Calculus:Early Transcendentals: International Edition

William L. Briggs / Lyle Cochran
Februar 2010
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For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors.


Briggs/Cochran is the most successful new calculus series published in the last two decades. The authors' decades of teaching experience resulted in a text that reflects how students generally use a textbook-they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows.


To further support student learning, the MyMathLab course features an eBook with 650 Interactive Figures that can be manipulated to shed light on key concepts. In addition, the Instructor's Resource Guide and Test Bank features quizzes, test items, lecture support, guided projects, and more.


An expanded version of this text, with an entire chapter devoted to differential equations, is also available. It is entitled Calculus for Scientists and Engineers: Early Transcendentals.


  • Topics are introduced through concrete examples, geometric arguments, applications, and analogies rather than through abstract arguments. The authors appeal to students' intuition and geometric instincts to make calculus natural and believable.
  • Figures are designed to help today's visually oriented learners. They are conceived to convey important ideas and facilitate learning, annotated to lead students through the key ideas, and rendered using the latest software for unmatched clarity and precision.
  • Comprehensive exercise sets provide for a variety of student needs and are consistently structured and labeled to facilitate the creation of homework assignments by inspection.
    • Review Questions check that students have a general conceptual understanding of the essential ideas from the section.
    • Basic Skills exercises are linked to examples in the section so students get off to a good start with homework.
    • Further Explorations exercises extend students' abilities beyond the basics.
    • Applications present practical and novel applications and models that use the ideas presented in the section.
    • Additional Exercises challenge students to stretch their understanding by working through abstract exercises and proofs.
  • Examples are plentiful and stepped out in detail. Within examples, each step is annotated to help students understand what took place in that step.
  • Quick Check exercises punctuate the narrative at key points to test understanding of basic ideas and encourage students to read with pencil in hand.
  • The MyMathLab course for the text features the following:
    • More than 7,000 assignable exercises provide you with the options you need to meet the needs of students. Most exercises can be algorithmically regenerated for unlimited practice.
    • Learning aids include guided exercises, additional examples, and tutorial videos. You control how much help your students can get and when.
    • 650 Interactive Figures in the eBook can be manipulated to shed light on key concepts. The figures are also ideal for in-class demonstrations.
    • Interactive Figure Exercises provide a way for you make the most of the Interactive Figures by including them in homework assignments.
    • A “Getting Ready for Calculus” chapter, with built-in diagnostic tests, identifies each student's gaps in skills and provides individual remediation directly to those skills that are lacking.
  • Guided Projects, available for each chapter, require students to carry out extended calculations (e.g., finding the arc length of an ellipse), derive physical models (e.g., Kepler's Laws), or explore related topics (e.g., numerical integration). The “guided” nature of the projects provides scaffolding to help students tackle these more involved problems.
  • The Instructor's Resource Guide and Test Bank provides a wealth of instructional resources including Guided Projects, Lecture Support Notes with Key Concepts, Quick Quizzes for each section in the text, Chapter Reviews, Chapter Test Banks, Tips and Help for Interactive Figures, and Student Study Cards.
  • Sequences and Series is the most challenging content in Calculus 2 for students, and the authors have spread the content over two chapters to help clarify and pace it more effectively.
    • Chapter 8, Sequences and Infinite Series, begins by providing a big picture with concrete examples of the difference between a sequence and a series followed by studying the properties and limits of sequences in addition to studying special infinite series and convergence tests. This chapter lays the groundwork for analyzing the absolute convergence for power series.
    • Chapter 9, Power Series, begins with approximating with polynomials. Power series are introduced as a new way to define functions, building on one series by generating new series using composition, differentiation and integration. Taylor series are then covered and the motivation that precedes the section should make the topic more accessible.

Table of Contents

1. Functions

1.1 Review of Functions

1.2 Representing Functions

1.3 Inverse, Exponential, and Logarithm Functions

1.4 Trigonometric Functions and Their Inverses


2. Limits

2.1 The Idea of Limits

2.2 Definitions of Limits

2.3 Techniques for Computing Limits

2.4 Infinite Limits

2.5 Limits at Infinity

2.6 Continuity

2.7 Precise Definitions of Limits


3. Derivatives

3.1 Introducing the Derivative

3.2 Rules of Differentiation

3.3 The Product and Quotient Rules

3.4 Derivatives of Trigonometric Functions

3.5 Derivatives as Rates of Change

3.6 The Chain Rule

3.7 Implicit Differentiation

3.8 Derivatives of Logarithmic and Exponential Functions

3.9 Derivatives of Inverse Trigonometric Functions

3.10 Related Rates


4. Applications of the Derivative

4.1 Maxima and Minima

4.2 What Derivatives Tell Us

4.3 Graphing Functions

4.4 Optimization Problems

4.5 Linear Approximation and Differentials

4.6 Mean Value Theorem

4.7 L'Hôpital's Rule

4.8 Antiderivatives


5. Integration

5.1 Approximating Areas under Curves

5.2 Definite Integrals

5.3 Fundamental Theorem of Calculus

5.4 Working with Integrals

5.5 Substitution Rule


6. Applications of Integration

6.1 Velocity and Net Change

6.2 Regions between Curves

6.3 Volume by Slicing

6.4 Volume by Shells

6.5 Length of Curves

6.6 Physical Applications

6.7 Logarithmic and exponential functions revisited

6.8 Exponential models


7. Integration Techniques

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitution

7.4 Partial Fractions

7.5 Other Integration Strategies

7.6 Numerical Integration

7.7 Improper Integrals

7.8 Introduction to Differential Equations


8. Sequences and Infinite Series

8.1 An Overview

8.2 Sequences

8.3 Infinite Series

8.4 The Divergence and Integral Tests

8.5 The Ratio and Comparison Tests

8.6 Alternating Series


9. Power Series

9.1 Approximating Functions with Polynomials

9.2 Power Series

9.3 Taylor Series

9.4 Working with Taylor Series


10. Parametric and Polar Curves

10.1 Parametric Equations

10.2 Polar Coordinates

10.3 Calculus in Polar Coordinates

10.4 Conic Sections


11. Vectors and Vector-Valued Functions

11.1 Vectors in the Plane

11.2 Vectors in Three Dimensions

11.3 Dot Products

11.4 Cross Products

11.5 Lines and Curves in Space

11.6 Calculus of Vector-Valued Functions

11.7 Motion in Space

11.8 Length of Curves

11.9 Curvature and Normal Vectors


12. Functions of Several Variables

12.1 Planes and Surfaces

12.2 Graphs and Level Curves

12.3 Limits and Continuity

12.4 Partial Derivatives

12.5 The Chain Rule

12.6 Directional Derivatives and the Gradient

12.7 Tangent Planes and Linear Approximation

12.8 Maximum/Minimum Problems

12.9 Lagrange Multipliers


13. Multiple Integration

13.1 Double Integrals over Rectangular Regions

13.2 Double Integrals over General Regions

13.3 Double Integrals in Polar Coordinates

13.4 Triple Integrals

13.5 Triple Integrals in Cylindrical and Spherical Coordinates

13.6 Integrals for Mass Calculations

13.7 Change of Variables in Multiple Integrals


14. Vector Calculus

14.1 Vector Fields

14.2 Line Integrals

14.3 Conservative Vector Fields

14.4 Green's Theorem

14.5 Divergence and Curl

14.6 Surface Integrals

14.7 Stokes' Theorem

14.8 Divergence Theorem


William Briggs has been on the mathematics faculty at the University of Colorado at Denver for twenty-three years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, Using and Understanding Mathematics; an undergraduate problem solving book, Ants, Bikes, and Clocks; and two tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform. He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President's Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.


Lyle Cochran is a professor of mathematics at Whitworth University in Spokane, Washington. He holds BS degrees in mathematics and mathematics education from Oregon State University and a MS and PhD in mathematics from Washington State University. He has taught a wide variety of undergraduate mathematics courses at Washington State University, Fresno Pacific University, and, since 1995, at Whitworth University. His expertise is in mathematical analysis, and he has a special interest in the integration of technology and mathematics education. He has written technology materials for leading calculus and linear algebra textbooks including the Instructor's Mathematica Manual for Linear Algebra and Its Applications by David C. Lay and the Mathematica Technology Resource Manual for Thomas' Calculus. He is a member of the MAA and a former chair of the Department of Mathematics and Computer Science at Whitworth University.


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