فهرست مطالب
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
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
