Chapter 7. Multidimensional Calculus

  1. André I. Khuri

Published Online: 26 MAR 2003

DOI: 10.1002/0471394882.ch7

Advanced Calculus with Applications in Statistics, Second Edition

Advanced Calculus with Applications in Statistics, Second Edition

How to Cite

Khuri, A. I. (2002) Multidimensional Calculus, in Advanced Calculus with Applications in Statistics, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471394882.ch7

Author Information

  1. University of Florida, Gainesville, Florida, USA

Publication History

  1. Published Online: 26 MAR 2003
  2. Published Print: 1 NOV 2002

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. David J. Balding,
  2. Peter Bloomfield,
  3. Noel A. C. Cressie,
  4. Nicholas I. Fisher,
  5. Iain M. Johnstone,
  6. J. B. Kadane,
  7. Louise M. Ryan,
  8. David W. Scott,
  9. Adrian F. M. Smith and
  10. Jozef L. Teugels

ISBN Information

Print ISBN: 9780471391043

Online ISBN: 9780471394884



  • composite function;
  • differentiation under the integral sign;
  • directional derivative;
  • gradient;
  • Hessian matrix;
  • iterated Riemann integral;
  • Lagrange multipliers;
  • maximum likelihood estimation;
  • multivariable function;
  • total derivative;
  • transformation of random vectors


This chapter extends the notions of limits, continuity, differentiation, and integration to functions of several variables. The material in Chapter 2 is needed here to understand the development of the methodology in the multidimensional case. This chapter also covers Taylor's theorem, the inverse and implicit function theorems, optimization, and the Riemann integral, all for multivariable functions. The last section gives applications useful for the study of multivariate distributions.