Description

For two-semester courses in Calculus.

 

Helps students “get the idea.”

Calculus for Business, Economics, Life Sciences, and Social Sciences, 14th Edition offers more built-in guidance than any other text in its field – with special emphasis on applications and prerequisite skills – and a host of student-friendly features to help students catch up or learn on their own. The text’s emphasis on helping students “get the idea” is enhanced in the new edition by a design refresh and updated data and applications.

 

 

MyLab™ Math is not included. Students, if MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

MyLab is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts.

Features

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.

 

 

Enhances student comprehension through extensive built-in guidance

·    More than 300 completely worked examples introduce concepts and demonstrate problem-solving techniques.

·    Matched Problems accompany each of the worked examples to help students gain solid knowledge of the basic topics and assess their own level of understanding before moving on.

·    In order to emphasize problem solving, concepts, and computational skills, most derivations and proofs are omitted, except where their inclusion adds significant insight into a particular concept. 

·    NEW! Full-color design and modern look helps students navigate the text and enhances its pedagogical features. The revised design is free of potentially distracting elements. The figures in the text have been re-rendered using the latest software and re-conceived to take advantage of a full color palette in order to maximize their instructional potential.

 

A flexible structure that helps instructors meet the varied needs of their students

·    The variety of exercise types and difficulty levels enable instructors to  easily craft homework assignments tailored to their students’ needs:

·    Exercise sets at the end of each section consist of Skills Warm-up problems that review prerequisite knowledge specific to that section, followed by problems that are categorized according to level of difficulty (A, B, and C), followed by Applications. 

·    Applications give students substantial experience in modeling and solving real-world problems. Almost every exercise set contains application problems that were derived from real-world situations. 

·    Chapter Reviews include a comprehensive summary of important terms, symbols, and concepts, keyed to completely worked examples, and are followed by a set of Review Exercises. 

·    A Diagnostic Prerequisite Test assesses students’ prerequisite skills prior to taking the course and provides a Basic Algebra Review to help them remediate in specific areas of need.

 

 

MyLab^TM Math not included. Students, if MyLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

 

 

 

Reach every student with MyLab

 

Deliver trusted content: You deserve teaching materials that meet your own high standards for your course. That’s why we partner with highly respected authors to develop interactive content and course-specific resources that you can trust – and that keep your students engaged.

·    Homework and practice 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 the optional learning aids Help Me Solve This, View an Example, videos, and/or the eText. Exercise types include:

o Instructors now have more exercises than ever to choose from in assigning homework. Most new questions are application-oriented. There are approximately 4,200 assignable exercises in MyLab Math for this text. 

o NEW! Setup & Solve exercises that require students to show how they set up a problem as well as the solution, better mirroring what is required of students on tests.

o NEW! Additional Conceptual Questions that provide support for assessing concepts and vocabulary. Many of these questions are application oriented.

·    NEW! A full suite of Interactive Figures has been added to support teaching and learning. The figures illustrate key concepts and allow manipulation. They have been designed to be used in lecture as well as by students independently. 

·    Instructional videos: Every example in the text has an instructional video tied to it for independent study. Videos are also available as learning aids within exercises and for self-study. MathTalk videos were added to highlight applications of the content of the course to business and the Guide to Video-Based Assignments shows which MyLab Math exercises can be assigned for each video (all videos are also assignable).

·    A complete eText: Students and instructors get unlimited access to the eText within any MyLab Math course using that edition of the textbook.

 

 

Empower each learner: Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need—when and where they need it—to be successful.

·    NEW! Enhanced Sample Assignments that were designed to 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 so students check their understanding. These assignments are editable in MyLab Math.

·    Learning Catalytics, now included in all MyLab Math courses, is a student response tool that uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking during lecture. Learning Catalytics fosters student engagement and peer-to-peer learning with real-time analytics. You can access pre-built exercises created specifically for this course.

 

Teach your course your way: Your course is unique. So whether you’d like to build your own assignments, teach multiple sections, or set prerequisites, MyLab gives you the flexibility to easily create your course to fit your needs.

·    ENHANCED! Instructor and student resources can be downloaded from MyLab Math and have been enhanced to include the following resources. 

o A Note-Taking Guide supports students as they take notes in class. It includes definitions, theorems, and statements of examples but has blank space for students to write solutions to examples and sample problems. The Note-Taking Guide corresponds to the Lecture PowerPoints that accompany the text.

o Learning Worksheets include key chapter definitions and formulas, followed by exercises for students to practice in class, for homework, or for independent study.

 

Improve student results: When you teach with MyLab, student performance improves. That’s why instructors have chosen MyLab for over 15 years, touching the lives of over 50 million students. 

New to this Edition

·    Full-color design and modern look helps students navigate the text and appeals to visual learners. This design refresh enhances the clean page layout that is free of potentially distracting elements. The figures in the text have been re-rendered using the latest software and re-conceived to take advantage of a full color palette in order to maximize their instructional potential.

·    Reminder features in the side margin either remind students of a concept that is needed at that point in the book or direct the student back to the section in which it was covered earlier.

·    Section 4.5 includes rewritten Theorem 3 on using the second-derivative test to find absolute extrema, making it applicable to more general intervals.

·    Section 6.3 includes rewritten material on the future value of a continuous income stream to provide a more intuitive and less technical treatment.

 

 

 

MyLab^TM Math not included. Students, if MyLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

·    Instructors now have more exercises than ever to choose from in assigning homework. Most new questions are application-oriented. There are approximately 4,200 assignable exercises in MyLab Math for this text. 

·    Setup & Solve exercises require students to show how they set up a problem as well as the solution, better mirroring what is required of students on tests.

·    Additional Conceptual Questions provide support for assessing concepts and vocabulary. Many of these questions are application oriented.

·    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 so students check their understanding. These assignments are editable in Mylab Math.

·    A full suite of Interactive Figures has been added to support teaching and learning. The figures illustrate key concepts and allow manipulation. They have been designed to be used in lecture as well as by students independently. 

·    Study skills modules help students with the life skills that can make the difference between passing and failing.

·    MathTalk videos highlight applications of the content of the course to business. The videos are supported by assignable exercises.

·    The Graphing Calculator Manual and Excel Spreadsheet Manual, both specific to this course, have been updated to support the TI-84 Plus CE (color edition) and Excel 2016, respectively. Both manuals also contain additional topics to support the course. These manuals are within the Tools for Success tab.

·    Instructor and student resources can be downloaded from MyLab Math and have been enhanced to include the following resources: 

o A Note-Taking Guide supports students as they take notes in class. It includes definitions, theorems, and statements of examples but has blank space for students to write solutions to examples and sample problems. The Note-Taking Guide corresponds to the Lecture PowerPoints that accompany the text.

o The Guide to Video-Based Assignments shows which MyLab Math exercises can be assigned for each video.

o An Instructor Answers document, with all answers in one place, augments the downloadable Instructor Solutions Manual.

Table of Contents

Preface

Diagnostic Prerequisite Test

 

1. Functions and Graphs

1.1 Functions 

1.2 Elementary Functions: Graphs and Transformations 

1.3 Linear and Quadratic Functions

1.4 Polynomial and Rational Functions 

1.5 Exponential Functions 

1.6 Logarithmic Functions 

1.7 Right Angle Trigonometry

1.8 Trigonometric Functions

Chapter 1 Summary and Review

Review Exercises 

 

2. Limits and the Derivative

2.1 Introduction to Limits 

2.2 Infinite Limits and Limits at Infinity 

2.3 Continuity 

2.4 The Derivative 

2.5 Basic Differentiation Properties 

2.6 Differentials 

2.7 Marginal Analysis in Business and Economics 

Chapter 2 Summary and Review

Review Exercises 

 

3. Additional Derivative Topics 

3.1 The Constant e and Continuous Compound Interest 

3.2 Derivatives of Exponential and Logarithmic Functions 

3.3 Derivatives of Trigonometric Functions 

3.4 Derivatives of Products and Quotients

3.5 The Chain Rule 

3.6 Implicit Differentiation 

3.7 Related Rates

3.8 Elasticity of Demand 

Chapter 3 Summary and Review 

Review Exercises 

 

4. Graphing and Optimization

4.1 First Derivative and Graphs

4.2 Second Derivative and Graphs

4.3 L’Hôpital’s Rule 

4.4 Curve-Sketching Techniques 

4.5 Absolute Maxima and Minima 

4.6 Optimization 

Chapter 4 Summary and Review 

Review Exercises 

 

5. Integration 

5.1 Antiderivatives and Indefinite Integrals 

5.2 Integration by Substitution

5.3 Differential Equations; Growth and Decay

5.4 The Definite Integral 

5.5 The Fundamental Theorem of Calculus 

5.6 Area Between Curves

Chapter 5 Summary and Review

Review Exercises 

 

6. Additional Integration Topics

6.1 Integration by Parts

6.2 Other Integration Methods

6.3 Applications in Business and Economics

6.4 Integration of Trigonometric Functions

Chapter 6 Summary and Review 

Review Exercises 

 

7. Multivariable Calculus

7.1 Functions of Several Variables 

7.2 Partial Derivatives 

7.3 Maxima and Minima 

7.4 Maxima and Minima Using Lagrange Multipliers

7.5 Method of Least Squares 

7.6 Double Integrals over Rectangular Regions 

7.7 Double Integrals over More General Regions 

Chapter 7 Summary and Review 

Review Exercises  

 

 

8. Differential Equations 

8.1 Basic Concepts 

8.2 Separation of Variables 

8.3 First-Order Linear Differential Equations 

Chapter 8 Summary and Review 

Review Exercises

 

9. Taylor Polynomials and Infinite Series 

9.1 Taylor Polynomials 

9.2 Taylor Series 

9.3 Operations on Taylor Series 

9.4 Approximations Using Taylor Series 

Chapter 9 Summary and Review 

Review Exercises

 

10. Probability and Calculus 

10.1 Improper Integrals 

10.2 Continuous Random Variables 

10.3 Expected Value, Standard Deviation, and Median 

10.4 Special Probability Distributions 

Chapter 10 Summary and Review 

Review Exercises

 

Appendix A: Basic Algebra Review 

A.1 Real Numbers 

A.2 Operations on Polynomials 

A.3 Factoring Polynomials 

A.4 Operations on Rational Expressions   

A.5 Integer Exponents and Scientific Notation 

A.6 Rational Exponents and Radicals   

A.7 Quadratic Equations 

 

Appendix B: Special Topics  (online)

B.1 Sequences, Series, and Summation Notation

B.2 Arithmetic and Geometric Sequences 

B.3 Binomial Theorem 

B.4 Interpolating Polynomials and Divided Differences 

 

Appendix C: Integration Using Tables

 

Answers 

Index

Index of Applications