Calculus & Its Applications, Brief Version, 14th edition

For one- or two-semester courses in Calculus for students majoring in business, social sciences, and life sciences.

Intuition before Formality

Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite integral intuitively via the notion of net change before they discuss Riemann sums. The strategic organization of topics makes it easy to adjust the level of theoretical material covered. The significant applications introduced early in the course serve to motivate students and make the mathematics more accessible. Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions.

Time-tested, comprehensive exercise sets are flexible enough to align with each instructor’s needs, and new exercises and resources in MyLab™ Math help develop not only skills, but also conceptual understanding, visualization, and applications. The 14th Edition features updated exercises, applications, and technology coverage, presenting calculus in an intuitive yet intellectually satisfying way.

Also available with MyLab Math

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. In the new edition, MyLab Math has expanded to include a suite of new videos, Interactive Figures, exercises that require step-by-step solutions, conceptual questions, calculator support, and more.

Students, if interested in purchasing this title with MyLab Math, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

• The student-oriented presentation enables them to study and learn independently, while showing them how the concepts apply to their future careers.
• ENHANCED! In the 14th edition, the author revised examples to more closely align with exercises sets.
• UPDATED! Relevant and varied applications contain real data and provide a realistic look at how calculus applies to other disciplines and everyday life. Whenever possible, applications are used to motivate the mathematics. The variety of applications is evident in the Index of Applications.
• EXPANDED! Time-tested exercise sets give instructors flexibility when building assignments, with exercises sorted by level and exercises that encourage students to use technology to solve problems. In the 14th Edition, 225 new exercises and 30 worked examples are added, bringing the total to 3,150 exercises and 350 examples.
• Just-in-time support throughout the chapters helps students of all skill levels study more efficiently.
• Prerequisite Skills Diagnostic Test within the text helps students gauge their level of readiness for this course. To complement that, Chapter 0 covers prerequisite content that can be covered all at once, or as discrete topics interspersed throughout the course, for students who need it.
• 350 worked-out examples provide support for students as they work exercises and learn the content. NEW! “Help text” within examples (shown in blue type) helps students understand key algebraic and numerical transitions.
• NEW! “For Review” side margin features remind students of a concept that is needed and direct them back to the section in which it was covered earlier in the text.
• “Now Try” Exercises appear after select examples, mirroring how an instructor might stop in class to ask students to try a problem, allowing them to immediately apply their understanding.
• Check Your Understanding problems appear at the end of each section to prepare students for the exercise sets, encouraging them to reflect on what they’ve learned before applying it further.
• End-of-Chapter study aids help students recall key ideas and focus on the relevance of these concepts. Fundamental Concept Check Exercises and Chapter Review Exercises prepare students for potential exam questions.
• UPDATED! Integrating Technology features within sections allow students to incorporate technology into the learning process, including graphing calculators. In the 14th Edition, graphing calculator screens have been updated to the TI-84 Plus CE format and are now in color.

Also available with MyLab Math

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

• Robust exercise sets and resources in MyLab Math help develop skills, conceptual understanding, visualization, and applications.
• A wide range of exercise types, each with immediate feedback–over 2,700 assignable exercises for this text regenerate algorithmically to give students unlimited opportunity for practice and mastery. MyLab Math provides helpful feedback when students enter incorrect answers and includes optional learning aids including Help Me Solve This, View an Example, videos, and an eText.
• NEW! Setup & Solve exercises require students to first describe how they will set up and approach the problem. This reinforces conceptual understanding of the process applied in approaching the problem, promotes long term retention of the skill and mirrors what students will be expected to do on a test.
• NEW!  Conceptual Question Library exercises provide additional conceptual, application-focused questions for instructors to use on homework or assessments.
• NEW! MathTalk videos connect the math to the real world (particularly business). The videos include assignable exercises to gauge students’ understanding of video content.
• UPDATED! Interactive Figures illustrate key concepts and allow manipulation for use as teaching and learning tools. These are now in HTML format (no plug-in required) and are supported by assignable exercises and tutorial videos.
• The complete eText is available to students through their MyLab Math courses for the lifetime of the edition, giving students unlimited access to the eText within any course using that edition of the textbook.
• Personalized learning and just-in-time support helps students of all skill levels study more efficiently.
• UPDATED! Over 275 Example-based videos, 85 of which are new to this edition, are available as learning aids within exercises and for self-study. The Guide to Video-Based Assignments makes it easy to assign videos for homework by showing which MyLab Math exercises correspond to each video.
• NEW! Skills for Success Modules help students with the life skills that can make the difference between passing and failing.
• NEW! An Integrated Review MyLab Math course contains pre-made quizzes to assess the prerequisite skills needed for each chapter, plus personalized remediation for any gaps in skills that are identified.
• Built-in technology support ensures students understand how to use the tools to do their assignments.
• NEW! Graphing Calculator and Excel Spreadsheet Manuals, specific to this course, are now downloadable from MyLab Math.
• NEW! Instructor’s Answers document (download only from MyLab Math)  provides all answers in one place and augments the downloadable Instructor’s Solutions Manual, which contains all solutions.
• Learning Catalytics^™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking.
• Help your students develop critical thinking skills.
• Monitor responses to find out where your students are struggling.
• Rely on real-time data to adjust your teaching strategy.
• Automatically group students for discussion, teamwork, and peer-to-peer learning.
• NEW! Upload a full PowerPoint^® deck for easy creation of slide questions.
• NEW! Team names are no longer case sensitive.
• Accessibility and achievement go hand in hand. MyLab Math is compatible with the JAWS screen reader, and enables multiple-choice and free-response problem types to be read and interacted with via keyboard controls and math notation input. MyLab Math also works with screen enlargers, including ZoomText, MAGic, and SuperNova. And all MyLab Math videos have closed-captioning. More information is available at http://mymathlab.com/accessibility.

• More intuitive organization and explanation within examples makes properties and theorems easier to follow and recall.
• 225 new exercises and 30 worked examples have been added, bringing the total to 3,150 exercises and 350 examples.
• “Help text” within examples (shown in blue type) helps students understand key algebraic and numerical transitions.
• “For Review” side margin features remind students of a concept that is needed and direct them back to the section in which it was covered earlier in the text.
• Graphing calculator screens have been updated to the TI-84 Plus CE format and are now in color.
• All 3-dimensional figures in the text have been re-rendered using the latest software. The authors took full advantage of the capabilities of the rendering software to make the figures more effective pedagogically.
• In cases where properties or theorems that were formerly numbered (e.g., Property 4) have a commonly used name (e.g., Power of a Quotient Rule), the authors used the name rather than the number. This allows for more intuitive explanations within examples and is better aligned to how concepts are explained in class.

Content Updates

Chapter 0

• Added an example and exercises in 0.1 to illustrate the concept of piecewise-defined functions.
• Rewrote and simplified the introduction to 0.5 Exponents and Power Functions to make it more intuitive and easier to reference. Additionally, we added several examples to illustrate the rules of exponents.
• Modified the discussion of compound interest to make it more suitable for the applications in later chapters.
• Added Examples 8 and 9 in 0.5 to illustrate the role of multiple factors in compound interest and investment accounts.
• Added Example 7 in 0.6 to illustrate various concepts from economics.
• Added four new exercises (45-48) in 0.6 to illustrate variations on the standard topic of compound interest.
• Modified over thirty exercises in the chapter.

Chapter 1

• Removed some of the proofs related to review material to simplify the presentation in 1.1. 
• Added four new exercises (5-8) in 1.2 to illustrate the geometric meaning of the slope of a graph as the slope of the tangent line. Additionally, we modified two other exercises requiring reading and interpreting slopes of graphs.
• Simplified the discussion of limits in Examples 2 and 4 in 1.4.
• Included a discussion and a new Example 4 in 1.8 to illustrate the concepts of displacement and velocity.

Chapters 2 and 3

• Modified the Technology Exercises in 2.1 to make them more straightforward for students to answer.
• Improved and simplified the solutions within Example 4 in 2.4.
• Removed Example 4 in 2.6 which required more symbolic manipulation and use of constants than students would encounter in the exercises.
• Rewrote five examples in the Summary section of Chapter 2.
• Added ten new exercises in Chapter 3.

Chapter 4

• Revised Example 2 in 4.2 to better prepare students for the variety of exercises within the homework.
• Moved the material on the properties and graphs of exponential functions from 4.3 to 4.2.
• Replaced Examples 1, 2, and 3 from 4.3 with new examples that better build on the properties of derivatives introduced earlier. Example 3 introduces a new concept of combined returns to illustrate applications of linear combinations of exponential functions.
• Moved the material on differential equations in 4.3 to Chapter 5.
• Introduced forty new exercises in 4.3, including one on investment portfolios.
• Rewrote the introduction of 4.4 to better display and present the properties of logarithms.
• Changed Example 1 in 4.4 to better match the types of exercises in the homework.
• Used investment portfolios to illustrate applications involving solutions of equations with logarithms in Example 4 in 4.4.
• Rewrote the introduction of 4.5 to better display properties of the natural logarithm and its derivative.
• Added a new example on differentiation of the natural logarithm in 4.5.
• Modified and added over twenty exercises in 4.5.
• Rewrote the introduction of 4.6 to better present further properties of the logarithm.

Chapter 5

• Rewrote 5.1 to better show the applications of the derivative as a rate of change in setting up and solving differential equations. Changes to 5.1 also include:
• Stated the solutions of the differential equation y ′ = ky in a theorem.
• Added an example on solving differential equations.
• Stated the solutions of the initial value problem y ′ = ky, y(0)=P₀ in a theorem.
• Illustrated the solutions of initial value problems with examples and a figure that a student can easily relate to.
• Simplified the discussion on exponential decay and carbon dating.
• Added twenty-three new exercises on differential equations and their applications.
• Rewrote and simplified the introduction to 5.2. Also in 5.2:
• Introduced continuous compounding as a limit of the ordinary compounding from Chapter 0 and as a solution of a differential equation of the type that was discussed in 5.1.
• Added narrative that compares continuous to ordinary compounding.
• Added discussion, an example, and exercises on negative interest rates.
• Rewrote the introduction to 5.3 to better explain the concept of relative rate of change and how it relates to common pricing applications.
• Added an example in 5.3 on logarithmic derivatives.
• Included a summary of solutions of differential equations and their properties in the Chapter Summary.

Chapter 6

• Simplified Example 1 in 6.1 by adding more details to the solution.
• Rewrote the introduction to 6.2 and simplified the presentation by relating the new concept of definite integral to a common problem involving velocity and position.
• Simplified the numerical computations in Examples 3 and 5 in 6.2.
• Added nine new exercises to 6.2.
• Added a new example on online transportation in 6.4, as an application of area between two curves.

Chapter 7

• Revised all 3-dimensional figures in the chapter using the latest software.
• Added more help to Example 1 in 7.2 and added a 3-dimensional graph.
• In Example 4 in 7.3, added a new application of the second derivative test in two dimensions.
• Added twenty new exercises to 7.2, ten new exercises to 7.4, and two new exercises to 7.5.

Chapters 8-12

• Removed the application on population genetics from 10.6 (as this is now covered in Chapter 5).
• Revised exercises and examples to update real-world data.

Also available with MyLab Math

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

New to MyLab Math

• Many improvements have been made to the overall functionality of MyLab Math since the previous edition. However, beyond that, we have also increased and improved the content specific to this text.
• Setup & Solve exercises require students to first describe how they will set up and approach the problem. This reinforces conceptual understanding of the process applied in approaching the problem, promotes long term retention of the skill and mirrors what students will be expected to do on a test.
• Conceptual Question Library exercises provide additional conceptual, application-focused questions for instructors to use on homework or assessments.
• MathTalk videos connect the math to the real world (particularly business). The videos include assignable exercises to gauge students’ understanding of video content.
• Interactive Figures illustrate key concepts and allow manipulation for use as teaching and learning tools. These are now in HTML format (no plug-in required) and are supported by assignable exercises and tutorial videos.
• Over 275 Example-based videos, 85 of which are new to this edition, are available as learning aids within exercises and for self-study. The Guide to Video-Based Assignments makes it easy to assign videos for homework by showing which MyLab Math exercises correspond to each video.
• Skills for Success Modules help students with the life skills that can make the difference between passing and failing.
• An Integrated Review MyLab Math course contains pre-made quizzes to assess the prerequisite skills needed for each chapter, plus personalized remediation for any gaps in skills that are identified.
• Graphing Calculator and Excel Spreadsheet Manuals, specific to this course, are now downloadable from MyLab Math.
• Instructor’s Answers document (downloadable from MyLab Math) provides all answers in one place and augments the downloadable Instructor’s Solutions Manual, which contains all solutions.