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
Using 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 08.03.2014The optimal method of teaching trigonometric equations in the high school mathematics course based on the curriculum. The place and meaning of trigonometric equations and inequalities in the school mathematics course, features of their solution.
статья, добавлен 07.09.2023Linear Principal Components. A linear model formulation. The Principal Curve and Surface models. Theory for principal curves and surfaces. Algorithmic details. Estimation of curves and surfaces. Gold assay pairs. Generalized linear principal components.
дипломная работа, добавлен 08.02.2013Applications of the mathematics of harmony as a new interdisciplinary direction of modern science. Algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions.
статья, добавлен 24.06.2016System of a quasidifferential equation with measures on the semiaxis. Linear differential operators generated by differential expressions. Asymptotics of a fundamental solution system for a quasidifferential equation with measures on the semiaxis.
статья, добавлен 25.03.2016Prime and composite numbers. The fundamental theorem of arithmetic states. Sample factorizations. Review of elementary number theory. Some essential algorithms. RSA public-key cryptosystem. Finding squares through products. Large prime variations.
статья, добавлен 15.09.2012- 32. Algorithms to determine solvability of linear integro-differential equations with analytic functions
Further, we found sufficient conditions on linear Volterra integro-differential equations of the third kind to be correct in analytical functions which generalize the well-known fact of correctness of a Volterra integral equation of the second kind.
статья, добавлен 12.08.2020 The basics of cryptography and its levels of reliability. Secret key cryptosystem and symmetric ciphers, message authentication codes. Fundamentals of discrete mathematics, homomorphisms and isomorphisms. Modular arithmetic and function Euler's Totient.
учебное пособие, добавлен 19.03.2014Properties of Probability Distributions. Conditional Distributions and Expectation. Characteristic Functions, Moments and Cumulants. Parametric Families of Distributions. Distribution Theory for Functions of Random Variables, Approximation of Integrals.
учебное пособие, добавлен 25.11.2013Finding common solutions of linear differential equations of the fourth order, the coefficients of which satisfy the system of three differential equations of the first order. The problem of conformal mapping of polygons, whose sides are arcs of circles.
статья, добавлен 04.02.2017Arithmetic operations and properties of decimals, proportion and percents. Fundamental concepts of algebra, functions and graphs. The fundamental operations with complex numbers. Limits of function values, one-sided limits, infinitesimal functions.
учебное пособие, добавлен 11.10.2014Separating the foundations of mathematics from philosophy. Difference between the theory of formal systems theory and evidence. Classical first order predicate logic. Elementary and full analysis. Existing proof theory. Infinitely long expressions.
статья, добавлен 09.09.2012Mathematics as a fundamental science. The place in its structure of differential equations is one of the most harmonious ways of knowing the universe. Study of the algorithm for constructing compartmental (SIR) models, based on differential equations.
статья, добавлен 10.08.2022Regression smoothing, basic idea of smoothing. Smoothing techniques, the speed at which the smooth curve converges. Choosing the smoothing parameter. Data sets with outliers. Looking for qualitative smoothing and incorporating parametric components.
учебное пособие, добавлен 25.11.2013Several aspects of systems theory. Arithmetic of cardinal numbers. Crises of naive set theory. Constructions of ordinal and cardinal number systems. Growth of the polish school of mathematics. Bellman’s principle of optimality and its generalizations.
книга, добавлен 25.11.2013Conditions for nite sequences of positive numbers to be certain parts of spectra of the Dirichlet-Dirichlet, Dirichlet-Neumann, Neumann-Dirichlet and Neumann-Neumann boundary value problems generated by the same Stieltjes string recurrence relations.
статья, добавлен 19.02.2016Dynamic Modeling with Difference Equations. Linear Models of Structured Populations. Nonlinear Models of Interactions. Modeling Molecular Evolution. Constructing Phylogenetic Trees. Infectious Disease Modeling. Curve Fitting and Biological Modeling.
учебное пособие, добавлен 25.11.2013Korobov polynomials as paradeterminants of triangular matrices. Some of the formulas of interpolation of functions of many variables and the discrete analogue of the summation formula of Euler - basic use of mathematical polynomials of this type.
статья, добавлен 25.03.2016- 44. Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit
Auto-associative models as a new tool for building nonlinear principal component analysis methods. The successive approximations of a dataset by manifolds of increasing dimensions. The theoretical comparison between PCA and auto-associative models.
статья, добавлен 08.02.2013 The spectral properties of a fourth-order functional-differential operator with a summable potential are studied. The boundary conditions are separated. The solution of the functional-differential equation. The solution of the Volterra integral equation.
статья, добавлен 14.08.2020Basic formulas of combinatorial analysis. Theorem of addition of probabilities of incompatible events. Theorem of multiplication of probabilities. Bayes’s formulas. Mathematical operations over random variables. Properties of a distribution function.
курс лекций, добавлен 27.10.2013The fundamentals of the theory of automata, formal languages, and regular, context-free grammar. Discussion of the principle of Turing, which formalize the concept of soluble and insoluble problems, the definition of time and space evaluation algorithms.
книга, добавлен 18.09.2012Using a generalized Dunkl translation, we obtain an analog of theorem 5.2 in Younis’ paper for the Dunkl transform for functions satisfying the (d, g)-Dunkl Lipschitz condition in the space L2(R,|x|2a+1dx). Consideration generalized Dunkl translation.
статья, добавлен 25.03.2016Formulation of the lemma before solving the problem. The search for the principle of solving the paradox. Mathematical problem solving. Philosophical proof of the theorem. Justification of conclusions that can be applied in solving paradoxical problems.
контрольная работа, добавлен 19.03.2024The article describes the main additional constructions used in planimetry. And also examples of tasks for a basic and advanced course of the geometry of 7-9 classes are considered for solving where the method of additional construction is used.
статья, добавлен 25.02.2021