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| Abell M.L., Braselton J.P. — Differential equations with Mathematica |
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| Предметный указатель |
Adjoint 381
Analytic function 218
Annihilator 108 111
Autonomous equation 145
Autonomous system 441
Auxiliary equation 135
Baer equation 245
Beam 200
Bernoulli's equation 35
Bessel functions of first kind 266 546
Bessel functions of second kind 266 546
Bessel functions, zeros of 548 577
Bessel's equation 245 266 545
Bonhoeffer — van der Pol 446
Boundary, conditions 552 555
Boundary, value problem 7
Cable 290
Cauchy — Euler equation 135 272
Center 442
Characteristic equation 101 384
Characteristic, polynomial 384
Clairaut's equation 38
Classification of differential equations 2 3
Cofactor matrix 381
Complex conjugate 101
Constant coefficients 90 394
Continuous, piecewise 538
Convergence of a Fourier series 538
Convergence of a power series 216
Convolution integral 361
Cooling 71
Cosine integral 133
Critically damped 167
Damped harmonic motion 166
Decay 69
Deflection of a beam 200
Delay equation 322
Determinant 91 380
Differential equation, autonomous 145
Differential equation, Baer 245
Differential equation, Bernoulli 35
Differential equation, Bessel 245 266
Differential equation, Cauchy — Euler 135 272
Differential equation, Clairaut 38
Differential equation, delay 322
Differential equation, equidimensional 151
Differential equation, exact 21 142
Differential equation, homogeneous 14 90 101 391
Differential equation, hypergeometric 280
Differential equation, Lagrange 45
Differential equation, Laguerre 245
Differential equation, Legendre 238
Differential equation, linear 3 26 90 391
Differential equation, logistic 64
Differential equation, nonhomogeneous 90
Differential equation, nonlinear 3 210 441
Differential equation, numerical methods 583
Differential equation, ordinary 1
Differential equation, partial 2
Differential equation, Ricatti 48
Differential equation, separable 8
Differential equation, system of 391
Differential operator 108 111
Diffusion 477
Dirac delta function 371
Direction fields 60 400
Dirichlet problem 563
Disk 570
Double pendulum 524
Eigenfunction 528
Eigenvalues of a matrix 384
Eigenvalues of a Sturm — Liouville Problem 528
Eigenvalues, complex 395
Eigenvalues, real and distinct 395
Eigenvalues, repeated 401
Eigenvectors of a matrix 384
Electrical networks 196 351 462
Equidimensional equation 151
Equilibrium point 441
Error function 232
Euler's method 583 588 598
Exact differential equation 21 142
Existence theorem 50 97
Expansion of a function in a Fourier series 532
Expansion of a function in a power series 220
Expansion of a function in a series of orthogonal functions 549
Explicit solution 4
Exponential, decay 69
Exponential, growth 63
Exponential, integral 127
Exponential, order 297
First-order differential equation, linear 26
First-order differential equation, separable 8
First-order differential equation, system 391
Forced motion 180 399
Fourier, convergence of a series 538
Fourier, cosine series 535
Fourier, series 532
Fourier, sine series 532
Fourier, trigonometric series 537
Frobenius, method of 245
Fundamental matrix 394
Fundamental set of solutions 96
General solution 6 97
Geometric series 219
Growth and decay 63 69
Harmonic motion 160 166 179
Heat equation 552
Hermite polynomials 237
Homogeneous, boundary conditions 552
Homogeneous, differential equation 14 90
Homogeneous, system of equations 391 394 419
Hooke's law 160 339
Hypergeometric differential equation 280
Identity matrix 380
Imaginary error function 232
Implicit solution 4
Impulse functions 370
Indicial equation 249
Initial condition 6
Initial value problem 6
Inner product 529
Integral equation 365
Integrodifferential equation 366
Inverse Laplace transform 301
Inverse matrix 381
Kirchhoff's, Current Law 462
Kirchhoff's, Voltate Law 197 462
Lagrange equation 45 264
Laguerre equation 263
Laplace transform of derivatives 297
Laplace transform of integrals 298
Laplace transform of periodic functions 299
Laplace transform, convolution 361
Laplace transform, definition 294
Laplace transform, differentiation 335
| Laplace transform, inverse 301
Laplace transform, operational properties 299
Laplace transform, table of 296
Laplace transform, translation theorems 299
Laplace's equation 563
Legendre polynomials 93 243
Legendre's equation 238
Limit cycle 460
Linear dependence of functions 90 393
Linear differential equations, constant coefficients 90
Linear differential equations, first-order 3 26
Linear differential equations, higher order 3 90 100
Linear differential equations, homogeneous 90 391 394
Linear differential equations, nonhomogeneous 90
Linear differential equations, particular solution 108
Linear differential equations, system of 391 394
Linear independence of functions 90 393
Linear systems 394
Linearization 446
Logistic equation 64
Lotka — Volterra system 453
LRC Circuits 196 351 366 462
Maclaurin, polynomial 217
Maclaurin, series 217 219
Matrix, derivative of 390
Matrix, identity 381
Matrix, integral of 390
Matrix, inverse 382
Matrix, transpose 380
Method of separation of variables 552
Method of undetermined coefficients 186
Method of variation of parameters 117 120 139 419
Nonhomogeneous, boundary conditions 555
Nonlinear differential equation 3 210 441
Numerical methods, Euler's 583 588 598
Numerical methods, Runge — Kutta 590 602
One-dimensional, heat equation 552
One-dimensional, wave equation 559
Order of a differential equation 2
Order of a numerical method 583 590 594
Order, exponential 297
Ordinary points 225
Orthogonal see "Polynomials"
Orthogonal, functions 237 529
Orthogonal, trajectories 54
Orthogonality relation 243
Overdamped 167 171
Partial  differential equation 2 552 559 563 570
Particular solution 108
Pendulum 203 524
Phase plane 60
Piecewise continuous 538
Point, ordinary 225
Point, regular 225
Point, singular 225
Polynomials, Hermite 237
Polynomials, Legendre 93 243
Population 63 356 496
Power series 216
Power series, solution 225 245
Predator-prey 453
Quasiperiod 175
Radius of convergence 216
Recurrence relation 239 286
Reduction of order 146
Regular singular point 245
Ricatti equation 48
Runge — Kutta method 590 602
Saddle 442
Second exponential integral 127
Second-order 101
Self-adjoint 531
Separable differential equation 8
Separation of variables 552
Series of Bessel functions 549
Series, convergence 216 538
Series, Fourier 535 532 537
Series, geometric 219
Series, hypergeometric 286
Series, Maclaurin 218
Series, power 217
Series, solution 225
Series, Taylor 218
Series, trigonometric 537
simple harmonic motion 160
simple pendulum 204
Sine integral 133
Singular point 225 245
Singular solution 41
Solution of a differential equation 4
Solution of a system of differential equations 394 441
Solution, existence 50 97
Solution, explicit 4
Solution, fundamental set 96
Solution, general 6 97
Solution, implicit 4
Solution, particular 107 420
Solution, power series 225 245
Solution, singular 41
Solution, steady-state 191
Solution, transient 191
Spiral, stable 442
Spiral, unstable 442
Spring 160 166 179 339 373 489 510
Stable node 442
Stable spiral 442
Steady-state 191 555
Step function 299
Sturm — Liouville problem 528
System of differential equations 391
System of homogeneous linear 394
System of nonlinear differential equations 441
Table of frequently used elementary operational properties of Laplace transforms 299
Table of frequently used Maclaurin series 219
Table of Laplace transforms 297
Taylor, polynomial 271
Taylor, series 217
Taylor, theorem 218
Trajectories 54
Transient solution 191
Transpose of a matrix 379
Trigonometric series 538 533 536
Two-dimensional wave equation 570
Underdamped 167
Undetermined coefficients 186
Unit step function 299
Unstable node 442
Unstable spiral 442
van der Pol equation 392 445
Variation of parameters 117 120 139 419
Verhulst 64
Vibrating cable 290
Voltage 196 351 462
Volterra 454
Wave equation 290 559 570
Weight function 529
wronskian 91 393
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