Index

A

algebraic multiplicity amplitude–phase form angular frequency

asymptotically stable augmented matrix autonomous

B

basis

beating

C

carrying capacity center characteristic polynomial characteristic values charcteristic polynomial coefficient function

coefficient matrix, [1] cofactor expansion conjugate constant-coefficient, [1] continuously stirred tank reactor Cramer's Rule critically damped

D

damping coefficient defective delta function

dependent variable, [1] determinant doubling time

E

eigenspace eigenvalue

eigenvector equilibrium equilibrium solution

F

first-order linear ODE first-order ODE forcing function, [1]

free column free oscillator fundamental matrix

G

gain Gaussian elimination

general solution, [1] geometric multiplicity

H

half-life

Heaviside function homogeneous, [1]

I

identity matrix imaginary part impulse impulse response, [1] inconsistent

independent variable, [1] initial condition, [1] initial-value problem integrating factor inverse invertible

J

Jacobian matrix, [1]

L

Laplace transform leading nonzero linear

linear combination linear ODE system linear operator logistic equation

M

matrix

method of undetermined coefficients modulus

N

natural frequency

node

O

overdamped

P

parameter particular solution phase line diagram, [1] phase plane

pivot column polar form pole, [1] pseudoresonance

R

real part relaxation time

resonance row elimination RREF

S

saddle scalar scalar multiplication second-order IVP second-order ODE separable ODE simple harmonic motion

singular solution spiral spring constant square stable steady state superposition

T

transfer function, [1]

U

underdamped oscillator

unit step function unstable

V

variation of parameters

vector

W

window function