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

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## G.E.H. Reuter:

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

Published $\text {1958}$, **Routledge & Kegan Paul**.

### Subject Matter

### Contents

- Preface

- CHAPTER $\text {I}$: 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 $\text {I}$

- CHAPTER $\text {II}$: 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 of an $n$th order equation*

- 2.1

- $\S 2$ Practical Instructions for Using the Method

- Problems for Chapter $\text {II}$

- Solutions to Problems

- INdex

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- 1958: G.E.H. Reuter:
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