# Spurs on mathematical analysis and linear algebra

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Spurs on mathematical analysis and linear algebra

Questions for the exams for "mathematical analysis and linear algebra":
№1. a) The concept of matrix. b) Types of matrices. c) matrix transposition. g) Equality of matrices. d) The algebraic operations on matrices: multiplication by a number, addition, multiplication of matrices.
№2. a) Determinants of the 2nd, 3rd and the n-th order (definition and from Holy Island). b) Theorem Laplace expansion of the determinant of the elements of a row or column.
№3.a) square matrix and its determinant. b) Special and non-singular square matrices. c) The attached matrix. g) The inverse of this, and an algorithm for its calculation.
№4. a) The concept of the minor to the first order. b) rank of the matrix (definition) .in) Calculation rank matrix by elementary preodrazovaniy.Primer.
№5. a) The linear independence of the columns (rows) of the matrix. b) The theorem on the rank of the matrix
№8. a) The system of m linear equations in n variables (general view). b) the matrix form of such a system. c) the solution of the system (definition) d) A Joint and incompatible, definite and indefinite system of linear equations.
№9. a) Gauss solutions of linear system of n-ur-states with n variables. b) The concept of the method of Gauss-Jordan.
№10. N Solving systems of linear equations in n variables by using the inverse matrix (derivation of the formula X = A-1B.
№11 theorem and Cramer solution of a system of n equations in n variables (no).
№12 Kronecker-Capelli theorem. Under certainty and uncertainty consistent systems of linear equations.
№13 concept of function, ways of defining f-tions. The domain of definition. The even and odd bounded, monotonic functions.
№14 a) The concept of elementary piano. b) Basic elementary-defined function and their graphs (constant power law, exponential, logarithmic).
№15 a) equation of the line on a plane. b) The point of intersection of the two liniy.v) Ogsnovnye kinds of equations line on the plane (one of them to withdraw).
№16. a) The total of the ur-line on the plane, his research. b) || Terms and ┴pryamyh.
№17 a) the limit of a sequence as n → ∞ for limit-defined function for x → ∞.b) for the existence of the limit (with proof of the theorem on the limit of the intermediate f-ii).
№18 a) Determination of the f-ii point. b) Basic theorems about the limits (one show).
№19. a) infinitesimal (definition). b) Holy Island infinitesimal (1 docking be)
№20. a) An infinitely large value (definition). b) Communication with infinitesimal quantities infinitely large.
№21. a) The second remarkable limit the number e. b) The concept of the natural logarithms.
№22. a) The limits of f-tions. Disclosure of the uncertainties of various kinds. B) L'Hospital Rule.
№23 a) Going-defined function at a point and promezhutke.b) Islands Holy f-tions, continuous on the interval. c) Points razryva.g) Examples.
№24 a) Derivative and its geometric smysl.b) Equation plane tangent to the curve at a given point.
№25 a) Differentiability Fct one peremennoy.b) Communication m / d differentiability and continuity of f-ii (to prove the theorem).
№26 The basic rules of differentiation of f-tions of one variable (one of them to prove).
№27.a) Formula derivatives of basic elementary p-tions (one of them to withdraw). b) Derivative difficult Fct.
№28 Rolle's theorem and Lagrange (without docking target). The geometrical interpretation of these theorems.
№29 Sufficient monotony of f-tions (one of them to prove).
№30 a) Determination of the f-ii a peremennoy.b) Necessary extremum sign (prove).
№31 Sufficient extremum existence (to prove a theorem).
№32 a) The concept of asymptote schedule Fct. b) horizontal, inclined and vertical asimptoty.v) Examples.
№33 general scheme of study piano rd and build their schedules. Example.
№34 a) f-tion of several variables. Primery.b) Partial derivatives (definition). c) The extremum Faculty of several

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