Introduction to Numerical Methods in Differential Equations

  • Mark H. Holmes
Part of the Texts in Applied Mathematics book series (TAM, volume 52)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 83-126
  3. Pages 127-154
  4. Pages 181-222
  5. Back Matter
    Pages 223-239

About this book

Introduction

This is a textbook for upper division undergraduates and beginning graduate students. Its objective is that students learn to derive, test and analyze numerical methods for solving differential equations, and this includes both ordinary and partial differential equations. In this sense the book is constructive rather than theoretical, with the intention that the students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. An essential component of this is the exercises, which develop both the analytical and computational aspects of the material. The importance of the subject of the book is that most laws of physics involve differential equations, as do the modern theories on financial assets. Moreover many computer animation methods are now based on physics based rules and are heavily invested in differential equations. Consequently numerical methods for differential equations are important for multiple areas.

The author currently teaches at Rensselaer Polytechnic Institute and is an expert in his field. He has previously published a book with Springer, Introduction to Perturbation Methods.

Keywords

Boundary value problem MATLAB arithmetic differential equation partial differential equation

Editors and affiliations

  • Mark H. Holmes
    • 1
  1. 1.Academic Science of the Material Science and EngineeringRensselaer Polytechnic InstituteTroy

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-68121-4
  • Copyright Information Springer Science+Business Media, LLC 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-30891-3
  • Online ISBN 978-0-387-68121-4
  • Series Print ISSN 0939-2475
  • About this book