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

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

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

### 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
$\S 2$ 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 $\text {I}$

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
$\S 2$ 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
Problems for Chapter $\text {II}$
Solutions to Problems
INdex

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