Solution of Ordinary Differential Equations by Continuous Groups

Solution of Ordinary Differential Equations by Continuous Groups

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Written by an engineer and sharply focused on practical matters, this text explores the application of Lie groups to solving ordinary differential equations (ODEs). Although the mathematical proofs and derivations in are de-emphasized in favor of problem solving, the author retains the conceptual basis of continuous groups and relates the theory to problems in engineering and the sciences. The author has developed a number of new techniques that are published here for the first time, including the important and useful enlargement procedure. The author also introduces a new way of organizing tables reminiscent of that used for integral tables. These new methods and the unique organizational scheme allow a significant increase in the number of ODEs amenable to group-theory solution. Solution of Ordinary Differential Equations by Continuous Groups offers a self-contained treatment that presumes only a rudimentary exposure to ordinary differential equations. Replete with fully worked examples, it is the ideal self-study vehicle for upper division and graduate students and professionals in applied mathematics, engineering, and the more

Product details

  • Hardback | 232 pages
  • 163.8 x 242.3 x 18.8mm | 562.34g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 4 black & white illustrations, 12 black & white tables
  • 1584882433
  • 9781584882435

Table of contents

BACKGROUND Introduction Continuous One-Parameter Group-I Group Concept Infinitesimal Transformation Global Group Equations Problems Method of Characteristics Theory Examples Problems Continuous One-Parameter Group-II Invariance The Once-Extended Group Higher-Order Extended Groups Problems ORDINARY DIFFERENTIAL EQUATIONS First-Order ODEs Invariance Under a One-Paramter Group Canonical Coordinates Special Procedures Compendium Examples Problems Higher-Order ODEs Invariant Equations Finding the Groups System of First-Order ODEs Compendium Examples Problems Second-Order ODEs Classification of Two-Parameter Groups Invariance and Canonical Coordinates Compendium Examples Problems APPENDICES Bibilography and References The Rotation Group Basic Relations Tables' Answers to Selected Problemsshow more