Solution of Ordinary Differential Equations by Continuous Groups

✍ Scribed by George Emanual

• Publisher: Chapman & Hall/CRC
• Year: 2000
• Tongue: English
• Leaves: 230
• Edition: 1
• Category: Library

✦ Synopsis

Completed with bookmarks and index.

The theory of continuous groups is employed to solve ordinary differential equations
(ODEs). The presentation is self-contained and presumes for background
only a rudimentary exposure to ordinary differential equations. A prior knowledge
of group theory, algebraic concepts, or the method of characteristics is not
required; when needed, these topics are developed in the text. The book is
thus intended for upper division or graduate students in applied mathematics,
engineering, or the sciences. As a book on applied mathematics, it may be
useful as a monograph. The author is an engineer, not a mathematician, and
is unaware of any university course that treats the subject matter of this book.
The principal audience is probably readers who are self-instructing themselves.
If you are in this category, be sure to examine the worked examples at the end
of the chapters in Part II.

✦ Table of Contents

Title Page
Preface
Table of Contents
I BACKGROUND
1 Introduction
2 Continuous One-Parameter Groups-I
3 Method of Characteristics
4 Continuous One-Parameter Groups-II
II ORDINARY DIFFERENTIAL EQUATIONS
5 First-Order ODEs
6 Higher-Order ODEs
7 Second-Order ODEs
III Appendices
A Bibliography and References
B The Rotation Group
C Basic Relations
D Tables
Table 2.1 Elementary One-Parameter Continuous Groups
Table 5.1. Selected First-Order ODEs Invariant Under a One-Parameter Group
Table 5.2. General Symbols, Canonical Coordinates, and ODE whose CanonicalCoordinate Form is dY/dX =g(X)
Table 5.3. Index for First-Order ODEs
Table 5.4. Catalogue of First-Order ODEs
Table 6.1. Catalogue of Second-Order ODEs
Table 7.1. Commutator and Phi for the Four Fundamental Forms of a Two-Parameter Group
Table 7.2. Canonical Forms for a Second-Order ODE Invariant Under a Two-Parameter Group (Axford, 1971)
Table 7.3. Canonical CoordinateTransformations for a Two-Parameter Group
Table 7.4. Constraints 011 a Two-ParameterGroup in its Fundamental Form
Table 7.5. Type, ODE, U[2] f, and Canonical Variables for a Two-Parameter Groupwhen U[1]f = A(x)B(y)f,y
Table 7.6. Catalogue of Second-Order ODEs Invariant Undera Two-Parameter Group
E Answers to Selected Problems
Index