Cover: Calculus: Early Transcendentals Multivariable, 4th Edition by Jon Rogawski; Colin Adams; Robert Franzosa

Calculus: Early Transcendentals Multivariable

Fourth Edition  ©2019 Jon Rogawski; Colin Adams; Robert Franzosa Formats: E-book

Authors

  • Headshot of Jon Rogawski

    Jon Rogawski

    Jon Rogawski received his undergraduate and master’s degrees in mathematics simultaneously from Yale University, and he earned his PhD in mathematics from Princeton University, where he studied under Robert Langlands. Before joining the Department of Mathematics at UCLA in 1986, where he was a full professor, he held teaching and visiting positions at the Institute for Advanced Study, the University of Bonn, and the University of Paris at Jussieu and Orsay. Jon’s areas of interest were number theory, automorphic forms, and harmonic analysis on semisimple groups. He published numerous research articles in leading mathematics journals, including the research monograph Automorphic Representations of Unitary Groups in Three Variables (Princeton University Press). He was the recipient of a Sloan Fellowship and an editor of the Pacific Journal of Mathematics and the Transactions of the AMS. As a successful teacher for more than 30 years, Jon Rogawski listened and learned much from his own students. These valuable lessons made an impact on his thinking, his writing, and his shaping of a calculus text. Sadly, Jon Rogawski passed away in September 2011. Jon’s commitment to presenting the beauty of calculus and the important role it plays in students’ understanding of the wider world is the legacy that lives on in each new edition of Calculus.


  • Headshot of Colin Adams

    Colin Adams

    Colin Adams is the Thomas T. Read professor of Mathematics at Williams College, where he has taught since 1985. Colin received his undergraduate degree from MIT and his PhD from the University of Wisconsin. His research is in the area of knot theory and low-dimensional topology. He has held various grants to support his research, and written numerous research articles. Colin is the author or co-author of The Knot Book, How to Ace Calculus: The Streetwise Guide, How to Ace the Rest of Calculus: The Streetwise Guide, Riot at the Calc Exam and Other Mathematically Bent Stories, Why Knot?, Introduction to Topology: Pure and Applied, and Zombies & Calculus. He co-wrote and appears in the videos “The Great Pi vs. E Debate” and “Derivative vs. Integral: the Final Smackdown.” He is a recipient of the Haimo National Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, an MAA Polya Lecturer for 1998-2000, a Sigma Xi Distinguished Lecturer for 2000-2002, and the recipient of the Robert Foster Cherry Teaching Award in 2003. Colin has two children and one slightly crazy dog, who is great at providing the entertainment.


  • Headshot of Robert Franzosa

    Robert Franzosa

    Robert (Bob) Franzosa is a professor of mathematics at the University of Maine where he has been on the faculty since 1983. Bob received a BS in mathematics from MIT in 1977 and a Ph.D. in mathematics from the University of Wisconsin in 1984. His research has been in dynamical systems and in applications of topology in geographic information systems. He has been involved in mathematics education outreach in the state of Maine for most of his career. Bob is a co-author of Introduction to Topology: Pure and Applied and Algebraic Models in Our World. He was awarded the University of Maine’s Presidential Outstanding Teaching award in 2003. Bob is married, has two children, three step-children, and one recently-arrived grandson.

Table of Contents

Chapter 10: Infinite Series
10.1 Sequences
10.2 Summing an Infinite Series
10.3 Convergence of Series with Positive Terms
10.4 Absolute and Conditional Convergence
10.5 The Ratio and Root Tests and Strategies for Choosing Tests
10.6 Power Series
10.7 Taylor Polynomials
10.8 Taylor Series
Chapter Review Exercises

Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections
11.1 Parametric Equations
11.2 Arc Length and Speed
11.3 Polar Coordinates
11.4 Area and Arc Length in Polar Coordinates
11.5 Conic Sections
Chapter Review Exercises

Chapter 12: Vector Geometry
12.1 Vectors in the Plane
12.2 Three-Dimensional Space: Surfaces, Vectors, and Curves
12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product
12.5 Planes in 3-Space
12.6 A Survey of Quadric Surfaces
12.7 Cylindrical and Spherical Coordinates
Chapter Review Exercises

Chapter 13: Calculus of Vector-Valued Functions
13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
13.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in 3-Space
13.6 Planetary Motion According to Kepler and Newton
Chapter Review Exercises

Chapter 14: Differentiation in Several Variables
14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
14.3 Partial Derivatives
14.4 Differentiability, Tangent Planes, and Linear Approximation
14.5 The Gradient and Directional Derivatives
14.6 The Chain Rule
14.7 Optimization in Several Variables
14.8 Lagrange Multipliers: Optimizing with a Constraint
Chapter Review Exercises

Chapter 15: Multiple Integration
15.1 Integration in Two Variables
15.2 Double Integrals Over More General Regions
15.3 Triple Integrals
15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
15.5 Applications of Multiple Integrals
15.6 Change of Variables
Chapter Review Exercises

Chapter 16: Line and Surface Integrals
16.1 Vector Fields
16.2 Line Integrals
16.3 Conservative Vector Fields
16.4 Parametrized Surfaces and Surface Integrals
16.5 Surface Integrals of Vector Fields
Chapter Review Exercises

Chapter 17: Fundamental Theorems of Vector Analysis
17.1 Green’s Theorem
17.2 Stokes’ Theorem
17.3 Divergence Theorem
Chapter Review Exercises

Product Updates

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  • Detailed Solutions: Setailed step-by-step solutions ensure students learn from a problem when they answer correctly or give up.
  • Guided Learn and Practice assignments include interactive content, videos, and instructional feedback to prepare students before they come to class.
  • Guided Learn and Practice Assignments contain CalcClips tutorial videos are integrated throughout the e-book.
  • Dynamic Figures powered by Desmos, take students experience further with conceptual and computational questions about the interactive Dynamic Figures. These book-specific figures are embedded directly in the e-book and additional assessment for the figures are found in the Guided Learn and Practice question banks.
  • LearningCurve adaptive quizzing offers individualized question sets and feedback for each student based on his or her correct and incorrect responses.

General themes of the revision include the following (a detailed list of changes is also available):

  • Rewrite portions to increase readability without reducing level of mathematical rigor. This includes increasing clarity, improving organization, and building consistency.
  • Add applications, particularly in life science and earth science to broaden the scientific fields represented in the book. In particular, there are a number of new examples and exercises in climate science, an area that is currently drawing a lot of interest in the scientific community.
  • Add conceptual and graphical insights to assist student understanding in places where pitfalls and confusion often occurs.
  • Add diversity to the Historical Perspectives and historical marginal pieces.
  • Maintain threads throughout the book by previewing topics that come up later and revisiting topics that have been presented before.
  • Expand the perspective on curve sketching--beyond just sketching a curve using calculus tools--to include analyzing given curves using calculus tools. (This is an addition of some elements of the “reform” perspective on calculus instruction.)
  • “Tighten” the presentation of the mathematics in the text, improving rigor (without increasing the overall level of formality). This includes correcting previous errors and omissions.

The authors goal for the book is that its clearly written, could be read by a calculus student and would motivate them to engage in the material and learn more. Moreover, to create a text in which exposition, graphics, and layout would work together to enhance all facets of a student’s calculus experience. They paid special attention to certain aspects of the text:

1. Clear, accessible exposition that anticipates and addresses student difficulties.
2. Layout and figures that communicate the flow of ideas.
3. Highlighted features that emphasize concepts and mathematical reasoning including Conceptual Insight, Graphical Insight, Assumptions Matter, Reminder, and Historical Perspective.
4. A rich collection of examples and exercises of graduated difficulty that teach basic skills as well as problem-solving techniques, reinforce conceptual understanding, and motivate calculus through interesting applications. Each section also contains exercises that develop additional insights and challenge students to further develop their skills.

Looking for instructor resources like Test Banks, Lecture Slides, and Clicker Questions? Request access to Achieve to explore the full suite of instructor resources.

ISBN:9781319270377

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