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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