Differential Equations: An Introduction to Modern Methods and Applications, 2nd Edition

INDEX

A

Abel’s theorem, 235–237

Absolute value (of a complex number), 587

Acoustic waveguides, 210

Action integral, 304

Adaptive method, 105

Addition, of matrices, 543

Algebraic multiplicity, 576

Almost linear systems, 486–495

damped pendulum, 492–495

effect of small perturbations on, 487–488

linear approximations to nonlinear systems, 488–492

stability (instability) properties of, 492

Ambient temperature, 2

Amplitude:

critical, 86

of motion, 255

Amplitude modulation, 281

Analytical approaches, 43

Angular velocity, 395

Antithetic variates, 122

Approximations:

linear, 488–492

numerical, 27–36, 99–105

successive, 448

Argument (complex numbers), 588

Asymptotically stable limit cycle, 197

Asymptotically stable nodes, 162

Asymptotically stable solutions, 10, 83, 115

Asymptotic stability, 478–480

global, 495

of limit cycle, 519

region of, 483

Augmented matrix, 552

Autonomous equations, 77–87

Autonomous systems, 476–477

defined, 191

dynamical, 216

nonlinear, 191–196

of two first order linear differential equations, 145–146

Auxiliary equations, see Characteristic equations

B

Backsubstitution, method of, 554

Basin of attraction, 483

Beat, 281, 282

Bernoulli, Daniel, 89, 90

Bernoulli, Jakob, 66, 376

Bernoulli, Johann, 66

Bernoulli equations, 76, 119

Bessel equations (Bessel functions), 225

BIBO stable system, see Bounded-input bounded-output stable system

Bifurcation, 526

Bifurcation diagram, 90–91

Bifurcation point(s), 90, 507–508

Black, Fischer, 121n.15

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