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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

Hermitian, Paragraph Section Section

orthogonal, Paragraph

Pauli, Paragraph Paragraph

symmetric, Paragraph

unitary, Paragraph Section Section

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

spherical harmonics, Section

Sturm–Liouville theory, Section

unimodular, Paragraphs

vector space

definition, Definition

examples, Paragraph

wave equation, Paragraphs