Springer Optimization and Its Applications

Fractional and Multivariable Calculus

Model Building and Optimization Problems

Authors: Mathai, A.M., Haubold, Hans

  • Broadens understanding of research fields through the framework of fractional and multivariate calculus
  • Reinforces basic principles of fractional calculus 
  • Maximizes readers insight into mathematical models and applications 
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eBook $54.99
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  • ISBN 978-3-319-59993-9
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-3-319-59992-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models.  Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations.

The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions.  Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three  discusses deterministic/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined.  Chapter four covers non-deterministic/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss–Markov theorem, quadratic forms, and generalized inverses of matrices are covered. Pathway, symmetric, and asymmetric models are covered in chapter six, the concepts are illustrated with graphs.


About the authors

A.M. Mathai is Emeritus Professor of Mathematics and Statistics, McGill University, Canada, and Director of the Centre for Mathematical and Statistical Sciences, India. He has published over 300 research papers and 25 books on topics in mathematics, statistics, physics, astrophysics, chemistry, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, served as President of the Mathematical Society of India, and a Member of the International Statistical Institute. 

H.J. Haubold is Professor of Theoretical Astrophysics. He has published over 200 research papers and 10 books in physics, astrophysics, and the development of basic space science worldwide. The United Nations Basic Space Science Initiative (UN BSSI) for the worldwide development of astronomy, physics, and mathematics was implemented in 1991 through the joint work of H.J Haubold and A.M. Mathai.

Table of contents (6 chapters)

  • Essentials of Fractional Calculus

    Mathai, A. M. (et al.)

    Pages 1-37

  • Multivariable Calculus

    Mathai, A. M. (et al.)

    Pages 39-88

  • Deterministic Models and Optimization

    Mathai, A. M. (et al.)

    Pages 89-106

  • Non-deterministic Models and Optimization

    Mathai, A. M. (et al.)

    Pages 107-181

  • Optimal Regression Designs

    Mathai, A. M. (et al.)

    Pages 183-208

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-319-59993-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA
  • ISBN 978-3-319-59992-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fractional and Multivariable Calculus
Book Subtitle
Model Building and Optimization Problems
Authors
Series Title
Springer Optimization and Its Applications
Series Volume
122
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-59993-9
DOI
10.1007/978-3-319-59993-9
Hardcover ISBN
978-3-319-59992-2
Series ISSN
1931-6828
Edition Number
1
Number of Pages
XIII, 234
Number of Illustrations and Tables
7 b/w illustrations
Topics