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Calculus and Its Applications, 2nd edition

Published by Pearson (April 26, 2019) © 2020

  • Marvin L. Bittinger Indiana University Purdue University Indianapolis
  • David J. Ellenbogen Community College of Vermont
  • Scott A. Surgent Arizona State University
  • Gene Kramer University of Cincinnati Blue Ash College

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For 2-semester courses in Applied Calculus.

Anticipating and meeting student needs

Calculus and Its Applications is acclaimed for its intuitive approach 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. New co-author Gene Kramer revisited every homework question and learning aid to improve clarity and accuracy. All aspects of this revision aim to motivate and help students more readily understand and apply calculus principles.

Hallmark features of this title

  • Informal explanations and visual representations are often provided in addition to formal definitions.
  • All exercise sets include real-world applications, detailed figures and graphs. Exercise sets also include Thinking and Writing, Synthesis, Technology Connection, and Concept Reinforcement exercises.
  • Technology Connection illustrates technology such as graphing calculators and Excel spreadsheets.
  • Extended Technology Applications are more challenging, using real applications and real data, and require step-by-step analysis that encourages group work.
  • Timely help for gaps in algebra skills helps students target weak areas and work on when needed.
  • Strategic use of color and a friendly writing style enhance readability.

New and updated features of this title

  • Recurring themes are reinforced and expanded throughout: for example, disjoint intervals are now introduced in R.3 to prepare students for appropriate intervals of domain later in the course.
  • Exponential and logarithmic functions are now covered earlier (Ch. 2), preparing students for more interesting applications earlier in the course.
  • Updated applications from a range of fields are integrated throughout as applied examples and exercises, and are featured in separate application sections. Applications now include even more real data.
  • Changes in Ch. 4 include increased focus on antidifferentiation as accumulation, using easy intuitive examples to appeal to a student's familiarity from real life. A new section 4.7 on numerical methods of integration has been added.
  • Former section 2.8 is split into two (3.8 and 3.9) to lighten the content load. 3.8 covers implicit differentiation (including a subsection on logarithmic differentiation), while 3.9 covers related rates with more examples than before.
  • New section 8.1 expands on the introduction to differential equations in 5.7. Full coverage of differential equations includes 5.7 and all of Ch. 8. Many topics discussed in Ch. 5, and even earlier in chapters 2 and 3, can now be discussed again as examples of differential equations.

Features of MyLab Math for the 2nd Edition

  • Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with spaced practice of key concepts, and provide opportunities to work exercises without learning aids.
  • Updated Assignable Exercises: New co-author Gene Kramer analyzed and aggregated student usage and performance data from the previous edition to help improve the quality and quantity of text and MyLab exercises and learning aids. There are approximately 5800 assignable exercises in MyLab Math.
  • New Setup & Solve Exercises require students to show how they set up a problem as well as the solution. Each is also available as a regular question where just the final answer is scored.
  • Additional Conceptual Questions provide support for assessing concepts and vocabulary; many are application oriented.
  • An expanded suite of Interactive Figures illustrate key concepts and allow manipulation. They are designed to be used both in lecture and independently by students.
  • New and revised Instructional videos: Approximately 90% of the instructional videos are brand new, featuring authors Gene Kramer and Scott Surgent along with instructors Mary Ann Barber and Thomas Hartfield. All videos are assignable and The Guide to Video-Based Assignments shows which MyLab Math exercises can be assigned for each.

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'Hôpital'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

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.

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