Index -- A -- adjoint nonlinear operators -- alternating-direction method -- approximation requirement -- Arzelà-Ascoli theorem -- B -- Banach space -- Bessel inequality -- Bochner transform -- boundary of the domain -- boundary-value conditions -- boundary-value conditions of the first -- boundary-value conditions of the third -- boundary-value problem -- Bubnov-Galerkin method -- C -- Cauchy problem -- Cauchy-Bunyakovskii inequality -- Cauchy-Kovalevskii theorem -- characteristic function -- Chebyshef polynomial -- Chernov formula -- Chézy coefficient -- class of functions -- closed linear operator -- coercivity condition -- collocation method -- compact set -- completeness equation -- convergence in respect to energy -- convergence theorem -- convolution transform -- Coriolis parameter -- Courant method -- Cranck-Nicholson scheme -- cylindrical coordinates -- cylindrical function -- D -- d'Alembert operator -- -- differential operator -- diffusion length -- dipole coefficient -- direct methods -- Dirichlet boundary condition -- Dirichlet integral -- Dirichlet problem -- discrete Laplace transform -- domain of definition of the equation -- Dubois-Raymond lemma -- E -- eigen subspace -- eigenfunction -- eigenvalue problems -- energetic space -- energy method -- energy space -- equation of state -- equations of continuity -- Euclidean distance -- Euclidean space -- Euler equation -- Euler equation of motion -- F -- factorisation method -- finite-difference methods -- first Green formula -- Fourier coefficient -- Fourier map -- Fourier series -- Fourier transform -- Fourier-Bessel integral -- Fréchet derivative -- Fréchet differential -- Fredholm equation -- Fredholm integral equation -- functional of the energy method -- G -- Galerkin approximation -- Galerkin method -- Galerkin-Petrov method -- Gateaux derivative.

Gauss hypergeometrical series -- generalized derivatives -- generalized Minkovskii inequality -- generalized solutions -- generating function -- Gilbert transform -- Green formula -- Green function -- H -- Haar system -- Hankel function -- Hankel image -- Hankel transform -- Hardy inequality -- heat conductivity equation -- Helmholtz equation -- Hermite polynomial -- Hermitian weakly polar kernel -- Hilbert spaces -- Hilbert transform -- Hilbert-Schmidt orthogonalization -- Hilbert-Schmidt theorem -- Hölder function -- Hölder inequality -- Hölder space -- hyperbolicity condition -- hyperplane method -- I -- ill-posed problem -- integral Green formula -- internal point of the set -- internal spherical functions -- isometric space -- isomorphous space -- J -- jump of the normal derivative -- K -- Kantorovich method -- Kellog theorem -- kernel -- kinetic coagulation equation -- Kontorovich-Lebedev transform -- Kummer function -- L -- Laguerre polynomial -- Laguerre transform -- Laplace equation -- Laplace operator -- Laplace-Beltrami operator -- law of oscillation -- Lebesgue integral -- Lebesgue space -- Legendre polynomial -- Legendre transform -- linear functional -- linear normalised space -- linear operator -- linear sets -- Lipschitz inequality -- Lipschits condition -- logarithmic potential -- logarithmic simple layer potential -- longitudinal-transverse sweep -- Lyapunov surface -- M -- MacDonald function -- Mathieu equation -- Mathieu function -- Maxwell equations -- Mehler-Fock transform -- Meller-Fock transform -- Mellin transform -- method of arbitrary lines -- method of eigenfunctions -- method of Gauss exclusion -- method of integral identities -- method of least squares -- method of Marchuk's integral identity -- method of stationarisation -- method of two-cyclic multi-component splitting -- method of weak approximation.

Meyer transform -- minimising sequence -- mixed problem -- moments method -- multiplicity -- N -- Navier-Stokes equation -- neighbourhood of the set -- net method -- Neumann condition -- Neumann problem -- Newton iteration process -- Newton potential -- nonhomogeneous evolution equation -- normalized eigenfunction -- O -- one-dimensional wave equation -- oriented surface -- orthogonal basis -- orthogonal system -- orthonormalized system -- Ostrogradskii-Gauss formula -- P -- Parseval equality -- Parseval identity -- Parseval-Steklov equality -- periodicity conditions -- piecewise smooth surface -- Poincaré inequality -- Poincaré-Perron method -- point spectrum -- Poisson equation -- Poisson integral -- potential of the vector field -- predictor-corrector method -- problem of a string -- projection method -- projection-grid method -- Q -- quadrature method -- R -- reflexive real Banach space -- Reiss-Fischer theorem -- retardation time -- Riesz theorem -- Ritz method -- Rodrig formula -- S -- Schmidt equation -- Schwarz method -- second Green formula -- second Hankel function -- simple eigenvalue -- simple layer potential -- Sobolev classes -- Sobolev space -- special functions -- spherical function -- splitting method -- -- stability -- standing wave -- steepest descent method -- Stricker coefficient -- Struve function -- Sturm-Liouville operator -- super-harmonic function -- support -- sweep method -- sweeping method -- symmetric hyperbolic systems -- symmetric kernel -- T -- The minimisation condition J(uN) leads to a system -- three-dimensional wave equation -- transfer equation -- Trefftz method -- Tricomi equation -- Trotter formula -- two-cyclic method of weak approximation -- two-dimensional wave equation -- V -- variational formulation of problems -- variational method -- Volterra equation -- W -- wavelet integral transform.

wavelet transform -- weakly polar kernel -- Weber transform -- Weierstrass theorem -- Weierstrasse theorem -- weight function -- Y -- Young inequality.