Abel's formula, 277, 289

Acceleration, 11

• constant, 12

Addition of matrices, 164

• associative law, 171

• commutative law, 171

• distributive law, 171

Addition of vectors, 212, 222

• parallelogram law, 212, 223

• triangle law, 212

Adjoint matrix, 199, 675

Air resistance, 20, 94

• proportional to square of velocity, 97

• proportional to velocity, 20, 95, 460

Airy equation, 625, 650

Airy function, 625

Algebra of inverse matrices, 178

Algebraic multiplicity, 354

Alligator population, 82

Almost linear system, 516

• stability, 519

Amplification factor, 330

Amplitude, 305

Analytic function, 606

Apollo (satellite orbit), 462

Approximate logistic solution, 112

Argument (of complex number), 298

Arnold, David, 28

Artin, Emil, (1898–1962), 644

Associated eigenvector, 339

Associated homogeneous equation, 266, 279, 377

Asymptotic stability, 508

Augmented coefficient matrix, 148

Automobile:

• simplified model, 312

• two-axle, 434

• vibrations, 331, 336

Autonomous differential equation, 88

• critical point, 88

• equilibrium solution, 88

• stable critical point, 89

• unstable critical point, 89

Autonomous system, 503

• linearized, 516

Auxiliary equation, see Characteristic equation

Average error, 80