The object of this book is to provide in a compact form an
account of the methods of integrating explicitly the
commoner types of ordinary differential equation, and in
particular those equations that arise from problems in
geometry and applied mathematics. It takes the existence
of solutions for granted; the reader who desires to look into
the theoretical background of the methods here outlined
will find what he seeks in my larger treatise Ordinary
Differential Equations (Longmans, Green & Co., Ltd., 1927).
With this qualification, it will be found to contain all the
material needed by students of mathematics in our
Universities who do not specialize in differential equations,
as well as by students of mathematical physics and,
technology.
As one of the first things a beginner has to learn is to
identify the type to which a given equation belongs, the
examples for solution have not been printed after the
sections to which they refer, but have been collected at the
end of the book. When the contents of the first chapter
have been mastered, the reader may test his skill by
attacking examples selected at random from Nos. 1 to 122,
and similarly for the later chapters. At the same time, the
examples occur roughly in the order of the table of contents,
so that working material is always available as reading
progresses.
In conclusion, I wish to record my thanks to the General
Editors for the compliment paid me in inviting me to
contribute this book to their series of University
Mathematical Texts, and for their encouragement and help during
its growth and passage through the press.