Differential equations

Title page 1.PRELIMINARY IDEAS 1 Ordinary and partial equations; order and degree 2 Solutions 3 Hyperbolic functions 2. THE FORMATION OF DIFFERENTIAL EQUATIONS 4 An inverse problem 5 Elimination by differentiation and combination 6 Isolation of constants 7 Elimination by determinants 8 The differential equation of a family of curves 3. DIFFERENTIAL EQUATIONS OF FIRST ORDER 9 Introduction 10 Separable equations 11 Particular solutions and particular values 12 Dynamics 13 Trial and error 14 Chemical reactions; first and second order processes 15 Pressure on a spherical surface; atmospheric and oceanic pressure 16 Steady-state heat flow 17 Integrable combinations 18 Homogeneous equations 19 Linear equatlons 20 Substitutions (a) Bernoulli's equation (b) Equations reducible to homogeneous (c) Substitution suggested by the form of equation 21 The equivalence of solutions 22 Chemical solutions 23 Electric circuits 24 Rope wound on a cylinder 25 Curves determined from geometric properties 26 Orthogonal trajectories 4. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 27 The linear equation 28 The differential operator 29 The linear equation with R=0 30 Rectilinear motion (a) Attractive force proportional to displacement; resistance negligible (b) Repulsive force proportional to displacement; resistance negligible (c) Attractive force proportional to displacement; resistance proportional to velocity 31 The linear equation with R≠0; simplest case 32 Deflection of beams 33 The linear equation with R≠0 34 Undetermined coefficients 35 Variation of parameters 36 Forced vibrations 37 Electric circuits 5. SOME SPECIAL HIGHER ORDER EQUATIONS 38 Equations reducible to linear with constant coefficients 39 Dependent variable absent 40 Independent variable absent 41 The general linear equation of second order 42 The inverse square law 43 The suspended cable 6. SIMULTANEOUS EQUATIONS 44 System of two first order equations 45 System of two linear equations 46 Motion of a projectile 47 The roots of unity 48 Cyclic systems of differential equations 49 A special case of Einstein's equations 7. SERIES SOLUTIONS 50 Power series 51 The series of Frobenius 52 Bessel functions of zero or positive integral order ANSWERS INDEX