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# IndexIndex

absolute convergence
acceleration
Airy's equation
algebraic multiplicity
almost linear
amplitude
analytic functions
angular frequency
antiderivative
antidifferentiate
associated homogeneous equation
asymptotically stable
asymptotically stable limit cycle
atan
atan2
attractor
augmented matrix
autonomous
autonomous equation
autonomous system
beating
Bendixson-Dulac Theorem
Bernoulli equation
Bessel function of second kind
Bessel function of the first kind
Bessel's equation
boundary conditions for a PDE
boundary value problem
Burger's equation
catenary
Cauchy-Euler equation
center
cgs units
chaotic systems
characteristic coordinates
characteristic equation
Chebyshev's equation of order 1
Chebyshev's equation of order $p$
closed curves
closed trajectory
coefficients
cofactor
cofactor expansion
column vector
commute, Item
complementary solution
complete eigenvalue
complex conjugate
complex number
complex roots
conservative equation
conservative vector field
constant coefficient
constant coefficients
constant of motion
convergence of a power series
convergent power series
converges absolutely
convolution
corresponding eigenfunction
cosine series
critical point
critically damped
d'Alembert solution to the wave equation
damped
damped motion, Item
damped nonlinear pendulum equation
defect
defective eigenvalue
deficient matrix
delta function
dependent variable
determinant
diagonal matrix
matrix exponential of
diagonalization
differential equation
Dirac delta function
direction field
Dirichlet boundary conditions
Dirichlet problem
displacement vector
distance
divergent power series
dot product
Duffing equation
dynamic damping
eigenfunction
eigenfunction decomposition
eigenvalue
eigenvalue of a boundary value problem
eigenvector
eigenvector decomposition
ellipses (vector field)
elliptic PDE
endpoint problem
envelope curves
equilibrium
equilibrium solution
Euler's equation
Euler's formula
Euler's method
Euler-Bernoulli equation
even function
even periodic extension
exact equation
existence and uniqueness
exponential growth model
exponential of a matrix
exponential order
extend periodically
first order differential equation
first order linear equation
first order linear system of ODEs
first order method
first shifting property
forced motion, Item
systems
Fourier series
fourth order method
Fredholm alternative
simple case
Sturm-Liouville problems
free motion, Item
free variable
Frobenius method
Frobenius-type solution
fundamental frequency
fundamental matrix
fundamental matrix solution
general solution
generalized eigenvectors
generalized function
Genius software
geometric multiplicity
geometric series
Gibbs phenomenon
half period
Hamiltonian
harmonic conjugate
harmonic function
harvesting
Heat equation
Heaviside function
Hermite's equation of order 2
Hermite's equation of order $n$
homogeneous
homogeneous equation
homogeneous linear equation
homogeneous side conditions
homogeneous system
Hooke's law
hyperbolic PDE
identity matrix
imaginary part
implicit solution
Improved Euler's method
impulse response
inconsistent system
indefinite integral
independent variable
indicial equation
inhomogeneous
initial condition
initial conditions for a PDE
inner product
inner product of functions
integral equation
integrate
integrating factor
integrating factor method
for systems
inverse Laplace transform
invertible matrix
IODE software
isolated critical point
Jacobian matrix
la vie
Laplace equation
Laplace transform
Laplacian
Laplacian in polar coordinates
Leibniz notation
limit cycle
linear combination
linear equation
linear first order system
linear operator
linear PDE
linearity of the Laplace transform
linearization
linearly dependent
linearly independent
for vector valued functions
logistic equation
with harvesting
Lorenz attractor
Lorenz system
Lotka-Volterra
mass matrix
mathematical model
mathematical solution
matrix
matrix exponential
matrix inverse
matrix valued function
Maxwell's equations
Mechanical vibrations
Method of Frobenius
method of partial fractions
Mixed boundary conditions
mks units
multiplication of complex numbers
multiplicity
multiplicity of an eigenvalue
natural (angular) frequency
natural frequency
natural mode of oscillation
Neumann boundary conditions
Newton's law of cooling
Newton's second law
nilpotent
nonhomogeneous
nonlinear equation
normal mode of oscillation
odd function
odd periodic extension
ODE
one-dimensional heat equation
one-dimensional wave equation
operator
order
ordinary differential equation
Ordinary differential equations, Item
ordinary point
orthogonal
functions
vectors
with respect to a weight
orthogonality
overdamped
overtones
parabolic PDE
parallelogram
partial differential equation
Partial differential equations, Item
partial sum
particular solution
PDE
period
periodic
periodic extension
periodic orbit
phase diagram
phase plane portrait
phase portrait
phase shift
Picard's theorem
piecewise continuous
piecewise smooth
Poincarè section
Poincarè-Bendixson Theorem
Poisson kernel
potential function
power series
practical resonance
practical resonance amplitude
practical resonance frequency
predator-prey
product of matrices
projection
proper rational function
pseudo-frequency
pure resonance
ratio test for series
real part
real world problem
recurrence relation
reduced row echelon form
reduction of order method
regular singular point
regular Sturm-Liouville problem
reindexing the series
relaxation oscillation
repeated roots
resonance
RLC circuit
Robin boundary conditions
row vector
Runge-Kutta method
sawtooth
scalar
scalar multiplication
second order differential equation
second order linear differential equation
second order method
second shifting property
semistable critical point
separable
separation of variables
shifting property
side conditions for a PDE
Sierpinski triangle
simple harmonic motion
simply connected region
sine series
singular matrix
singular point
singular solution
sink
slope field
solution
solution curve
source
spectrum
spiral sink
spiral source
square wave
stable center
stable critical point
stable node
stiff problem, Item
stiffness matrix
strange attractor
Sturm-Liouville problem
regular
superposition
symmetric matrix
system of differential equations
Taylor series
tedious
thermal conductivity
three mass system
three-point beam bending
timbre
total derivative
trajectory
transfer function
transient solution
Transport equation
transpose
trigonometric series
undamped
undamped motion, Item
systems
underdamped
undetermined coefficients
for second order systems
for systems
unforced motion, Item
unit step function
unstable critical point
unstable node
upper triangular matrix
Van der Pol oscillator
variation of parameters
for systems
vector
vector field
vector valued function
velocity
Volterra integral equation
wave equation
Wave equation in 2 dimensions
weight function