Overview
- Offers an in-depth visual approach to multivariable and vector calculus
- Complements existing textbooks on the subject by being concise and portable
- Includes over one hundred carefully drawn figures that illustrate the material with clarity and ingenuity
- Includes supplementary material: sn.pub/extras
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Table of contents (5 chapters)
Keywords
- Multivariable calculus textbook
- Calculus 3 textbook
- Vector calculus textbook
- A practical guide to multivariable calculus
- Multivariable calculus for engineers
- Multivariable calculus visualization
- Vector calculus visualization
- Multivariable vector calculus
- Implicit function theorem
- Multiple integrals calculus
- Separations of variables
- Lagrange multipliers
- Vector fields
- Calc 3
- Calc 3 help
- Calc 3 visualization
- Chain rule for second derivatives
- Least-square approximation
About this book
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion.
Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques.An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
Reviews
“The book is self-contained. … It is suitable as a textbook for students having completed courses in single variable calculus and linear algebra. Alternatively, the book can be used as a reference text to complement the textbooks in advanced calculus, giving the students a different visual perspective.” (Mihail Voicu, zbMATH 1441.26002, 2020)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Illustrative Guide to Multivariable and Vector Calculus
Authors: Stanley J. Miklavcic
DOI: https://doi.org/10.1007/978-3-030-33459-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-33458-1Published: 18 February 2020
Softcover ISBN: 978-3-030-33461-1Published: 18 February 2021
eBook ISBN: 978-3-030-33459-8Published: 17 February 2020
Edition Number: 1
Number of Pages: XVI, 309
Number of Illustrations: 101 b/w illustrations, 183 illustrations in colour
Topics: Calculus