Introduction to Nonlinear Analysis - ISBN:0070149178

Introduction to Nonlinear Analysis

Date: 22 May 2011, 17:49

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This book is intended to provide the engineer and scientist with
information about some of the basic techniques for finding solutions for
nonlinear differential equations having a single independent variable.
Physical systems of many types and with very real practical interest
tend increasingly to require the use of nonlinear equations in their mathe-
matical description, in place of the much simpler linear equations which
have often sufficed in the past. Unfortunately, nonlinear equations gen-
erally cannot be solved exactly in terms of known tabulated mathematical
functions. The investigator usually must be satisfied with an approxi-
mate solution, and often several methods of approach must be used to
gain adequate information. Methods which can be used for attacking
a variety of problems are described here.
Most of the material presented in this book has been given for several
years in a course offered to graduate students in electrical engineering
at Yale University. Emphasis in this course has been on the use of
mathematical techniques as a tool for solving engineering problems.
There has been relatively little time devoted to the niceties of the mathe-
matics as such. This viewpoint is evident in the present volume.
Students enrolled in the course have had backgrounds in electrical
circuits and mechanical vibrations and a degree of familiarity with linear
differential equations. Their special field of interest has often been that
of control systems. A knowledge of these general areas is assumed on
the part of the reader of this volume.
Nonlinear problems can be approached in either of two very different
ways. One approach is based on the use of a minimum of physical
equipment, making use only of pencil, paper, a slide rule, and perhaps a
desk calculator. The degree of complexity of problems which can be
successfully handled in a reasonable time with such facilities is admittedly
not very great. A second approach is based on the use of what may be
exceedingly complicated computing machinery of either the analog or
the digital variety. Such machinery allows much more information to
be dealt with and makes feasible the consideration of problems of com-
plexity far greater than can be handled in the first way. The efficient
use of computing machinery is a topic too large to be considered in the
present discussion. Only techniques useful with the modest facilities
available to almost everyone are considered here.

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