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Calculus: Late Transcendentals Multivariable
Third Edition| ©2015 Jon Rogawski; Colin Adams
This alternative version of Rogawski and Adams’ Calculus includes chapters 11-18 of the Third Edition, and is ideal for instructors who just want coverage of topics in multivariable calculus.
The most successful calculus book of its generation, Jon Rogawski’s Calculus offers an ideal balance of formal precision and dedicated conceptual focus, helping students build strong computational skills while continually reinforcing the relevance of calculus to their future studies and their lives. Guided by new author Colin Adams, the new edition stays true to the late Jon Rogawski’s refreshing and highly effective approach, while drawing on extensive instructor and student feedback, and Adams’ three decades as a calculus teacher and author of math books for general audiences. The Third Edition is also a fully integrated text/media package, with its own dedicated version of WebAssign Premium that boasts a robust collection of interactive learning aids.Features
New to This Edition
Colin Adams is an award-winning teacher, widely read author, and distinguished researcher. A user of Jon Rogawski’s textbook, he brings his own classroom experience to the project, as well as a well-regarded ability to make calculus more engaging and meaningful to students without sacrificing its precision and rigor.
Refined Exercises
The exercise sets were reviewed extensively by longtime users to ensure the utmost accuracy, clarity, and complete content coverage. Exercise sets were also modified to improve upon the grading by level of difficulty and to ensure even/odd pairing.
In addition, numerous new exercises have been added throughout the text, particularly where new applications are available or to enhance conceptual development.
New Examples, including
New Content Based on User and Reviewer FeedbackDetermining Which Convergence Test To Apply (new in Ch. 11, sec. 5) reviews each test and provides strategies on when to apply them.
New Illustrations
This edition includes a number of new figures that help students visualize concepts, including illustrations that explain:
Standardized Notation
Notational changes bring this edition in line with standard notation usage in mathematics and other fields that use mathematics, presenting a consistent message to students. Other notational changes make it easier for students to comprehend the concepts.
For example, in multivariable chapters, notation for vector-valued functions is now written r(t) = <x(t), y(t)> instead of c(t) = (x(t), y(t)) and the standard notation V is used for potential functions.
LearningCurve
In a game-like format, LearningCurve adaptive and formative quizzing provides an effective way to get students involved in the coursework. It offers:
- A unique learning path for each student , with quizzes shaped by each individual’s correct and incorrect answers.
ONLINE HOMEWORK OPTION
In addition to the robust online homework system in LaunchPad, instructors can take advantage of the following W. H. Freeman partnerships:WeBWorK
webwork.maa.org
W. H. Freeman offers approximately 2,500 algorithmically generated questions (with full solutions) through this free open source online homework system developed at the University of Rochester. Adopters also have access to a shared national library test bank with thousands of additional questions, including 1,500 problem sets correlated to the Third Edition.
WebAssign Premium
www.webassign.net/whfreeman
Premium for Calculus, Third Edition integrates the book’s exercises into the world’s most popular and trusted online homework system, making it easy to assign algorithmically generated homework and quizzes. WebAssign Premium also offers access to all of the book’s digital resources, with the option of including the complete e-Book.
Calculus: Late Transcendentals Multivariable
Third Edition| ©2015
Jon Rogawski; Colin Adams
Digital Options
Calculus: Late Transcendentals Multivariable
Third Edition| 2015
Jon Rogawski; Colin Adams
Table of Contents
Chapter 11: Infinite Series
11.1 Sequences
11.2 Summing an Infinite Series
11.3 Convergence of Series with Positive Terms
11.4 Absolute and Conditional Convergence
11.5 The Ratio and Root Tests and Strategies for Choosing Tests
11.6 Power Series
11.7 Taylor Polynomials
11.8 Taylor Series
Chapter Review Exercises
Chapter 12: Parametric Equations, Polar Coordinates, and Conic Sections
12.1 Parametric Equations
12.2 Arc Length and Speed
12.3 Polar Coordinates
12.4 Area and Arc Length in Polar Coordinates
12.5 Conic Sections
Chapter Review Exercises
Chapter 13: Vector Geometry
13.1 Vectors in the Plane
13.2 Three-Dimensional Space: Surfaces, Vectors, and Curves
13.3 Dot Product and the Angle Between Two Vectors
13.4 The Cross Product
13.5 Planes in 3-Space
13.6 A Survey of Quadric Surfaces
13.7 Cylindrical and Spherical Coordinates
Chapter Review Exercises
Chapter 14: Calculus of Vector-Valued Functions
14.1 Vector-Valued Functions
14.2 Calculus of Vector-Valued Functions
14.3 Arc Length and Speed
14.4 Curvature
14.5 Motion in 3-Space
14.6 Planetary Motion According to Kepler and Newton
Chapter Review Exercises
Chapter 15: Differentiation in Several Variables
15.1 Functions of Two or More Variables
15.2 Limits and Continuity in Several Variables
15.3 Partial Derivatives
15.4 Differentiability, Tangent Planes, and Linear Approximation
15.5 The Gradient and Directional Derivatives
15.6 Multivariable Calculus Chain Rules
15.7 Optimization in Several Variables
15.8 Lagrange Multipliers: Optimizing with a Constraint
Chapter Review Exercises
Chapter 16: Multiple Integration
16.1 Integration in Two Variables
16.2 Double Integrals over More General Regions
16.3 Triple Integrals
16.4 Integration in Polar, Cylindrical, and Spherical Coordinates
16.5 Applications of Multiple Integrals
16.6 Change of Variables
Chapter Review Exercises
Chapter 17: Line and Surface Integrals
17.1 Vector Fields
17.2 Line Integrals
17.3 Conservative Vector Fields
17.4 Parametrized Surfaces and Surface Integrals
17.5 Surface Integrals of Vector Fields
Chapter Review Exercises
Chapter 18: Fundamental Theorems of Vector Analysis
18.1 Green’s Theorem
18.2 Stokes’ Theorem
18.3 Divergence Theorem
Chapter Review Exercises
Appendices
A. The Language of Mathematics
B. Properties of Real Numbers
C. Induction and the Binomial Theorem
D. Additional Proofs
ANSWERS TO ODD-NUMBERED EXERCISES
REFERENCES
INDEX
Additional content can be accessed online at www.macmillanlearning.com/calculuset4e:
Additional Proofs:
L’Hôpital’s Rule
Error Bounds for Numerical
Integration
Comparison Test for Improper
Integrals
Additional Content:
Second-Order Differential
Equations
Complex Numbers
Calculus: Late Transcendentals Multivariable
Third Edition| 2015
Jon Rogawski; Colin Adams
Authors
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.
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.
Calculus: Late Transcendentals Multivariable
Third Edition| 2015
Jon Rogawski; Colin Adams
Related Titles
Calculus: Late Transcendentals Multivariable
Third Edition| 2015
Jon Rogawski; Colin Adams
Videos
Colin Adams' Calculus 3e Co-authorship Video
Colin Adams discusses how he became involved with co-authoring Calculus 3e.
Colin Adams' knot theory Video
Colin Adams describes how he began working on Knot Theory.
Colin Adams' Various Calculus Books Video
Colin Adams describes his supplemental texts and new novel, Zombies & Calculus.
Minimizing Memorization Video
Colin Adams discusses his focus on concepts and minimizing memorization in Calculus 3e.
Notation Video
Colin Adams explains important updates to the notation in Calculus 3e.
Transitioning to Homework Video
Colin Adams describes how Calculus 3e helps students transition from class to homework.
Understanding Formulas Video
Colin Adams talks about how the new edition helps students understand formulas.
Select a demo to view: