers and the Extreme-Value Theorem
6.6 Double Integrals
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application: Minimizing Employees' Travel Time in a Building
7. Trigonometric Functions
7.1 Basics of Trigonometry
7.2 Derivatives of Trigonometric Functions
7.3 Integration of Trigonometric Functions
7.4 Inverse Trigonometric Functions and Applications
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
8. Differential Equations
8.1 Direction Fields, Autonomic Forms, and Population Models
8.2 Applications: Inhibited Growth Models
8.3 First-Order Linear Differential Equations
8.4 Higher-Order Differential Equations and a Trigonometry Connection
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
9. Sequences and Series
9.1 Arithmetic Sequences and Series
9.2 Geometric Sequences and Series
9.3 Simple and Compound Interest
9.4 Annuities and Amortization
9.5 Power Series and Linearization
9.6 Taylor Series and a Trigonometry Connection
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
10. Probability Distributions
10.1 A Review of Sets
10.2 Theoretical Probability
10.3 Discrete Probability Distributions
10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
11. Systems and Matrices (online only)
11.1 Systems of Linear Equations
11.2 Gaussian Elimination
11.3 Matrices and Row Operations
11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples
11.5 Matrix Multiplication, Multiplicative Identities, and Inverses
11.6 Determinants and Cramer's Rule
11.7 Systems of Linear Inequalities and Linear Programming
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
12. Combinatorics and Probability (online only)
12.1 Compound Events and Odds
12.2 Combinatorics: The Multiplication Principle and Factorial Notation
12.3 Permutations and Distinguishable Arrangements
12.4 Combinations and the Binomial Theorem
12.5 Conditional Probability and the Hypergeometric Probability Distribution Model
12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model
12.7 Bayes Theorem
Chapter Summary
Chapter Review Exercises
Chapter Test
Extended Technology Application
Cumulative Review
Appendices
A. Review of Basic Algebra
B. Indeterminate Forms and l'Hopital's Rule
C. Regression and Microsoft Excel
D. Areas for a Standard Normal Distribution
E. Using Tables of Integration Formulas
Answers Index of Applications Index