Educational MATERIALS in ENGLISH

Educational MATERIALS in ENGLISH

SUBJECT "Intoduction to Calculus"

Theme+0. Preliminary remarks (*.pdf file)
Theme01. Numerical sequence and its properties (*.pdf file)
Theme02. Function. Function limit. Continuity (*.pdf file)
Theme03. Derivative at a point. Derivative function (*.pdf file)
Theme04. Differentials. Properties of differentiable functions (*.pdf file)
Theme05. Taylor formula (*.pdf file)
Theme06. Calculating limits using Taylor's formula (*.pdf file)
Theme07. Study of properties of functions. Plotting graphs (*.pdf file)
Theme08. Drawing parametrically defined lines (*.pdf file)
Theme09. Elements of differential geometry (*.pdf file)

SUBJECT "Multy-dimentional Analysis. Integrals and Series"

Theme+0. Indefinite integral (*.pdf file)
Theme01. Function in E^n (*.pdf file)
Theme02. Continuity in E^n (*.pdf file)
Theme03. Derivatives in E^n (*.pdf file)
Theme04. Differentiation in E^n (*.pdf file)
Theme05. Definite integral (*.pdf file)
Theme06. Improper integral (*.pdf file)
Theme07. Numerical series (*.pdf file)
Theme08. Functional sequence (*.pdf file)
Theme09. Functional series (*.pdf file)
Theme10. Power series (*.pdf file)

SUBJECT "Analytic Geometry"

Theme01. Matrix objects (*.pdf file)
Theme02. Vectors (*.pdf file)
Theme03. Cartesian coordinate system (*.pdf file)
Theme04. Products of vectors (*.pdf file)
Theme05. Straight line in the plane (*.pdf file)
Theme06. Straight line and plane in space (*.pdf file)
Theme07. Lines and surfacess (*.pdf file)
Theme08. Second-order curves in the plane (*.pdf file)
Theme09. Second-order surfaces (*.pdf file)
Theme10a. Affine transformations of the plane (theory) (*.pdf file)
Theme10b. Affine transformations of the plane (tasks) (*.pdf file)
Theme11. Determinants and their properties (*.pdf file)
Theme12. Cramer's rule. Rank of a matrix (*.pdf file)

SUBJECT "Linear Algebra"

Theme01. Systems of m linear equations with n unknowns (*.pdf file)
Theme02. Vector space (*.pdf file)
Theme03. Linear operators in vector space (*.pdf file)
Theme04. Eigenvalues and eigenvectors (*.pdf file)
Theme05. Invariant subspaces (*.pdf file)
Theme06. Bilinear and quadratic forms (*.pdf file)
Theme07. Euclidean space (*.pdf file)
Theme08. Linear operators in Euclidean space (*.pdf file)
Theme09. Quadratic forms in Euclidean space (*.pdf file)

SUBJECT "Multiple integrals and field theory"

Theme01. Differentiation of composite functions (*.pdf файл)
Theme02. Extremum of functions of several variables (*.pdf файл)
Theme03. Conditional extremum of functions of several variables (*.pdf файл)
Theme04. Multiple integrals (*.pdf файл)
Theme05. Curvilinear and surface integrals (*.pdf файл)
Theme06. Elements of field theory (*.pdf файл)
Theme07. Tensors in field theory (*.pdf файл)

SUBJECT "Harmonic Analysis"

Theme01. Introduction to Harmonic Analysis (*.pdf файл)
Theme02. Trigonometric Fourier Series (*.pdf файл)
Theme03. Metric Sets and Normed Spaces (*.pdf файл)
Theme04. Completeness of Function Systems (*.pdf файл)
Theme05. Proper Integrals Depending on a Parameter (*.pdf файл)
Theme06. Improper integrals depending on a parameter (*.pdf файл)
Theme07. Calculation of improper integrals depending on a parameter (*.pdf файл)
Theme08. Special functions (*.pdf файл)
Theme09. Fourier integral (*.pdf файл)
Theme10. Fourier transform (*.pdf файл)
Theme11. Generalized functions 'Distributions' (*.pdf файл)
Theme12. Operations with Generalized functions (*.pdf файл)

SUBJECT "Parametric Sets of Second-Order Lines on a Plane"

Parametric Sets of Second-Order Lines on a Plane (*.pdf файл)