# The Ordinary Differential Equations Project

## IndexIndex

Abel’s Theorem
basis
standard basis
beats
bifurcation
bifurcation value
diagram
pitch fork
bifurcation value
carrying capacity, Item
Convolution Theorem
coordiantes
change of
coordinates
Coulomb’s Law
differential equation
autonomous
exact
first-order linear
one-parameter family
order
separable
solution
Dirac delta function
direction field
discontinuity
jump discontinuity
driving frequency
Duffing’s equation
eigenvalue
dominant
eigenvector
envelope
equilibrium solution
center
linear system
nodal sink
nodal source
node
sink
source
spiral sink
spiral source
stable
stable line
systems of differential equations
unstable
unstable plane
Euler’s method
error bound
improved
step size
Existence and Uniqueness Theorem
exponential growth
frequency
function
exponentially bounded
gamma function
Heaviside function
piecewise continuous
step function
gain
gamma function
general solution
generalized function
half difference
harmonic oscillator
critically-damped, Item
damped
over-damped
under-damped
harvesting
Heaviside function
Hooke’s Law
Hopf bifurcation
impulse
unit impulse function
impulse forcing
impulse response
initial condition
initial value problem
integral curves
integral equation
integrating factor
IVP
Kirchhoff’s Second Law
Laplace transform
definition
inverse Laplace transform
linear map
invertible
linear operator
linear system
particular solution
straight-line solution
linear transformation
linearly dependent
linearly independent
Lipschitz condition
logistic equation
logistic population model
Lorenz equations
Lyapunov function
matrix
characteristic polynomial
coefficient matrix
determinant
identity
invertible matrix
nonsingular matrix
trace
transpose
uppper triangular
mean frequency
Method of Undetermined Coefficients
Method of Variation of Parameters
mixing problems
natural frequency
negative definite function
negative semidefinite function
Newton’s law of cooling
nonautonomous system
nullcline
Ohm’s Law
parameter
parameter plane
particular solution
period of a function
periodic function
phase angle
phase line
phase plane
Picard iteration
positive definite function
positive semidefinite function
Principle of Superposition
RC circuit
reduction of order
resonance
retirement model
Ricatti equation
Runge-Kutta method
order 4
second-order
satiation constant
second-order differential equation
sinusoidal forcing
SIR model
slope field
solution curves
stable line of solutions
step function
system
autonomous
decoupled
direction field
equilibrium solution
first-order linear
homogeneous first-order linear
partially coupled
planar
Taylor’s theorem
trace-determinant plane
transfer function
transient term
uniform continuity
unstable line
vector field
vectors
linear combination
linearly dependent
linearly independent
Wronskian