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  2. Green's identities - Wikipedia

    en.wikipedia.org/wiki/Green's_identities

    This identity is derived from the divergence theorem applied to the vector field F = ψ ∇φ while using an extension of the product rule that ∇ ⋅ (ψ X) = ∇ψ ⋅X + ψ ∇⋅X: Let φ and ψ be scalar functions defined on some region U ⊂ R d, and suppose that φ is twice continuously differentiable, and ψ is once continuously differentiable.

  3. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  4. File:ZX-calculus red and green identity rules.svg - Wikipedia

    en.wikipedia.org/wiki/File:ZX-calculus_red_and...

    You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.

  5. Green's function - Wikipedia

    en.wikipedia.org/wiki/Green's_function

    Green's functions are also useful tools in solving wave equations and diffusion equations. In quantum mechanics, Green's function of the Hamiltonian is a key concept with important links to the concept of density of states. The Green's function as used in physics is usually defined with the opposite sign, instead.

  6. Green's function for the three-variable Laplace equation

    en.wikipedia.org/wiki/Green's_function_for_the...

    Using the Green's function for the three-variable Laplace operator, one can integrate the Poisson equation in order to determine the potential function. Green's functions can be expanded in terms of the basis elements (harmonic functions) which are determined using the separable coordinate systems for the linear partial differential equation ...

  7. Triple product - Wikipedia

    en.wikipedia.org/wiki/Triple_product

    In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.

  8. Lagrange's identity (boundary value problem) - Wikipedia

    en.wikipedia.org/wiki/Lagrange's_identity...

    In the study of ordinary differential equations and their associated boundary value problems in mathematics, Lagrange's identity, named after Joseph Louis Lagrange, gives the boundary terms arising from integration by parts of a self-adjoint linear differential operator. Lagrange's identity is fundamental in Sturm–Liouville theory.

  9. Green's matrix - Wikipedia

    en.wikipedia.org/wiki/Green's_matrix

    The concept is named after George Green. For instance, consider x ′ = A ( t ) x + g ( t ) {\displaystyle x'=A(t)x+g(t)\,} where x {\displaystyle x\,} is a vector and A ( t ) {\displaystyle A(t)\,} is an n × n {\displaystyle n\times n\,} matrix function of t {\displaystyle t\,} , which is continuous for t ∈ I , a ≤ t ≤ b {\displaystyle ...