Calculus, 7th Edition

    9781119330387.pdf

    Calculus, 7th Edition

    By Deborah Hughes-Hallett, Andrew M. Gleason, and William G. McCallum, et al.

    Calculus continues the Harvard Consortium’s effort to promote courses in which understanding and computation reinforce each other to reduce complicated problems to simple procedures without losing sight of the practical value of mathematics. With a focus on the development of mathematical thinking supported by theory and modeling, this course offers a flexible approach with a variety of problems and examples from the physical, health, and biological sciences as well as engineering and economics. This approach to instruction allows a variance in the level of theory while emphasizing the connection between calculus and multiple fields of study.

    Available Digital Formats

    What's Inside

    Adaptive Practice

    Adaptive practice provides plenty of practice to effectively prepare students.

    Students begin with a quick, section-level diagnostic to determine their initial level of understanding. They can use the dashboard and quick reports to see what topics they know and don’t know.

    Interactive Exploration

    Visualizing more challenging concepts helps improve comprehension.

    The HTML5 Interactive Exploration applets help students better understand and visualize difficult concepts. The Interactive Explorations include quizzes to ensure students understand key concepts.

    worked-example-video

    Videos clearly explain concepts for all types of students.

    The Assignable Video Series is a full suite of worked example videos of the most difficult examples in each section of the program.

    FEATURES INCLUDE

    • Instructor’s Manual
    • Excel Report Sheet Templates
    • Instructor’s Manual
    • Instructor’s Manual
    • Excel Report Sheet Templates
    • Instructor’s Manual

    About the Authors

    The Calculus Consortium was founded in 1988 in response to the call for change at the “Lean and Lively Calculus” and “Calculus for a New Century” conferences. These conferences urged mathematicians to redesign the content and pedagogy used in calculus. The Consortium initially brought together mathematics faculty from Harvard, Stanford, the University of Arizona, Southern Mississippi, Colgate, Haverford, Suffolk Community College, and Chelmsford High School to address the issue. Finding surprising agreement among their diverse institutions, the Consortium was awarded funding from the National Science Foundation to design a new calculus course. A subsequent NSF grant supported the development of a precalculus and multivariable calculus curriculum.

    Since its inception, the Calculus Consortium has consisted of members of high school, college, and university faculty, all working together towards a common goal. The collegiality of such a disparate group of instructors is one of the Consortium’s greatest strengths.

    Contributors include:

    Deborah Hughes-Hallett, University of Arizona
    Andrew M. Gleason, Harvard University
    William G. McCallum, University of Arizona
    Eric Connally, Harvard University Extension
    Daniel E. Flath, Macalester College
    Selin Kalaycioglu, New York University
    Brigitte Lahme, Sonoma State University
    Patti Frazer Lock, St. Lawrence University
    David O. Lomen, University of Arizona
    David Lovelock, University of Arizona
    Guadalupe I. Lozano, University of Arizona
    Jerry Morris, Sonoma State University
    David Mumford, Brown University
    Brad G. Osgood, Stanford University
    Cody L. Patterson, University of Texas at San Antonio
    Douglas Quinney, University of Keele
    Karen R. Rhea, University of Michigan
    Ayse Arzu Sahin, Wright State University
    Adam H. Spiegler, Loyola University-Chicago
    Jeff Tecosky-Feldman, Haverford College
    Thomas W. Tucker, Colgate University
    Aaron D. Wootton, University of Portland
    Elliot J. Marks

    Table of Contents

    1. Foundation for Calculus: Functions and Limits
    2. Key Concept: The Derivative
    3. Short-Cuts to Differentiation
    4. Using the Derivative
    5. Key Concept: The Definite Integral
    6. Constructing Antiderivatives
    7. Integration
    8. Using the Definite Integral
    9. Sequences and Series
    10. Approximating Functions Using Series
    11. Differential Equations
    12. Functions of Several Variables
    13. A Fundamental Tool: Vectors
    14. Differentiating Functions of Several Variables
    15. Optimization: Local and Global Extrema
    16. Integrating Functions of Several Variables
    17. Parameterization and Vector Fields
    18. Line Integrals
    19. Flux Integrals and Divergence
    20. The Curl and Stokes Theorem
    21. Parameters, Coordinates, and Integrals

    What's New

    Calculus enhancements include:

    • WileyPLUS: A flexible platform with customizable content to elevate students’ experience in the modern classroom. Algorithmic auto-graded homework questions and adaptive practice with many viewable metrics and analytics provide a comprehensive, data-driven approach to engaging students.
    • Assignable Video Series: This course includes a full suite of worked example videos for the most difficult examples in each section of the program.
    • Adaptive Practice: Every student has a different starting point, and adaptive practice provides countless opportunities for students to prepare for class or exams and quizzes. Active retrieval of information with practice questions is proven to improve retention of information better than re-reading or reviewing the material, and students who use adaptive practice to prepare for exams do significantly better than those who do not.
    HH-Calc-7-ORION

    Adaptive practice provides plenty of practice to effectively prepare students.

    Students begin with a quick, section-level diagnostic to determine their initial level of understanding. They can use the dashboard and quick reports to see what topics they know and don’t know.

    Interactive Exploration

    Visualizing more challenging concepts helps improve comprehension.

    The HTML5 Interactive Exploration applets help students better understand and visualize difficult concepts. The Interactive Explorations include quizzes to ensure students understand key concepts.

    worked-example-video

    Videos clearly explain concepts for all types of students.

    The Assignable Video Series is a full suite of worked example videos of the most difficult examples in each section of the program.

    Calculus enhancements include:

    • WileyPLUS: A flexible platform with customizable content to elevate students’ experience in the modern classroom. Algorithmic auto-graded homework questions and adaptive practice with many viewable metrics and analytics provide a comprehensive, data-driven approach to engaging students.
    • Assignable Video Series: This course includes a full suite of worked example videos for the most difficult examples in each section of the program.
    • Adaptive Practice: Every student has a different starting point, and adaptive practice provides countless opportunities for students to prepare for class or exams and quizzes. Active retrieval of information with practice questions is proven to improve retention of information better than re-reading or reviewing the material, and students who use adaptive practice to prepare for exams do significantly better than those who do not.

    The Calculus Consortium was founded in 1988 in response to the call for change at the “Lean and Lively Calculus” and “Calculus for a New Century” conferences. These conferences urged mathematicians to redesign the content and pedagogy used in calculus. The Consortium initially brought together mathematics faculty from Harvard, Stanford, the University of Arizona, Southern Mississippi, Colgate, Haverford, Suffolk Community College, and Chelmsford High School to address the issue. Finding surprising agreement among their diverse institutions, the Consortium was awarded funding from the National Science Foundation to design a new calculus course. A subsequent NSF grant supported the development of a precalculus and multivariable calculus curriculum.

    Since its inception, the Calculus Consortium has consisted of members of high school, college, and university faculty, all working together towards a common goal. The collegiality of such a disparate group of instructors is one of the Consortium’s greatest strengths.

    Contributors include:

    Deborah Hughes-Hallett, University of Arizona
    Andrew M. Gleason, Harvard University
    William G. McCallum, University of Arizona
    Eric Connally, Harvard University Extension
    Daniel E. Flath, Macalester College
    Selin Kalaycioglu, New York University
    Brigitte Lahme, Sonoma State University
    Patti Frazer Lock, St. Lawrence University
    David O. Lomen, University of Arizona
    David Lovelock, University of Arizona
    Guadalupe I. Lozano, University of Arizona
    Jerry Morris, Sonoma State University
    David Mumford, Brown University
    Brad G. Osgood, Stanford University
    Cody L. Patterson, University of Texas at San Antonio
    Douglas Quinney, University of Keele
    Karen R. Rhea, University of Michigan
    Ayse Arzu Sahin, Wright State University
    Adam H. Spiegler, Loyola University-Chicago
    Jeff Tecosky-Feldman, Haverford College
    Thomas W. Tucker, Colgate University
    Aaron D. Wootton, University of Portland
    Elliot J. Marks

    1. Foundation for Calculus: Functions and Limits
    2. Key Concept: The Derivative
    3. Short-Cuts to Differentiation
    4. Using the Derivative
    5. Key Concept: The Definite Integral
    6. Constructing Antiderivatives
    7. Integration
    8. Using the Definite Integral
    9. Sequences and Series
    10. Approximating Functions Using Series
    11. Differential Equations
    12. Functions of Several Variables
    13. A Fundamental Tool: Vectors
    14. Differentiating Functions of Several Variables
    15. Optimization: Local and Global Extrema
    16. Integrating Functions of Several Variables
    17. Parameterization and Vector Fields
    18. Line Integrals
    19. Flux Integrals and Divergence
    20. The Curl and Stokes Theorem
    21. Parameters, Coordinates, and Integrals