Index Index
addition and subtraction of complex numbers
exponential form, Paragraphs
rectangular form, Paragraphs
amplitude
definition, Definition
analytic continuation, Definition
example, Paragraph
ansatz
definition, Definition
homogeneous, linear ODE with constant coefficients, Paragraphs
inhomogeneous, linear ODE with constant coefficients, Paragraphs Paragraphs Paragraphs
power series solutions for ODEs, Paragraph
Argand diagram, Paragraphs
boundary value problem, Definition
characteristic equation
for linear ODEs with constant coefficients, Definition
commutator
definition, Definition
commuting operators
definition, Definition
complete basis
definition, Definition
complete set, Paragraphs
completeness relation
definition, Definition
complex conjugate, Definition
complex number
definition, Definition
exponential form, Definition
rectangular form, Definition Paragraph
complex plane, Paragraphs
continuous variable
definition, Definition
degeneracy
in matrix eigenvalues, Definition Paragraphs
in ODEs, Paragraphs
in the quadratic formula, Definition
diagonal matrix, Definition
diagonalization
definition, Paragraph
differential equation
definition, Definition
degree of, Definition
general solution, Definition
homogeneous, Definition
inhomogeneous, Definition
order of, Definition
ordinary, Definition
partial, Definition
particular solution, Definition
solution of, Definition
differential operator
linear, Notation
diffusion equation, Paragraphs
Dirac delta function (alternatively, distribution)
definition, Definition
discrete variable
definition, Definition
eigenspace
for matrices, Definition
eigenvalue
for matrices, Definition
eigenvalue/eigenvector equation
definition, Definition
eigenvector
for matrices, Definition
informal definition, Paragraphs
Euler’s formula, Definition
exponential function
for a complex variable, Definition
first-order ODEs
differential form, Definition
separable form, Definition
standard form, Definition
forcing function
in an ODE, Paragraphs
Gram-Schmidt orthogonalization, Paragraphs
Heaviside function
definition, Definition
Helmholtz’s equation, Paragraphs
Hermitian adjoint
definition, Definition
imaginary axis, Paragraphs
imaginary number, Notation
inhomogeneous
in an ODE, Paragraphs
initial value problem, Definition
inner product
definition, Definition
Fourier series, Definition
Laplace’s equation, Paragraphs
length
of abstract vectors, Paragraph
linear ODEs with constant coefficients
solution method, homogeneous, Paragraphs
solution method, inhomogeneous, Paragraphs
linear operator
definition, Definition
derivatives as, Paragraphs
Hermitian operators as, Paragraphs
matrices as, Paragraphs
magnitude
of a complex number, Definition
matrices, types of
anti-symmetric, Definition
anti_Hermitian, Definition
Hermitian, Definition Section Section
orthogonal, Paragraph
symmetric, Definition
multiplication and division of complex numbers
exponential form, Paragraphs
multiplication of complex numbers
rectangular form, Paragraphs
multiplicity
in matrix eigenvalues, Definition
negative vector, Item
norm
of a complex number, Definition
of abstract vectors, Paragraph
normalized vector
definition, Definition
null vector
definition, Item
orthogonal
for abstract vectors, Paragraph
for functions, Definition
outer product
definition, Definition
partial differential equations
diffusion equation, Paragraphs
Helmholtz’s equation, Paragraphs
Klein-Gordon equation, Paragraphs
Laplace’s equation, Paragraphs
Poisson’s equation, Paragraphs
Schrödinger’s equation, Paragraphs
wave equation, Paragraphs
perpendicular
for abstract vectors, Paragraph
phase
definition, Definition
piecewise
definition, Definition
Poisson’s equation, Paragraphs
projection operator
definition, Definition
pure imaginary number, Notation
pure real number, Notation
real axis, Paragraphs
real number, Notation
scalar identity
in a vector space, Item
Schrödinger’s equation, Paragraphs
separation constants, Paragraphs
separation of variables in PDEs
separation constants, Paragraphs
source
in an ODE, Paragraphs
span, Paragraphs
spectral theorem, Paragraphs
spherical harmonics, Section
standard basis, Paragraphs Paragraphs
step function
definition, Definition
Sturm-Liouville theory
introduction, Paragraph
Sturm–Liouville theory, Section
theta function
definition, Definition
unimodular, Paragraphs
