© 2020

An Illustrative Guide to Multivariable and Vector Calculus


Table of contents

  1. Front Matter
    Pages i-xvi
  2. Stanley J. Miklavcic
    Pages 1-47
  3. Stanley J. Miklavcic
    Pages 49-123
  4. Stanley J. Miklavcic
    Pages 125-175
  5. Stanley J. Miklavcic
    Pages 177-222
  6. Stanley J. Miklavcic
    Pages 223-300
  7. Back Matter
    Pages 301-309

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.


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Authors and affiliations

  1. 1.University of South Australia (Mawson Lakes Campus)AdelaideAustralia

About the authors

Stanley J. Miklavcic is a Professor of Mathematics at the University of South Australia. He was awarded a BSc Hons in Applied Mathematics and the University Medal by the University of New South Wales and holds a PhD from the Australian National University. His research interests include the application of mathematics and modelling in biology, physics and chemistry. A one-time recipient of a Queen Elizabeth Research Fellowship, Stanley has held academic positions in both Sweden and Australia and has published over 150 papers. Stanley is a Fellow of the Australian Mathematical Society and Member of both the Australasian Colloid and Interface Society and the Australian Society of Plant Scientists.

Bibliographic information

  • Book Title An Illustrative Guide to Multivariable and Vector Calculus
  • Authors Stanley J. Miklavcic
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-33458-1
  • Softcover ISBN 978-3-030-33461-1
  • eBook ISBN 978-3-030-33459-8
  • Edition Number 1
  • Number of Pages XVI, 309
  • Number of Illustrations 101 b/w illustrations, 183 illustrations in colour
  • Topics Calculus
  • Buy this book on publisher's site


“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)