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
2×2, 188
3×3, 189
n×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,
autonomous, 88
Bernoulli, 61
Clairaut, 71
differential form, 65
Euler, 277
exact, 65
first-order,
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,
order,
order n,
ordinary,
partial,
particular solution, 10
Riccati, 70, 651
second-order, 11, 68
separable, 32
singular solution, 35
solution,
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