матем / Mathematics in economics

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Vectors. Meaning, geometric representation, and types of vectors.

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Operations on vectors. Addition and scalar multiplication.

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The properties of vector addition and scalar multiplication.

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Linear combination of vectors.

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Linear dependence of vectors and

linear independence of vectors.

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Scalar product of vectors and its properties.

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Vector spaces. One-dimensional and two- dimensional vector space.

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Let u=[1, 3, 5] and v=[2, 4 ,6]. Find the following:

1. u+v. 2) u−v.

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Let u=[1, 3] and v =[2, 4]. Find, and illustrate, the following:

1. u+v; 2) u−v

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Find the scalar products of the following vectors:

u=[5, 15, 25] and v =[1, 3, 5].

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Find the domain of the following functions:

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Let .

Which of these matrices are conformable for addition and subtraction? Find the sums and differences of those matrices that are conformable for addition and subtraction.

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Use the sum-or-difference and power rules to find given

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Find the following indefinite integrals:

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Solve the following SSLEs using the Gauss method:

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Let . Calculate the determinant of this matrix using the expansion of the elements of the thrid columns.

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Find the limit, if it exist, of the following function:

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Find the following indefinite integral:

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Solve the following LP problem: maximize П=4x+3y, subject to 2x+4y≤40, 4x+2y≤50, 2x+2y≤40, and x,y≥0.

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Evaluate the following definite integral: .

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Matrices. Types of matrices.

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Matrix operation: scalar multiplication, addition and subtraction.

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Matrix operation: multiplication. The properties of matrix multiplication

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Transpose of a matrix. Symmetric matrix. Properties of matrix transposition.

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The system of linear algebraic equations and solution methods. Formula Cramer.

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Gauss method and its characteristics.

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Functions. Univariate functions.

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Types of functions and their graphs.

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Find the scalar products of the following vectors:

u=[5, -3, 2] and v =[-1, 2, 4].

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Find the transpose of the following matrice:

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Find the limit, if it exist, of the following function:

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Let Find

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Find partial derivatives of function .

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Solve the following LP problems:

Minimize C=3x+2y, subject to x+10y≥20, 10x+y≥40, and x,y≥0

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Calculate the indefinite integral by substitution methods:

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Find the initial support solution to the transportation problem by northwestern methods.

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Let . Find the product of this matrices: AB=?

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Let . Calculate the determinant of this matrix using the expansion of the elements of the fourth row.

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Find the following indefinite integrals: .

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Limit of functions. Properties of limits.

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Continuity function. Properties of continuity.

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Derivatives of univariate functions and notations.

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Rules of differentiation of univariate functions.

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Indefinite integrals. Integration as anti-differentiation. Notations and concepts.

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Rules of integration. Integration by parts.

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Definite or Riemann integrals. Notations and concept.

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Fundamental theorem of integral calculus. Newton –Leibniz formula.

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Find the transpose of the following matrice:

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Suppose that we have an equation of matrices given by 4A−2B=C. Let . Find C.

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Find the derivative of a composite function

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Find the limit of the function by using the second remarkable limit: .

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Find the gradient and its modulus of the function at said point: .

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Calculate the integral by the method integration by parts:

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Find the limit of the function by using the first remarkable limit: .

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Find the initial support solution to the transportation problem by minimum tariff.

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Find the derivative of a composite function:

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Find the solution of a system of linear equations by Gauss methods:

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Let . Find the minor and cofactor of the element of the matrix .