Calculus: Multivariable, 2nd Edition

Book Cover

Calculus: Multivariable, 2nd Edition

By Brian E. Blank, Steven G. Krantz

Calculus: Multivariable provides high-quality problem sets, study aids, and algebra and trigonometry refreshers to help students be successful in calculus. Calculus brings together time-tested methods and innovative thinking, using meaningful examples, credible applications, and incisive technology to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. This course makes the language of mathematics accessible, understandable and enjoyable, while maintaining high standards for mathematical rigor.

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Students learn course concepts using the complete online eTextbook, flashcards, crossword puzzles, practice questions, videos, and animations. Organized by learning objective, students can filter for relevant learning resources based on what they need to study most and print any section of the eTextbook.

ORION Adaptive Practice (when available)

Every student has a different starting point, and adaptive practice provides endless opportunities for practice to effectively prepare for class or quizzes and exams. 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. Students begin with a quick, chapter-level diagnostic to determine their initial level of understanding, and they can use the dashboard and quick reports to see what topics they know and don’t know.


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Brian E Blank is an associate professor of mathematics at Washington University in St. Louis. He received his Ph.D. in 1980 at Cornell University, with Anthony Knapp as advisor. His 20th century work involved harmonic analysis.

Steven G Krantz is an American scholar, mathematician, and writer. He has authored more than 235 research papers and more than 125 books. Additionally, Krantz has edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.

Chapter 9. Vectors
Chapter 10. Vector-Valued Functions
Chapter 11. Functions of Several Variables
Chapter 12. Multiple Integrals
Chapter 13. Vector Calculus

A. Table of Integrals
B. Formulas from Calculus: Single Variable
Answers to Selected Exercises