# Book:G.E.H. Reuter/Elementary Differential Equations & Operators

## Contents

## G.E.H. Reuter: *Elementary Differential Equations & Operators*

Published $1958$, **Routledge & Kegan Paul**.

### Subject Matter

### Contents

- Preface

- CHAPTER 1: LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS
- $\S$ 1 THE FIRST ORDER EQUATION
- 1.1
*Introduction* - 1.2
*The integrating factor* - 1.3
*The form of the general solution*

- 1.1

- $\S$ 1 THE FIRST ORDER EQUATION

- $\S$ 2 THE SECOND ORDER EQUATION
- 2.1
*The reduced equation* - 2.2
*The general equation* - 2.3
*Particular solution: polynomial $f \left({x}\right)$* - 2.4
*Particular solution: exponential $f \left({x}\right)$* - 2.5
*Particular solution: trigonometric $f \left({x}\right)$* - 2.6
*Particular solution: some further cases* - 2.7
*Arbitrary constants and initial conditions* - 2.8
*Recapitulation*

- 2.1

- $\S$ 2 THE SECOND ORDER EQUATION

- $\S$ 3 EQUATIONS OF HIGHER ORDER AND SYSTEMS OF FIRST ORDER EQUATIONS
- 3.1
*The $n$ order equation* - 3.2
*First order systems* - 3.3
*Arbitrary constants and initial conditions*

- 3.1

- $\S$ 3 EQUATIONS OF HIGHER ORDER AND SYSTEMS OF FIRST ORDER EQUATIONS

- PROBLEMS FOR CHAPTER I

- CHAPTER II: THE OPERATIONAL METHOD
- $\S$ 1 PRELIMINARY DISCUSSION OF THE METHOD
- 1.1
*The operator $Q$* - l.2 Formal calculations with $Q$
- 1.3
*Operators* - 1.4
*The inverse of an operator* - 1.5
*Inverse of a product* - 1.6
*Partial fractions for inverses*

- 1.1

- $\S$ 1 PRELIMINARY DISCUSSION OF THE METHOD

- $\S$ 2 PRACTICAL INSTRUCTIONS FOR USING THE METHOD
- 2.1
*The symbol $p$* - 2.2
*Procedure for solving $n$th order equations* - 2.3
*Some remarks on partial fractions* - 2.4
*Further examples* - 2.5
*Simultaneous equations* - 2.6
*Justification of the method* - 2.7
*The general solution on an $n$th order equation*

- 2.1

- $\S$ 2 PRACTICAL INSTRUCTIONS FOR USING THE METHOD

- PROBLEMS FOR CHAPTER II

- SOLUTIONS TO PROBLEMS

- INDEX