Higher Education

Calculus of a Single Variable: Early Transcendental Functions, 6th Edition

  • Ron Larson The Pennsylvania State University, The Behrend College
  • Bruce H. Edwards University of Florida
  • ISBN-10: 1285774795  |  ISBN-13: 9781285774794
  • 896 Pages
  • Previous Editions: 2011, 2007, 2003
  • © 2015 | Published
  • College Bookstore Wholesale Price = $230.25
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About

Overview

Known for its continued excellence, CALCULUS OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, offers instructors and students innovative teaching and learning resources. The Larson team always has two main objectives for text revisions: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the sixth of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas.

Features and Benefits

  • Applications-Carefully chosen applied exercises and examples are included throughout to address the question, "When will I use this?" These applications are pulled from diverse sources, such as current events, world data, industry trends, and more, and relate to a wide range of interests.
  • Writing About Concepts-Writing exercises at the end of each section are designed to test students' understanding of basic concepts in each section, encouraging them to verbalize and write answers and promote technical skills that will be invaluable in their future careers.
  • Theorems-Theorems provide the conceptual framework for calculus. Theorems are clearly stated and separated from the rest of the text by boxes for quick visual reference. Key proofs often follow the theorem and can be found on LarsonCalculus.com.
  • Definitions-As with theorems, definitions are clearly stated using precise, formal wording and are separated from the text by boxes for quick visual reference.
  • Explorations-Explorations provide unique challenges to study concepts that have not yet been formally covered in the text. They allow students to learn by discovery and introduce topics related to ones presently being studied. Exploring topics in this way encourages students to think outside the box.
  • Historical Notes and Biographies-Historical notes provide students with background information on the foundations of calculus. The Biographies introduce students to the people who created and contributed to calculus.
  • Technology-Throughout the book, technology boxes show students how to use technology to solve problems and explore concepts of calculus. These tips also point out some of the pitfalls of using technology.
  • Section Projects-Projects appear in selected sections and encourage students to explore applications related to the topics they are studying. They provide an interesting and engaging way for students to work and investigate ideas collaboratively.
  • Putnam Exam Challenges-Putnam Exam Questions appear in selected sections. These actual Putnam Exam Questions will challenge students and push them to the limits of their understanding of calculus.

Table of Contents

1. PREPARATION FOR CALCULUS.
Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Fitting Models to Data. Inverse Functions. Exponential and Logarithmic Functions. Review Exercises. P.S. Problem Solving.
2. LIMITS AND THEIR PROPERTIES.
A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits. Section Project: Graphs and Limits of Trigonometric Functions. Review Exercises. P.S. Problem Solving.
3. DIFFERENTIATION.
The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Section Project: Optical Illusions. Derivatives of Inverse Functions, Related Rates. Newton's Method. Review Exercises. P.S. Problem Solving.
4. APPLICATIONS OF DIFFERENTIATION.
Extrema on an Interval. Rolle's Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Section Project: Rainbows. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Section Project: Connecticut River. Differentials. Review Exercises. P.S. Problem Solving.
5. INTEGRATION.
Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Section Project: Demonstrating the Fundamental Theorem. Integration by Substitution. Numerical Integration. The Natural Logarithmic Function: Integration. Inverse Trigonometric Functions: Integration. Hyperbolic Functions. Section Project: St. Louis Arch. Review Exercises. P.S. Problem Solving.
6. DIFFERENTIAL EQUATIONS.
Slope Fields and Euler's Method. Differential Equations: Growth and Decay. Differential Equations: Separation of Variables. The Logistic Equation. First-Order Linear Differential Equations. Section Project: Weight Loss. Predator-Prey Differential Equations. Review Exercises. P.S. Problem Solving.
7. APPLICATIONS OF INTEGRATION.
Area of a Region Between Two Curves. Volume: The Disk Method. Volume: The Shell Method. Section Project: Saturn. Arc Length and Surfaces of Revolution. Work. Section Project: Tidal Energy. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force. Review Exercises. P.S. Problem Solving.
8. INTEGRATION TECHNIQUES, L'HOPITAL'S RULE, AND IMPROPER INTEGRALS.
Basic Integration Rules. Integration by Parts. Trigonometric Integrals. Section Project: Power Lines. Trigonometric Substitution. Partial Fractions. Integration by Tables and Other Integration Techniques. Indeterminate Forms and L'Hopital's Rule. Improper Integrals. Review Exercises. P.S. Problem Solving.
9. INFINITE SERIES.
Sequences. Series and Convergence. Section Project: Cantor's Disappearing Table. The Integral Test and p-Series. Section Project: The Harmonic Series. Comparisons of Series. Section Project: Solera Method. Alternating Series. The Ratio and Root Tests. Taylor Polynomials and Approximations. Power Series. Representation of Functions by Power Series. Taylor and Maclaurin Series. Review Exercises. P.S. Problem Solving.
10. CONICS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES.
Conics and Calculus. Plane Curves and Parametric Equations. Section Project: Cycloids. Parametric Equations and Calculus. Polar Coordinates and Polar Graphs. Section Project: Anamorphic Art. Area and Arc Length in Polar Coordinates. Polar Equations of Conics and Kepler's Laws. Review Exercises. P.S. Problem Solving.
Appendix A: Proofs of Selected Theorems (Web).
Appendix B: Integration Tables.
Appendix C: Pre-calculus Review (Web).
Appendix C1: Real Numbers and the Real Number Line.
Appendix C2: The Cartesian Plane.
Appendix C3: Review of Trigonometric Functions.
Appendix D: Rotation and the General Second-Degree Equation (Web).
Appendix E: Complex Numbers (Web).

What's New

  • LarsonCalulus.com-This robust companion website offers multiple tools and resources. Access to these features is free. Students can watch videos explaining concepts or proofs from the book, explore examples, view three-dimensional graphs, download articles from math journals, and much more!
  • Interactive Examples-Examples throughout the book are accompanied by interactive examples at LarsonCalculus.com. These interactive examples use Wolfram's free CDF Player and allow students to explore calculus by manipulating functions or graphs, and observing the results.
  • Proof Videos-Students can watch videos of co-author Bruce Edwards as he explains the proofs of the theorems in CALCULUS OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, at LarsonCalculus.com.
  • How Do You See It?-The "How Do You See It?" feature in each section presents a real-life problem that students solve by visual inspection using the concepts learned in the lesson. This exercise is excellent for classroom discussion or test preparation.
  • Remark-These hints and tips reinforce or expand on concepts, help students learn how to study mathematics, caution students about common errors, address special cases, or show alternative or additional steps to a solution of an example.
  • Exercise Sets-The exercise sets have been carefully and extensively examined to ensure they are rigorous and relevant and include all topics our users have suggested. The exercises have been reorganized and titled so students can better see the connections between examples and exercises. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by giving students the opportunity to apply the concepts in real-life situations.
  • Appendix A (Proofs of Selected Theorems) now appears in video format on LarsonCalculus.com. The proofs also appear in text form at CengageBrain.com.

Alternate Formats

Choose the format that best fits your student's budget and course goals

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  • Hybrid Edition

    ISBN-10: 1285777050 | ISBN-13: 9781285777054

    List Price = $163.95  | CengageBrain Price = $163.95  | College Bookstore Wholesale Price = $121.50

Learning Resource Bundles

Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Learning Consultant for more information.

Bundle: Text (Calc SV:ET) + CourseMate Printed Access Card

ISBN-10: 1305516230  | ISBN-13: 9781305516236

List Price = $319.95  | College Bookstore Wholesale Price = $240.25

This Bundle Includes:

  • Calculus of a Single Variable: Early Transcendental Functions
    List Price = $306.95  | CengageBrain Price = $306.95  | College Bookstore Wholesale Price = $230.25
  • CourseMate, 2 terms (12 months) Printed Access Card
    List Price = $254.00  | College Bookstore Wholesale Price = $190.00


Printed Text + CourseMate Instant Access

ISBN-10:  1305615751 | ISBN-13:  9781305615755

List Price = $319.95  | CengageBrain Price = $319.95  | College Bookstore Wholesale Price = $240.25

This Bundle Includes:

  • Calculus of a Single Variable: Early Transcendental Functions
    List Price = $306.95  | CengageBrain Price = $306.95  | College Bookstore Wholesale Price = $230.25
  • CourseMate, 2 terms (12 months) Instant Access
    List Price = $254.00  | CengageBrain Price = $254.00  | College Bookstore Wholesale Price = $254.00


Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

PowerLecture with ExamView® and JoinIn™ Student Response System  (ISBN-10: 1285085833 | ISBN-13: 9781285085838)

This comprehensive instructor DVD includes resources such as electronic versions of the Instructor’s Resource Guide and Printed Test Bank, complete pre-built PowerPoint lectures, all art from the text in both jpeg and PowerPoint formats, ExamView® algorithmic computerized testing software, JoinIn™ content for audience response systems (clickers), and a link to Solution Builder.

Solution Builder  (ISBN-10: 1285778324 | ISBN-13: 9781285778327)

This online instructor database offers complete worked-out solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class.

Complete Solutions Manual, Volume 1, Chapters 1-6  (ISBN-10: 1285774817 | ISBN-13: 9781285774817)

This manual contains worked-out solutions to all exercises in Chapters 1-6 of CALCULUS OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, and CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition.

Complete Solutions Manual, Volume 2, Chapters 7-10  (ISBN-10: 1285774825 | ISBN-13: 9781285774824)

This manual contains worked-out solutions to all exercises in Chapters 7-9 of CALCULUS OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, and CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition.

Cengage Learning Testing, powered by Cognero Instant Access  (ISBN-10: 1285978838 | ISBN-13: 9781285978833)

Student Solutions Manual  (ISBN-10: 1285774809 | ISBN-13: 9781285774800)

This manual contains worked-out solutions for all odd-numbered exercises in Larson/Edwards's CALCULUS OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition (Chapters 1-10 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition).

List Price = $101.95  | CengageBrain Price = $101.95  | College Bookstore Wholesale Price = $76.50

CourseMate, 2 terms (12 months) Instant Access  (ISBN-10: 1285775872 | ISBN-13: 9781285775876)

CourseMate is a perfect study tool for students, and requires no set up from instructors. CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. CourseMate for Larson's CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, includes an interactive eBook, animations, videos, quizzes, and more! For instructors, CourseMate includes Engagement Tracker, a first-of-its kind tool that monitors student engagement.

List Price = $254.00  | CengageBrain Price = $254.00  | College Bookstore Wholesale Price = $254.00

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Instant Access Code Homework with e-Book  (ISBN-10: 133729697X | ISBN-13: 9781337296977)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive eBook, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Instant Access Code Homework Only  (ISBN-10: 133729926X | ISBN-13: 9781337299268)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback and rich tutorial content, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Printed Access Card Homework with e-Book  (ISBN-10: 1337296961 | ISBN-13: 9781337296960)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive eBook, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign® International Printed Access Card Homework Only  (ISBN-10: 1337299251 | ISBN-13: 9781337299251)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback and rich tutorial content, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Student Supplements

Student Solutions Manual  (ISBN-10: 1285774809 | ISBN-13: 9781285774800)

This manual contains worked-out solutions for all odd-numbered exercises in Larson/Edwards's CALCULUS OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition (Chapters 1-10 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition).

List Price = $101.95  | CengageBrain Price = $101.95  | College Bookstore Wholesale Price = $76.50

CourseMate, 2 terms (12 months) Instant Access  (ISBN-10: 1285775872 | ISBN-13: 9781285775876)

CourseMate is a perfect study tool for students. CourseMate brings course concepts to life with interactive learning, study, and exam preparation tools that support the printed textbook. CourseMate for Larson's CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, includes an interactive eBook, animations, videos, quizzes, and more!

List Price = $254.00  | CengageBrain Price = $254.00  | College Bookstore Wholesale Price = $254.00

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Instant Access Code Homework with e-Book  (ISBN-10: 133729697X | ISBN-13: 9781337296977)

Enhanced WebAssign® engages you with immediate feedback, rich tutorial content, and an interactive eBook, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Instant Access Code Homework Only  (ISBN-10: 133729926X | ISBN-13: 9781337299268)

Enhanced WebAssign® engages you with immediate feedback and rich tutorial content, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Printed Access Card Homework with e-Book  (ISBN-10: 1337296961 | ISBN-13: 9781337296960)

Enhanced WebAssign® engages you with immediate feedback, rich tutorial content, and an interactive eBook, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign® International Printed Access Card Homework Only  (ISBN-10: 1337299251 | ISBN-13: 9781337299251)

Enhanced WebAssign® engages you with immediate feedback and rich tutorial content, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Meet the Author

Author Bio

Ron Larson

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage Learning.

Bruce H. Edwards

Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. He taught mathematics at a university near Bogotá, Colombia, as a Peace Corps volunteer. While teaching at the University of Florida, Professor Edwards has won many teaching awards, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year, and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991–1993. Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson.