Skip to main content

Multivariate Calculus and Geometry

  • Textbook
  • © 2014
  • Latest edition


  • Places the differential and integral calculus of several variables in its natural geometric environment
  • Presents interesting non-trivial applications of the differential calculus
  • Shows how the differential calculus and classical geometry evolved into differential geometry
  • Includes supplementary material:

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

This is a preview of subscription content, log in via an institution to check access.

Access this book

eBook USD 16.99 USD 29.99
Discount applied Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 37.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

About this book

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook not only follows this programme, but additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations.

In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions.

Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Similar content being viewed by others


Table of contents (18 chapters)


“The book is very useful for those who wish to learn the theory properly. … the book is very clearly written–the theory is nicely presented with important topics being well explained and illustrated with examples. … Each chapter begins with an outline of its content, and ends with suitably constructed exercises, with solutions given at the end of the book. … it is also an excellent reference text on multivariate calculus and the basics in differential geometry.” (Peter Shiu, The Mathematical Gazette, Vol. 100 (547), 2016)

“A textbook aimed at undergraduate mathematics students. … The text is accompanied with a large number of figures and explanatory text. Each chapter is concluded by a collection of exercises of both routine and more theoretical nature. The textbook is written in a readable way, especially it is one of rare cases of multivariate calculus texts consequently linked to the geometric roots of the subject.” (Vladimír Janiš, zbMATH 1312.26001, 2015)

Authors and Affiliations

  • School of Mathematical Sciences, University College Dublin, Dublin, Ireland

    Seán Dineen

About the author

Sean Dineen taught for many years at University College Dublin where he is now an emeritus professor. He is the author of many research articles and monographs and of a number of successful and popular textbooks including: Analysis; A Gateway to Understanding Mathematics (World Scientific, 2012) and Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula (AMS, Second Edition, 2013).

Bibliographic Information

  • Book Title: Multivariate Calculus and Geometry

  • Authors: Seán Dineen

  • Series Title: Springer Undergraduate Mathematics Series

  • DOI:

  • Publisher: Springer London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag London Ltd., part of Springer Nature 2014

  • Softcover ISBN: 978-1-4471-6418-0Published: 29 September 2014

  • eBook ISBN: 978-1-4471-6419-7Published: 18 September 2014

  • Series ISSN: 1615-2085

  • Series E-ISSN: 2197-4144

  • Edition Number: 3

  • Number of Pages: XIV, 257

  • Number of Illustrations: 103 b/w illustrations

  • Topics: Mathematics, general

Publish with us