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

## Contents

## 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

- Necessary and sufficient conditions that the equation

- Appendix B
- An equation with no
*special*integrals

- An equation with no

- 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