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Index Index

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