Damped nonlinear vibrations, 542

Damped pendulum oscillations, 548

Damping constant, 302

Death rate, 75

Decay constant, 36

Defect (of eigenvalue), 439

Defective eigenvalue, 439

Dependence (linear), 214, 232, 270, 282, 378

Dependence on parameters, 91

Dependent variable missing, 68

Derivative (of matrix function), 375

Determinant, 188, 189, 190

• $2\times 2$, 188

• $3\times 3$, 189

• $n\times n$, 190

• and invertibility, 196, 672

• and matrix product, 196, 672

• and elementary row operations, 192, 669

• by cofactor expansion, 190

• by elimination method, 194

• by permutations, 669

• coefficient, 188

• row and column properties, 192

• Vandermonde, 204, 289

Diagonal (principal), 162

Diagonal matrix, 174

Diagonalizable matrix, 349, 352

Diagonalization, criterion for, 349

Differential equation, 1

• autonomous, 88

• Bernoulli, 61

• Clairaut, 71

• differential form, 65

• Euler, 277

• exact, 65

• first-order, 7

• general solution, 10, 11, 35, 271, 272, 286, 379, 382, 386

• homogeneous, 59, 279

• implicit solution, 35

• linear, 47, 50, 265, 279

• logistic, 21, 44, 76, 80

• matrix, 469

• normal form, 7

• order, 6

• order n, 6

• ordinary, 7

• partial, 7

• particular solution, 10

• Riccati, 70, 651

• second-order, 11, 68

• separable, 32

• singular solution, 35

• solution, 6

Differential equations and determinism, 313

Differential form, 65

Differential operator, 293

Differentiation of transforms, 589

Dimension and rank, 248

Dimension of a vector space, 237

Direction field, 18, 505

Direction of flow, 413

Displacement vector, 425

Distance between points, 252

Distinct real eigenvalues, 387, 399, 402

Dog problem, 71

Doomsday versus extinction, 81, 536

Dot product, 250

Drag coefficient, 96

Drug elimination, 37

Duplication (undetermined coefficients), 319

Dynamic damper, 434

Dynamic phase plane graphics, 421