Контрольная работа по математике

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Institute of Management and Law

1) Matrices and operations on them
The theoretical material:
1) Addition (deduction) matrices.
2) Matrix multiplication by a number, multiplying matrix A by matrix B.
3) matrix transposition.
4) The construction of the matrix A in the whole positive degree.
5) matrix.
6) The inverse matrix.

2 Qualifiers
The theoretical material
1) Properties of determinants.
2) Minor, the cofactor.
3) Calculation of determinants.
4) non-singular matrix.

Z.Rang matrix
The theoretical material:
1) the rank of the matrix and rank the properties of the matrix.
2) Elementary transformations that do not change the rank of a matrix.
3) Equivalent matrices.
4) The eigenvalues \u200b\u200band eigenvectors

4. The system of linear equations
The theoretical material:
1) The general form, matrix form and tabular form of m linear equations in n unknowns.
2) Theorem of Kronecker-Capelli.
3) Joint and inconsistent system, the general solution, basic and free unknowns, basic solution.
4) The method of Gauss, Jordan -Gaussa method, matrix method.

5. The equation of a straight line on the plane
The theoretical material:
1) Equation of the line (in common with the slope in the segments).
2) The distance between two points M, (I ,, y), M2 (x2, y2).
3) The distance (1 from point A (x0, y0) to the line Ax + By + C = O.
4) The condition parallel and perpendicular lines.
5) The equation of the line passing through two points Nx {{y, x) and M (hg.ug).

6. Direct plane and in the space
The theoretical material:
1) The equation of the plane (common in pieces, normal).
2) The angle f between the two planes.
3) A distance d from the point M0 (x0, y0, z0) to the plane.
4) The equation of the plane passing through three points of M1 (x1, y1, z1), M2 (x2, y2, z2) and M3 (x3, y3, z3)
4) The equation of a straight line in space.
5) Condition parallel and perpendicular to the two planes, two lines, line and plane.

7. Limits and continuity.
The theoretical material:
1) Determination of the function y = f (x) as x -> to the infinite. and
x-> x0
2) The infinitely small and infinitely large functions.
3) The first and second remarkable limits.
4) Continuity function. Breaks the 1st and 2nd kind.

The theoretical material:
1) Determination of the derivative.
2) The differentiability and continuity of function.
3) Rules of differentiation.
4) Derivatives of higher orders.

9. Appendix derivative.
The theoretical material:
1) Rule L'Hopital.
2) Intervals of monotony and extrema of the function.
3) The ranges of convexity and points of inflection.
4) asymptote. Research functions and graphing. 5) Differential function.

10. The indefinite integral.
The theoretical material:
1) primitive function and indefinite integral.
2) The properties of indefinite integral. The tabulated integrals.
3) change of variable method.
4) Integration by parts.
5) The integration of simple rational functions, some
kinds of irrational, trigonometric functions.

11. The definite integral
The theoretical material:
1) The area of \u200b\u200bthe curvilinear trapezoid. The geometric meaning of the definite integral.
2) Properties of the definite integral.
3) The Newton-Leibniz.
4) Change of variable and integration by parts in the integral opredelёn¬nom.
5) Improper integrals.
6) Calculate the area of \u200b\u200ba plane figure.
7) Calculation of volumes of solids of revolution.

12. Probability.
• Theoretical material:
1) Basic concepts of combinatorics: factorial permutations placement combinations.
2) Operations on events: the addition of probabilities, conditional probability, multiplication probability formula of total vero¬yatnosti, Bayes formula.
3) Independent tests Bernoulli formula. Appr


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