ProofWiki:Books/G.E.H. Reuter/Elementary Differential Equations & Operators

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

Published 1958, Routledge & Kegan Paul.

Subject Matter

• Differential Equations

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