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Index Index

analytic continuation, Definition
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
boundary value problem, Definition
characteristic equation
for linear ODEs with constant coefficients, Definition
complex conjugate, Paragraph
degeneracy
in matrix eigenvalues, Paragraph
in ODEs, Paragraphs
in the quadratic formula, Definition
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
Euler's formula, Definition
first-order ODEs
differential form, Definition
separable form, Definition
standard form, Definition
forcing function
in an ODE, Paragraphs
Helmholtz's equation, Paragraphs
inhomogeneous
in an ODE, Paragraphs
initial value problem, Definition
inner product
definition, Definition
Klein-Gordon equation, Paragraphs
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
matrices, types of
anti-symmetric, Paragraph
anti_Hermitian, Paragraph
orthogonal, Paragraph
symmetric, Paragraph
negative vector, Item
norm
of a complex number, Paragraph
of abstract vectors, Paragraph
null vector
definition, Item
orthogonal
for abstract vectors, Paragraph
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
Poisson's equation, Paragraphs
quadratic formula
definition, Definition
proof, Paragraph
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
Sturm–Liouville theory, Section
unimodular, Paragraphs
vector space
definition, Definition
examples, Paragraph
wave equation, Paragraphs