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Calculus & Its Applications, 15th edition

Published by Pearson (January 23, 2022) © 2023

  • Larry J. Goldstein Goldstein Educational Technologies
  • David C. Lay University of Maryland
  • David I. Schneider University of Maryland
  • Nakhle H. Asmar University of Missouri, Columbia
  • William Edward Tavernetti University of California at Davis

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For 1- or 2-semester Calculus courses taken by business, social science and biological science majors.

Intuition before formality

Calculus and Its Applications builds intuition with key concepts before presenting analytical material, using a strategic and distinctive topic organization. Significant applications introduced early on make the mathematics more accessible, and comprehensive exercise sets suit varying course needs.

The 15th Edition introduces fresh insights from new co-author Edward Tavernetti of University of California - Davis. It improves and expands applications, updates example and exercise data, and provides new material on modeling with differential equations.

Hallmark features of this title

  • Relevant, varied applications illustrate calculus in daily life and motivate the mathematics wherever possible.
  • Over 500 worked examples are provided. Computational details aid comprehension for students who need skills reinforcement.
  • Exercises to meet all student needs: Now Try Exercises appear after select examples, as an instructor might stop in class to ask students to try a problem. Fundamental Concept Check Exercises and Chapter Review Exercises prepare students for exams.
  • Check Your Understanding problems at the end of each section prepare students for the exercise sets.
  • Integrating Technology features within sections incorporate technology including graphing calculators, spreadsheets and Wolfram|Alpha®.

New and updated features of this title

  • New co-author William Edward Tavernetti from the University of California - Davis brings excellent insights and a fresh view of the text and the available MyLab Math® course.
  • Greatly increased video coverage adds 25 new videos, bringing the total to 237. Videos were produced and incorporated for a modern and clear presentation of the examples; they are integrated into MyLab problems as learning aids and in the MyLab Video & Resource Library.
  • Updated and improved exercises and applications, focusing on currency of data and topics, continue to draw students into the material and inspire learning. Hundreds of exercises have been improved and many exercises added to this revision.
  • The scope of applications is expanded beyond typical offerings in a first applied calculus course.
    • The new applications start in a rewritten section 5.4 (Applications of the Exponential and Natural Logarithmic Functions) and are revisited and expanded further in sections 6.5, 9.5, and 10.4.
    • Topics in these sections are aligned with a common theme of expanding students' understanding of modeling with differential equations based on the fundamental interpretation of the derivative as a rate of change.

Features of MyLab Math for the 15th Edition:

  • Review and enhancement of MyLab course by new co-author Edward Tavernetti includes overall accuracy and fidelity with the text, all exercises and solutions, video program and more.
  • New Integrated Review bolsters prerequisite skills if needed. Skills Check assessment in each chapter pinpoints topics students need to review. Personalized homework asks them to practice only those topics requiring extra help. Integrated Review videos and worksheets offer more instruction on those topics.
  • Expanded suite of Interactive Figures: Created in GeoGebra, these illustrate key concepts, can be manipulated by users, and can be used in lectures or independently by students.
  • New Mindset Videos and assignable, open-ended Exercises encourage students to maintain a positive attitude and view mistakes as learning opportunities. New Personal Inventory Assessments promote self-reflection and engagement with topics such as Stress Management, Motivation and Time Management.
  • New Early Alerts in Performance Analytics identify struggling students. Instructors can email feedback to students individually or by group.
  • New Enhanced Assignments provide spaced practice of previously learned concepts and contain personalized prerequisite skills exercises. Learning aids are turned off for some exercises to ensure comprehension.
  • Prerequisite Skills Diagnostic Test
  • Introduction
  1. Functions
    • 0.1 Functions and Their Graphs
    • 0.2 Some Important Functions
    • 0.3 The Algebra of Functions
    • 0.4 Zeros of Functions - The Quadratic Formula and Factoring
    • 0.5 Exponents and Power Functions
    • 0.6 Functions and Graphs in Applications
    • Chapter Summary and Chapter Review Exercises
  2. The Derivative
    • 1.1 The Slope of a Straight Line
    • 1.2 The Slope of a Curve at a Point
    • 1.3 The Derivative and Limits
    • *1.4 Limits and the Derivative
    • *1.5 Differentiability and Continuity
    • 1.6 Some Rules for Differentiation
    • 1.7 More About Derivatives
    • 1.8 The Derivative as a Rate of Change
    • Chapter Summary and Chapter Review Exercises
  3. Applications of the Derivative
    • 2.1 Describing Graphs of Functions
    • 2.2 The First- and Second-Derivative Rules
    • 2.3 The First- and Section-Derivative Tests and Curve Sketching
    • 2.4 Curve Sketching (Conclusion)
    • 2.5 Optimization Problems
    • *2.6 Further Optimization Problems
    • *2.7 Applications of Derivatives to Business and Economics
    • Chapter Summary and Chapter Review Exercises
  4. Techniques of Differentiation
    • 3.1 The Product and Quotient Rules
    • 3.2 The Chain Rule
    • *3.3 Implicit Differentiation and Related Rates
    • Chapter Summary and Chapter Review Exercises
  5. The Exponential and Natural Logarithm Functions
    • 4.1 Exponential Functions
    • 4.2 The Exponential Function ex
    • 4.3 Differentiation of Exponential Functions
    • 4.4 The Natural Logarithm Function
    • 4.5 The Derivative of ln x
    • 4.6 Properties of the Natural Logarithm Function
    • Chapter Summary and Chapter Review Exercises
  6. Applications of the Exponential and Natural Logarithm Functions
    • 5.1 Exponential Growth and Decay
    • 5.2 Compound Interest
    • *5.3 Applications of the Natural Logarithm Function to Economics
    • *5.4 Further Applications in Business and Economics
    • Chapter Summary and Chapter Review Exercises
  7. The Definite Integral
    • 6.1 Antidifferentiation
    • 6.2 The Definite Integral and Net Change of a Function
    • 6.3 The Definite Integral and Area Under a Graph
    • 6.4 Areas in the xy-Plane
    • 6.5 Applications of the Definite Integral
    • Chapter Summary and Chapter Review Exercises
  8. Functions of Several Variables
    • 7.1 Examples of Functions of Several Variables
    • 7.2 Partial Derivatives
    • 7.3 Maxima and Minima of Functions of Several Variables
    • 7.4 Lagrange Multipliers and Constrained Optimization
    • *7.5 The Method of Least Squares
    • *7.6 Double Integrals
    • Chapter Summary and Chapter Review Exercises
  9. The Trigonometric Functions
    • 8.1 Radian Measure of Angles
    • 8.2 The Sine and the Cosine
    • 8.3 Differentiation and Integration of sin t and cos t
    • 8.4 The Tangent and Other Trigonometric Functions
    • Chapter Summary and Chapter Review Exercises
  10. Techniques of Integration
    • 9.1 Integration by Substitution
    • 9.2 Integration by Parts
    • 9.3 Evaluation of Definite Integrals
    • *9.4 Approximation of Definite Integrals
    • *9.5 Applications in Business and Economics
    • 9.6 Improper Integrals
    • Chapter Summary and Chapter Review Exercises
  11. Differential Equations
    • 10.1 Solutions of Differential Equations
    • 10.2 Separation of Variables
    • *10.3 First-Order Linear Differential Equations
    • *10.4 Applications of First-Order Linear Differential Equations
    • 10.5 Graphing Solutions of Differential Equations
    • 10.6 Applications of Differential Equations
    • *10.7 Numerical Solution of Differential Equations
    • Chapter Summary and Chapter Review Exercises
  12. Taylor Polynomials and Infinite Series
    • 11.1 Taylor Polynomials
    • *11.2 The Newton–Raphson Algorithm
    • 11.3 Infinite Series
    • 11.4 Series with Positive Terms
    • 11.5 Taylor Series
    • Chapter Summary and Chapter Review Exercises
  13. Probability and Calculus
    • 12.1 Discrete Random Variables
    • 12.2 Continuous Random Variables
    • 12.3 Expected Value and Variance
    • 12.4 Exponential and Normal Random Variables
    • 12.5 Poisson and Geometric Random Variables
    • Chapter Summary and Chapter Review Exercises
  • *These sections are optional in the sense that they are not prerequisites for later material.

Appendix: Areas under the Standard Normal Curve

Learning Objectives

Sources

Selected Answers

Index of Applications

Index

About our authors

Larry Goldstein has received several distinguished teaching awards, given more than 50 Conference and Colloquium talks & addresses, and written more than 50 books in math and computer programming. He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.

David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT. He is currently an emeritus professor of mathematics at the University of Maryland. He has authored 8 widely used math texts, 14 highly acclaimed computer books, and 3 widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.

Martha Siegel holds a BA from Russell Sage College, attended Rensselaer Polytechnic Institute as a special student, and received her PhD at the University of Rochester. From 1966 until 1971 she taught at Goucher University in Baltimore. Since 1971 she has been a professor at Towson State University, also in Maryland. Professor Siegel has been on the writing team of this book since the 5th Edition and is also the co-author of a precalculus reform book.

William Tavernetti holds a PhD in Applied Mathematics from University of California - Davis and currently is a continuing lecturer there in the department of Mathematics. He earned a BS in Mathematical Science and a BA in Philosophy of Ethics and Public Policy from University of California - Santa Barbara. He also worked on the NASA Altair Lunar Lander as a risk analyst. He was the 2018 winner of the UC Davis University Honors Program Outstanding Teaching Award, the Thomas Salle Teaching Award (twice), the Henry Adler Prize for excellence in teaching, and also has a TEDx talk on the "Beauty and Power of Mathematics." He also works as an instructor for the California State Summer School for Mathematics and Science (COSMOS).

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