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An Illustrative Guide to Multivariable and Vector Calculus Hardcover – Import, 18 February 2020

4.7 4.7 out of 5 stars 33 ratings

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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.

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Review

“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)

From the Back Cover

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.

Product details

  • Publisher ‏ : ‎ Springer Nature Switzerland AG; 1st ed. 2020 edition (18 February 2020)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 309 pages
  • ISBN-10 ‏ : ‎ 3030334589
  • ISBN-13 ‏ : ‎ 978-3030334581
  • Item Weight ‏ : ‎ 771 g
  • Dimensions ‏ : ‎ 15.88 x 2.54 x 24.13 cm
  • Customer Reviews:
    4.7 4.7 out of 5 stars 33 ratings

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Stanley J. Miklavcic
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4.7 out of 5 stars
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  • Ron Toolsie
    4.0 out of 5 stars Not for the casual reader
    Reviewed in the United States on 22 November 2023
    Verified Purchase
    There are quite a few books on multivariable calculus. This one is pitched at a higher level and in places seems quite abstract, making it less useful for the first time student of this field. But like most Springer math texts, this is probably at the advanced undergraduate/graduate level. Mathematicians I am sure will appreciate the rigor of this book, but physics/enginnering students less so.

    Out of all of the MV Calculus books I have, my preference is 'Vector Calculus' by Susan Colley. In spite of its title it is much more than vector calculus, and indeed is a full MV calculus text that is extremely understandable with numerous worked examples.
  • DrRolandBr
    4.0 out of 5 stars Great fun to read !
    Reviewed in Germany on 10 December 2024
    Verified Purchase
    The hardbound edition is of excellent quality, the whole book convinces with a cleancut structure.
    I wish I had this book during my university courses, instead of the bone-dry text we were forced to toil through.

    Unfortunately, no solutions are given for the exercises. Yet, solved practising problems are strewn throughout the text.
  • AMB
    2.0 out of 5 stars Not for synaesthetes
    Reviewed in the United States on 4 April 2021
    Verified Purchase
    Too much color coding. This is why I got turned off with math since middle school.

    Also not enough interesting illustrations. The author needs to think about the connotations of the word illustrative.