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| Ïîèñê ïî óêàçàòåëÿì |
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| Bredensteiner E.J. — Differential Equations |
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| Ïðåäìåòíûé óêàçàòåëü |
Adams — Bashforth — Moulton method 109 111—112
Amplitude 53
Analytic functions 86—87
Archimedes' principle 51
Bernoulli equations 6 14
Bessel functions 99—100
Boundary-value problems 5 115—120
Buoyancy problems 51—52
Characteristic equations 34—35 73
Circular frequency 53
Classifying solutions 52—53
Coefficients see “Constant coefficients” “Undetermined “Variable
Completing the square 58
Constant coefficients 30
Constant coefficients, Laplace transforms solutions 66—67
Constant coefficients, linear equations 79—83
Constant matrix 70
Convolutions 59—60
Critically damped motion 53
Damped motion 53
Decay problems 20—21
Defining properties 10—11
Denominators 58—59
derivatives 65—66 72
Differential equations see also “Linear differential equations”
Differential equations, applications 20—26
Differential equations, classifying 5—7
Differential equations, definitions 2—5
Differential equations, first-order 8—14 20—26 105—112
Differential equations, general solutions 4—5
Differential equations, notation 3
Differential equations, order 3
Differential equations, particular solutions 4
Differential equations, solutions 3—5 8—14
Differential forms 5—6
Dilution problems 23—25
Direction fields 105
Dummy index 101
Eigenfunctions 117 119—120
eigenvalue problems 117
Eigenvalues 117
Electrical circuit problems 49—51
electrical circuits 25—26
Equations see also “Differential” “Linear
Equations, Bernoulli 6 14
Equations, characteristic 34—35 73
Equations, exact 7 10—12
Equations, homogeneous 6—7 9—10 30 87—88
Equations, indicial 91
Equations, n-th order 34—35
Equations, nonhomogeneous 32 39—44 88—89
Equations, ordinary differential 2
Equations, partial differential 2—3
Equations, second-order 34 35—36
Equations, separable 7
Equilibrium position 47
Euler's method 106 108 111
exact equations 7 10—12
Falling body problems 21—22
First-order differential equations 8—14
First-order differential equations, applications 20—26
First-order differential equations, numerical methods 105—112
First-order systems 79—83 110
Forced motion 53
Fourier series 120—121
Free motion 52—53
Froebenius, method of 90—91
Functions, Bessel 99—100
Functions, gamma 98—99
Gamma functions 98—99
general solutions 4—5 32
Growth problems 20—21
Homogeneous equations 6—7 9—10 30 87—88;
Hooke's law 48—49
Identity matrix 72
Independent variables 57
Indicial equation 91
Initial-value problems 5 9 44 82 89
integral 72
Integrating factors 11—12
Inverse Laplace transforms 57—58
Isoclines 105
Kirchhoff's law 50
Laplace transforms 56—62 124—132
Laplace transforms, inverse 57—58
Laplace transforms, solutions by 65—67
Laws, Hooke's 48—49
Laws, Kirchhoff's 50—51
Laws, Newton's of cooling 21
Laws, Newton's second of motion 22
Line elements 105
Linear differential equations 6 12—14
Linear differential equations, first-order 105—112
Linear differential equations, homogeneous 30 34—37 39—44
Linear differential equations, nonhomogeneous 39—44
Linear differential equations, reduction to first-order system 79—83
| Linear differential equations, second-order 47—53 86 115—117
Linear differential equations, solutions 34—37 79—83
Linear differential equations, theory of solutions 29—32
Linear systems 67
Linearly dependent solutions 31
Linearly independent solutions 31
Matrices 70—75
Matrix addition 71
Matrix exponential 73—75
Matrix multiplication 71
Matrix solution methods 79—83
Method of Frobenius 90—91
Method of undetermined coefficients 40—42
Methods, Adams — Bashforth — Moulton 109 111—112
Methods, Euler's 106 108 111
Methods, Frobenius 90—91
Methods, modified Euler's 108
Methods, numerical for first-order equations 105—112
Methods, predictor-corrector 108
Methods, Runge — Kutta 108—109 111
Methods, undetermined coefficients 40—42
Modified Euler's method 108
Motion 52—53
Natural frequency 53
Natural length 49
Newton's law of cooling 21
Newton's Second Law of Motion 22
Nonhomogeneous equations 32 39—44 88—89
Notation 3
nth-order equations 34—36
Numerators 59
Numerical instability 107
Numerical methods 105—112
Ordinary differential equations 2
Ordinary points 87
Orthogonal trajectories 26
Oscillatory damped motion 53
Overdamped motion 53
Partial differential equation 2—3
Partial fractions 58—59
Particular solutions 4
Period 53
Phase angle 53
Power scries 86—92
Power scries method 87—88
Predictor-corrector method 108
Problems, boundary-value 5 115—120
Problems, buoyancy 51—52
Problems, decay 20—21
Problems, dilution 23—25
Problems, eigenvalue 117
Problems, electrical circuit 49—51
Problems, falling body 21—22
Problems, growth 20—21
Problems, initial-value 44 82
Problems, spring 47—49
Problems, Sturm — Liouville 117—118
Problems, temperature 21
Recurrence formula 88
Regular singular points 89—90
Runge — Kutta method 108—109 111
Scalar multiplication 71
Second-order equations 34 35—36
Second-order linear differential equations 47—53 86 115—117
separable equations 7
simple harmonic motion 53
Solutions 3—5
Solutions, classifying 52—53
Solutions, first-order differential equations 8—14
Solutions, initial-value problems 82
Solutions, Laplace transforms 65—67
Solutions, linear differential 34—37 79—83
Solutions, linear systems 67
Solutions, linearly dependent 31
Solutions, linearly independent 31
Solutions, matrix methods 79—83
Solutions, no initial conditions 82—83
Solutions, particular 4
Solutions, power scries 86—92
Solutions, theory of 29—32
Spring problems 47—49
Square matrix 70
Standard forms 5—6
Steady-state motion 53
Step sizes 107
Sturm — Liouville problems 117—118
Temperature problems 21
Transient motion 53
Translations 61—62
Undamped motion 53
Underdamped motion 53
Undetermined coefficients 40—42
Unit step function 60—61
Variable coefficients 30 86
Variation of parameters 42—44
Vectors 70
Wronskian, the 31—32
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