Page 399 - Schaum's Outline of Differential Equations

INDEX •

Adams-Bashforth-Moulton method, 177 Completing the square, method of, 224
for systems, 196, 207 Constant coefficients, 73, 83, 89, 94, 254
Addition of matrices, 131 Constant matrix, 131
Amplitude, 118 Convolution, 233
Analytic functions, 262 Cooling problems, 50
Applications: Critically damped motion, 117
to buoyancy problems, 116
to cooling problems, 50
to dilution problems, 52 Damped motion, 117
to electrical circuits, 52, 115 Decay problems, 50
to falling-body problems, 51 Derivative:
of first-order equations, 50 of a Laplace transform, 211
to growth and decay problems, 50 of a matrix, 132
to orthogonal trajectories, 53 Difference, 325
of second-order equations, 114 Difference equations, 9, 325
to spring problems, 114 Differential equation, 1
to temperature problems, 50 Bernoulli, 42
Archimedes principle, 116 with boundary conditions, 2, 309
exact, 15, 31
homogeneous, 15, 21, 73 (See also Homogeneous
Bernoulli equation, 14, 42 linear differential equations)
Bessel functions, 295 with initial conditions, 2, 110
Bessel's equation, of order/), 296 linear, 14, 42, 73 (See also Linear differential
of order zero, 299 equations)
Boundary conditions, 2, 309 order of, 1
Boundary-value problems: ordinary, 1
definition, 2, 309 partial, 1, 304
Sturm-Liouville problems, 310 separable, 15, 21
Boyle's law, 10 solution of (see Solutions of ordinary differential
Buoyancy problems, 116 equations)
systems of (see Systems of differential equations)
Differential form, 14
Cayley-Hamilton theorem, 133 Dilution problems, 52
Characteristic equation: Direction field, 157
for a linear differential equation, 83, 89
of a matrix, 133
A(
Characteristic value (see Eigenvalue) e , 140, 254
Charles' law, 12 Eigenfunctions, 307, 310, 318
Chebyshev's differential equation, 290 Eigenvalues:
Chebyshev's polynomials, 291 for a boundary-value problem, 307, 310
Circular frequency, 118 of a matrix, 133
Complementary solution, 74 for a Sturm-Liouville problem, 310

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