Methods of applied mathematics
Normed linear spaces and Banach spaces. Basic properties of inner-products. Best approximation and orthogonal projections. Compact operators on a Banach space. Boundary value problems. Dierential calculus in Banach spaces and the calculus of variations.
Подобные документы
Examination of unlimited closed convex subsets of Banach space X, having the same recessive cone, and metric spaces, which they form with the Hausdorff metric. Receiving an analog of the theorem of approximation of convex compacts by normal polyhedrons.
статья, добавлен 12.05.2018Normed linear spaces. Contraction mapping theorem. Applications to differential and integral equations. Linear transformations. Product spaces and Fubini's theorem. Projection and self-adjoint operators. Gram-Schmidt orthonormalization. Fourier analysis.
курс лекций, добавлен 03.07.2013Thin and sparse metric spaces as asymptotic counterparts of discrete and very close to discrete metric spaces respectively. Classify thin metric spaces up to coarse equivalence. The types of sparse spaces and construct the spaces of distinct types.
статья, добавлен 19.02.2016Solving Linear Systems with the Inverse. Transposes and Symmetric Matrices. General Linear Systems. The Fundamental Matrix Subspaces. Minimization of Quadratic Functions. Computations in Orthogonal Bases. Orthogonal Polynomials and Least Squares.
учебное пособие, добавлен 25.11.2013Tiling of the limit space under the action of a (self-similar) subgroup. Self-similar groups and their limit spaces. Subgroup tilings of limit spaces. Tilings of limit spaces of abelian and nilpotent groups. Functional analysis to nilpotent Lie groups.
статья, добавлен 27.06.2016Description of combinatorial DG-Hopf color cooperadic models for configuration spaces of points in the first quarter and in the N-gon. The proof version of the formality theorem of Kontsevich to the two subspaces in the vector space and for the morphism.
курсовая работа, добавлен 27.08.2016The definition of real and complex vector spaces. The calculation of the reference type. Rules of addition and multiplication of scalars. The concept of subset. The direct sum of two subspaces. The calculation of the projection of the vector on the area.
презентация, добавлен 13.04.2016A generalization of the classical theorem of T. Kato on similarity for sequences of projections in Hilbert spaces to the case of unconditional Schauder decompositions. Refinement of the theorem of V.N. Vizitei on the stability of Schauder decompositions.
статья, добавлен 30.10.2016The emergence of noncommutative geometry, its relationship with the corresponding selected algebra function. The establishment of the anti-equivalence between the category of spaces and the corresponding category of algebras of functions on such spaces.
дипломная работа, добавлен 30.07.2016Sums, floors and recurrences. Finite and infinite calculus. Hypergeometric functions and transformations. Special, exponential generating functions. Euler’s summation formula. Domino theory and change. Partial hypergeometric sums. Stirling numbers.
учебное пособие, добавлен 25.11.2013The manual contains definitions, formulas, theorems of the differential calculus of functions of one variable. Derivative and its geometrical and physical meaning. Applying differential to approximate calculations. Extremum of function, the quotient rule.
учебное пособие, добавлен 11.10.2014Measure theory, discrete time martingales and discrete time option pricing. Continuous time martingales. Stochastic integrals, calculus and differential equations. Option pricing in continuous time. Random measures, stochastic calculus (characteristics).
книга, добавлен 13.01.2013An optimal boundary control problem associated to the linear parabolic equation. The characteristic feature of this equation, skew-symmetric. A unique solution to the original optimal boundary control problem, singular character of the original matrix.
статья, добавлен 30.10.2016Characterization of symmetric linear functionals as the simplest polynomials. The proof of the theory that every symmetric continuous linear functional on the complex space L (0,1) can be represented as the Lebesgue integral, multiplied by a constant.
статья, добавлен 25.03.2016The study of optimal control problems for linear parabolic equations with unbounded coefficients in the main part of elliptic operator. The peculiarities of this type of equations. Setting of the optimal control problem and its preliminary analysis.
статья, добавлен 23.06.2016Combinatorial description. Teichmuller curves. Recurrence relation. Asymptotics of numbers of branched coverings of a torus, volumes of moduli spaces of holomorphic differentials. The character of the infinite wedge representation. Cylinder decomposition.
контрольная работа, добавлен 26.08.2016Approximations in Scientic Computation, сomputer Arithmetic, mathematical Software. Linear Systems, solving Linear Systems, Iterative Methods for Linear Systems. Linear Least Squares, eigenvalues and Singular Values, Nonlinear Equations, optimization.
учебное пособие, добавлен 25.11.2013The theory of inverse problems for differential equations as fields of applied mathematics. In article attention that when training in the inverse problems for differential equations at students scientific and cognitive potential develops is paid.
статья, добавлен 29.03.2021Generalization old result of Bowman system. Study of homomorphisms between topological Clifford semigroups. Ditopological unosemigroup in the mathematics. The main class of compact topological Clifford semigroups. The theory of partial symmetries.
статья, добавлен 25.03.2016The textbook includes topics of discrete mathematics. Relations: binary relations, pictorial representatives of relations, inverse relation, functional relation. Mathematical logic: propositions and compound statements, basic laws of logical operations.
учебное пособие, добавлен 11.10.2014The article is devoted to the study of the place of plot mathematical problems in the course mathematics of the primary school of Ukraine; determination of results in teaching problem solving; clarification of the essence of the problem-solving process.
статья, добавлен 16.09.2022The algorithm of the basic components of a linear analysis. Work on nonlinear PCA, or NLPCA, autoassociative's neural networks, principal curves and manifolds, kernel the combination's of these approaches. The problem areas that require research.
статья, добавлен 08.02.2013Teaching students of mathematical fields of training to inverse problems. Implementation of the scientific, educational potential of teaching university students inverse problems for differential equations. Computational methods of mathematical physics.
статья, добавлен 01.04.2021Role of Euler`s number in differential and integral calculus, in algebra. Consideration of a new limit for the number e and giving its rigorous proof using the apparatus of mathematical analysis. Combinatorial interpretation is given for Euler’s number.
статья, добавлен 28.08.2020Using methods of discrete mathematics in the field of virtual isolation and its application in the scientific theory of numbers, groups, combinatorics and graph theory. Specifics arithmetic methods data comparisons. Construction of a matrix atom.
книга, добавлен 08.03.2014