Program of lectures
--------------------------------------------------
1 Linear algebra. Operations with matrices. Determinants. Properties of determinants.
2 Rank of a matrix. Inverse matrix.
3 Solution of linear equations. Frobenius theorem. Cramer's rule.
4 Gaussian elimination algorithm.
5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous,
even, odd, periodic. One-to-one function, inverse and composite functions.
6 Elementary functions.
7 Limit of a function. Continuous and discontinuous functions.
8 Differential calculus of one variable. Derivative of a function, its geometrical and
physical applications. Rules of differentiation.
9 Derivatives of elementary functions.
10 Differential functions. Derivative of a function defined parametrically. Derivatives of
higher orders. L'Hospital's rule.
11 Use of derivatives to detect monotonicity, convexity and concavity features.
12 Extrema of functions. Asymptotes. Graph of a function.
13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties.
14 Equation of a line. Equation of a plane. Relative positions problems.
Metric or distance problems.
Program of exercises and seminars:
--------------------------------------------------
1 Basic operations with matrices. Determinants. Calculation of determinant developing the elements of any series.
2 Rank of matrix, inverse matrix.
3 Solution of linear equations.
4 Solution of systems of linear equations.
5 1. test (calculate determinant, rank of matrix, solution of the system, the inverse matrix).
6 Functions of a simple, inverse, compound. Elementary functions. Trigonometric functions.
7 2.test (domain, inverse function). Limits of functions.
8 Differentiation of functions.
9 Derivations and differential, equations of tangents and normals point functions.
10 Calculation of the limit L'Hospital rule functions. Extremes of function.
11 Convex and concave function, inflection point.
12 3.test (derivative of the function, use). Asymptotes of the curve. A function.
13 Analytic geometry.
14 Reserve and credits.
--------------------------------------------------
1 Linear algebra. Operations with matrices. Determinants. Properties of determinants.
2 Rank of a matrix. Inverse matrix.
3 Solution of linear equations. Frobenius theorem. Cramer's rule.
4 Gaussian elimination algorithm.
5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous,
even, odd, periodic. One-to-one function, inverse and composite functions.
6 Elementary functions.
7 Limit of a function. Continuous and discontinuous functions.
8 Differential calculus of one variable. Derivative of a function, its geometrical and
physical applications. Rules of differentiation.
9 Derivatives of elementary functions.
10 Differential functions. Derivative of a function defined parametrically. Derivatives of
higher orders. L'Hospital's rule.
11 Use of derivatives to detect monotonicity, convexity and concavity features.
12 Extrema of functions. Asymptotes. Graph of a function.
13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties.
14 Equation of a line. Equation of a plane. Relative positions problems.
Metric or distance problems.
Program of exercises and seminars:
--------------------------------------------------
1 Basic operations with matrices. Determinants. Calculation of determinant developing the elements of any series.
2 Rank of matrix, inverse matrix.
3 Solution of linear equations.
4 Solution of systems of linear equations.
5 1. test (calculate determinant, rank of matrix, solution of the system, the inverse matrix).
6 Functions of a simple, inverse, compound. Elementary functions. Trigonometric functions.
7 2.test (domain, inverse function). Limits of functions.
8 Differentiation of functions.
9 Derivations and differential, equations of tangents and normals point functions.
10 Calculation of the limit L'Hospital rule functions. Extremes of function.
11 Convex and concave function, inflection point.
12 3.test (derivative of the function, use). Asymptotes of the curve. A function.
13 Analytic geometry.
14 Reserve and credits.