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

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

Published $1958$, Routledge & Kegan Paul.

### 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
$\S$ 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
$\S$ 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
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
$\S$ 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
PROBLEMS FOR CHAPTER II
SOLUTIONS TO PROBLEMS
INDEX

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