Calculus

Fourth Edition

Publication Date: January 01, 2019

E-book ISBN: 9781319248567

Pages: 1150

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...

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Chapter 1: Precalculus Review

Chapter 2: Limits

Chapter 3: Differentiation

Chapter 4: Applications of the Derivative

Chapter 5: Integration

Chapter 6: Applications of the Integral

Chapter 7: Exponential and Logarithmic Functions

Chapter 8: Techniques of Integration

Chapter 9: Further Applications of the Integral

Chapter 10: Introduction to Differential Equations

Chapter 11: Infinite Series

Chapter 12: Parametric Equations, Polar Coordinates, and Conic Sections

Chapter 13: Vector Geometry

Chapter 14: Calculus of Vector-Valued Functions

Chapter 15: Differentiation in Several Variables

Chapter 16: Multiple Integration

Chapter 17: Line and Surface Integrals

Chapter 18: Fundamental Theorems of Vector Analysis

Conceptual Insights encourage students to develop a conceptual understanding of calculus by explaining important ideas clearly but informally.

Graphical Insights enhance students’ visual understanding by making the crucial connections between graphical properties and the underlying concepts.

Reminders are margin notes that link the current discussion to important concepts introduced earlier in the text to give students a quick review and make connections with related ideas.

Caution notes warn students of common pitfalls they may encounter in understanding the material. Examples work through problems to instruct students on concepts. They contain full, stepped-out solutions for each part.

Historical Perspectives are brief vignettes that place key discoveries and conceptual advances in their historical context. They give students a glimpse into some of the accomplishments of great mathematicians and an appreciation for their significance.

Assumptions Matter uses short explanations and well-chosen counterexamples to help students appreciate why hypotheses are needed in theorems.

Section Summaries summarize a section’s key points in a concise and useful way and emphasize for students what is most important in each section.

Section Exercise Sets offer a comprehensive set of exercises closely coordinated with the text. These exercises vary in difficulty from routine, to moderate, to more challenging.

Chapter Review Exercises offer a comprehensive set of exercises closely coordinated with the chapter material to provide additional problems for self-study or assignments.

ACHIEVE FOR CALCULUS

Achieve focuses on engaging students through pre-class and post-class assessment, interactive activities, and a full e-book. Achieve is a complete learning environment with easy course setup, gradebook and LMS integration.

The easy-to-use Homework Math Palette adapts its front page to the content of the problem, bringing forward the most appropriate buttons. This helps students focus on the math rather than the format.
Homework Warnings: Our propriety grading algorithm conbines our homegrown parser and the computer algebra system, SymPy. It is programed to accept every valid equivalent answer and to trigger warnings for answers entered in an incorrect format.
Targeted Feedback ensures the focus is on learning.
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.

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.

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.

Achieve is the culmination of years of development work put toward creating the most powerful online learning tool for calculusstudents. It houses all of our renowned assessments, multimedia assets, e-books, and instructor resources in a powerful new platform.

Achieve supports educators and students throughout the full range of instruction, including assets suitable for pre-class preparation, in-class active learning, and post-class study and assessment. The pairing of a powerful new platform with outstanding calculus content provides an unrivalled learning experience.

Highlights include:

A design guided by learning science research. Co-designed through extensive collaboration and testing by both students and faculty including two levels of Institutional Review Board approval for every study of Achieve
A learning path of powerful content including pre-class, in-class, and post-class activities and assessments.
A detailed gradebook with insights for just-in-time teaching and reporting on student achievement by learning objective.
Easy integration and gradebook sync with iClicker classroom engagement solutions.
Simple integration with your campus LMS and availability through Inclusive Access programs.

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Achieve is our online learning system backed by extensive development and research. Proven to increase student engagement and boost performance. Achieve offers:

Access to the ebook to download, read and virtually annotate for a completely flexible experience
Course and book-specific resources including adaptive quizzing (Learning Curve) to personalize the experience for students
A grade book, assignable assessments with targeted feedback, insights and reporting, instructor resources - all with seamless integration options.

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