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

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

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

Subject Matter

• Differential Equations

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

Next

Cited by

• 1968: Peter D. Robinson: Fourier and Laplace Transforms

Source work progress

• 1958: G.E.H. Reuter: Elementary Differential Equations & Operators ... (previous) ... (next): Chapter $1$: Linear Differential Equations with Constant Coefficients: Problems for Chapter $1$: $10$