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

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