Table of contents

  1. Front Matter
    Pages i-xiv
  2. Seán Dineen
    Pages 13-23
  3. Seán Dineen
    Pages 25-34
  4. Seán Dineen
    Pages 35-45
  5. Seán Dineen
    Pages 47-53
  6. Seán Dineen
    Pages 55-67
  7. Seán Dineen
    Pages 69-81
  8. Seán Dineen
    Pages 83-92
  9. Seán Dineen
    Pages 93-102
  10. Seán Dineen
    Pages 103-120
  11. Seán Dineen
    Pages 121-134
  12. Seán Dineen
    Pages 135-147
  13. Seán Dineen
    Pages 149-159
  14. Seán Dineen
    Pages 161-178
  15. Seán Dineen
    Pages 179-191
  16. Seán Dineen
    Pages 193-205
  17. Seán Dineen
    Pages 207-215
  18. Seán Dineen
    Pages 217-227
  19. Back Matter
    Pages 229-257

About this book


Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It 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.


Curvature and Torsion of Curves Double and Triple Integrals Frenet-Serret Equations Gaussian Curvature Geodesic Curvature Lagrange Multipliers Line Integrals Stokes Theorem Surface Integrals The Hessian The Weingarten Mapping

Authors and affiliations

  • Seán Dineen
    • 1
  1. 1.School of Mathematical SciencesUniversity College DublinDublinIreland

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London 2014
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-6418-0
  • Online ISBN 978-1-4471-6419-7
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site