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

Subject Matter

 * Differential Equations

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