Book:H.T.H. Piaggio/An Elementary Treatise on Differential Equations and their Applications/Revised Edition

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H.T.H. Piaggio: An Elementary Treatise on Differential Equations and their Applications (Revised and Enlarged Edition)

Published $1952$, Bell.


Subject Matter


Contents

Preface (February, 1920)
Preface to the Revised and Enlarged Edition (May, 1928)
Preface to the Revised Edition (May, 1952)
Historical Introduction
Chapter I. Introduction and Definitions. Elimination. Graphical Representation.
Chapter II. Equations of the First Order and First Degree
Chapter III. Linear Equations with Constant Coefficients
Chapter IV. Simple Partial Differential Equations
Chapter V. Equations of the First Order, but Not of the First Degree
Chapter VI. Singular Solutions
Chapter VII. Miscellaneous Methods for Equations of the Second and Higher Order
Chapter VIII. Numerical Approximations to the Solution of Differential Equations
Chapter IX. Solution in Series. Method of Frobenius
Chapter X. Existence Theorems of Picard, Cauchy, and Frobenius
Chapter XI. Ordinary Differential Equations with Three Variables and the Corresponding Curves and Surfaces
Chapter XII. Partial Differential Equations of the First Order. Particular Methods
Chapter XIII. Partial Differential Equations of the First Order. General Methods.
Chapter XIV. Partial Differential Equations of the Second and Higher Orders
Chapter XV. Miscellaneous Methods


Appendix A
Necessary and sufficient conditions that the equation
$M dx + N dy = 0$
should be exact
Appendix B
An equation with no special integrals
Appendix C
The equation found by Jacobi's method of Art. $140$ is always integrable
Appendix D
Suggestions for further reading


Miscellaneous Examples of the Whole Book
Answers to the Examples
Note on Limiting Solutions
Index


Further Editions