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Abell M., Braselton J. — Differential Equations with Mathematica
Abell M., Braselton J. — Differential Equations with Mathematica

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Название: Differential Equations with Mathematica

Авторы: Abell M., Braselton J.

Аннотация:

Most topics covered include typical examples solved by both traditional methods, and by the computer math aid, Mathematica. The authors also use Mathematica to establish well-known algorithms for solving elementary differential equations. Practical problems for scientists and engineers are discussed, along with theoretical concepts. Many illustrations show what to type into Mathematica and just what comes out. Contains a glossary of commands.


Язык: en

Рубрика: Руководства по программному обеспечению/Системы компьютерной алгебры/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 641

Добавлена в каталог: 05.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 cosine series      535
Fourier series      532
Fourier sine series      532
Fourier trigonometric series      537
Fourier, convergence of a series      538
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 — Yolterra system      453
LRC Circuits      196 351 366 462
Maclaurin polynomial      217
Maclaurin series      217 219
Matrix identity      381
Matrix, derivative of      390
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
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 functions      237 529
Orthogonal trajectories      54 see
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      590 602
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, existence      50 97
Solution, explicit      4
Solution, fundamental set      96
Solution, general      6 97
Solution, implicit      4
Solution, of a system of differential equations      394 441
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
Total differential      91
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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