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2540 results in Computational Science

Page 59 of 127

  • 8 - MuPAD

  • from Practice Set B - Math, Graphics, and Programming
  • Brian R. Hunt, University of Maryland, College Park, Ronald L. Lipsman, University of Maryland, College Park, Jonathan M. Rosenberg, University of Maryland, College Park
  • Book:
    A Guide to MATLAB®
    Published online:
    28 May 2018
    Print publication:
    21 August 2014, pp 111-120

  • Summary

    In this chapter, we discuss the MuPAD language, which underlies MATLAB's Symbolic Math Toolbox. We believe that the most practical uses of MuPAD are to be found in calculus, linear algebra, number theory, combinatorics, and differential equations. We shall show how to use MuPAD directly to deal with issues from some of those topics. We shall comment more fully below on why you might want to do so. For additional basic information on MuPAD (beyond what you will find in this book), we recommend the MuPAD Tutorial, which you can find at the mathworks.com web site. (MathWorks is the software company that produces MATLAB and MuPAD.)

    As we mentioned at the end of Chapter 4, all of the commands in the Symbolic Math Toolbox rely on a software package called MuPAD. Most of the time you may not need to know this, but for sophisticated symbolic calculations it helps to work directly in MuPAD, without going through MATLAB as an intermediary. A rather dramatic example of this is described in the authors' book Differential Equations with MATLAB, 3rd ed., Wiley, New York, 2012, where in the topic of series solutions of ordinary differential equations, it is far clumsier to work through MATLAB than it is to invoke MuPAD symbolic commands directly.

  • Preface

  • Peter E. Hydon, University of Surrey
  • Book:
    Difference Equations by Differential Equation Methods
    Published online:
    05 August 2014
    Print publication:
    07 August 2014, pp xi-xiv

  • Summary

    Difference equations are prevalent in mathematics, occurring in areas as disparate as number theory, control theory and integrable systems theory. They arise as mathematical models of discrete processes, as interesting dynamical systems, and as finite difference approximations to differential equations. Finite difference methods exploit the fact that differential calculus is a limit of the calculus of finite differences. It is natural to take this observation a step further and ask whether differential and difference equations share any common features. In particular, can they be solved by the same (or similar) methods?

    Just over twenty years ago, a leading numerical analyst summarized the state of the art as follows: problems involving difference equations are an order of magnitude harder than their counterparts for differential equations. There were two major exceptions to this general rule. Linear ordinary difference equations behave similarly to their continuous counterparts. (Indeed, most of the best-known texts on difference equations deal mainly with linear and linearizable problems.) Discrete integrable systems are nonlinear, but have some underlying linear structures; they have much in common with continuous integrable systems, together with some interesting extra features.

Python for Scientists
  • John M. Stewart
  • Published online:
    05 August 2014
    Print publication:
    10 July 2014
  • Python is a free, open source, easy-to-use software tool that offers a significant alternative to proprietary packages such as MATLAB® and Mathematica®. This book covers everything the working scientist needs to know to start using Python effectively. The author explains scientific Python from scratch, showing how easy it is to implement and test non-trivial mathematical algorithms and guiding the reader through the many freely available add-on modules. A range of examples, relevant to many different fields, illustrate the program's capabilities. In particular, readers are shown how to use pre-existing legacy code (usually in Fortran77) within the Python environment, thus avoiding the need to master the original code. Instead of exercises the book contains useful snippets of tested code which the reader can adapt to handle problems in their own field, allowing students and researchers with little computer expertise to get up and running as soon as possible.

Difference Equations by Differential Equation Methods
  • Peter E. Hydon
  • Published online:
    05 August 2014
    Print publication:
    07 August 2014
  • Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.

Page 59 of 127