Higher Mathematics

Course Annotation

 

Title of the Cource

Higher Mathematics

Lecturare

Drozdenko Vitaliy Oleksandrovych,

Candidate of Physical and Mathematical Sciences,

Associate Professor of the

Department of Higher Mathematics and Physics

Educational year and study semester during which the course is supposed to be delivered

1 educational year, 1semester  

Faculty, students of which are going to study the course

The Faculty of Agronomy

 

List of the competence and corresponding study results provided by the course

By following the course students are supposed to get the following knowledge and skills:

Knowledge

- definition of the knowtion of matrix, inverse matrix, matrix operations, rank of the matrix;

- definition of the determinant of the second, the third, and the  –th order, properties of the determinants;

- general methods of solving of systems of linear algebraic equations (matrix method, Cramer’s method, Gauss’ method, Jordan-Gauss’ method);

- rules for solvability and detrminicity of systems of algebraic linear equations;

- definition of a vector and linear operations performed by the vectors;

- definition of the collinear and coplanar vectors; conditions of collinearity and coplanarity;

- definitions of the scalar, the vector, and the mixed products of the vectors;

- definition of the linear dependence and independence of the system of linear equations;

- definition of the Decart coordinate system on the plain and in three dimensional space;

- main types of equations of the straight lines on the plane and in three dimensional space;

- main types of equation of the plane in three dimensional space; conditions for mutual location of a plane and a straight line in the three dimensional space;

- equations of the second order lines on the plane (circle, ellipse, hyperbola, parabola); general equation of the second order line on the plane;

- definition of function of one and several variables, ranges and domain of the function, odd and even functions, increasing and decreasing functions, periodic function, bounded function, inverce function, superposition of the functions;

- definition of a sequence, limit of the sequence, properties of the limits of sequences;

- definition of the limit of funtion at a point, properties of the limits; important limits;

- different definitions of continuity of the function at a point; definition of the function continuous on the interval;

- definition of the derivative and differential of a function of one and several variables, differentiation rules, main theorems of the differential calculus;

- necessary and sufficient conditions of extrema of functions of one and two variables;

- definitions of antiderivative as well as defined and unproper integrals;

- main integration methods;

- main applicutions of the defined integral to solving of the applied problems;

- main theorems of probability theory;

- probability distributions as well as numerical characteristics of the random variables;

- limit theorems of probability theory;

- statistical (pointwise and interval) estimations of the distribution parameters;

- main notions of the regression theory, dispersion analysis as well as correlation analysis.

 

Skills

- performing of matrix operations (transposing, addition, subtraction and multiplicution of the matrixes);

- finding of rank of the matrix, finding inverce matrix;

- calculating of the determinants of the second the third and of the higher orders;

- solving of systems of algebraic linear equations using different computation methods (matrix method, Cramer’s method, Gauss’ method, Jordan-Gauss’ method;

- applying of elements of matrix theory to solving of the applied problems;

- performing of vector operations; applying of concepts of vectors to solving of geometrical and applied problems;

- determining of linear dependence and linear indepndence of the vectors;

- decomposing of vectors using a basis of the vector system;

- investigating of colinearity and complenarity;

- defining of the angle between vectors;

- finding of scalar, vector, and mixed products of the vectors;

- composing of different types of equations of lines on the planes and in the space as well as applying them to solving of the problems;

- defining mutualle location of two stright lines on the plain and in the space;

- finding of angles between lines on the plane and in the space;

- finding of distance between a point and a line as well as distance between two non-intersecting lines;

- reducing of general equations of the second order curves to their canonical forms;

- finding of ranges and domains of functions of one and several variables;

- investigating of the odd and even structure of a function, monotonicity, periodicity, boundedness, continuity; defining of the character of the discontinuity points;

- finding of limits of the sequences of functions;

- finding of the derivative, differential, partial derivatives as well as full differentials of the functions;

- performing of complete investigation of the function as well as plotting its graph;

- finding of the undefined, defined, and unpropper integrals;

- applying of the defined integrals to finding of areas, volumes, curve length, rotation figures, etc.;

- investigating of extrema of functions of two variables;

- having abbility to choose appropriate probability models as well as methodological tricks of statistical analysis for solwing of applied problems;

- applying of modern statistical methods to solving of practical probles and obtaining of solving skills and skills of using of mathematical literature and mathematical software.

Course Description

 

Prerequisites for the cource

 

Maximal number of students that can simultaneously follow the course

 

Topics of the lessons

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Teaching lenguages

 

High school mathematics

 

 

120 students

 

 

Topics of the lectures

1. Matrixes and matrix operatios.

2. Determinants. Minores. Algebraic conjugates.

3. Systems of linear equations. Solving of proffecionaly oriented problems using methods of linear algebra.

4. Recrangular coordinate systems on the plane and in space. Stright line and planes in space.

5. Second order plain curves.

6. Function. Main elementary functions. Limit of the functions. Continuities and discontinuities of the functions.

7. Main rules and formulas of differential calculus. Partial cases of differentiability. Applicution of the derivatives to investigation of the functions.

8. Antiderivative. Main integration methods. Integration of the fractionally-rational expressions. Integration of some tregonometry expressions.

9. Defined integral.

10. Applicutions of the defined integrals.

11. Main theorems of probability theory.

12. Limit theorems of probability theory.

13. Discrete and continuous random variables and their characteristics.

14. Statistical (pointwise and interval) estimation of the distribution parameters. Elements of the correlation theory.

 

Topics for the seminar lessons

1. Matrixes and matrix operatios.

2. Determinants. Minores. Algebraic conjugates.

3. Systems of linear equations. Solving of proffecionaly oriented problems using methods of linear algebra.

4. Recrangular coordinate systems on the plane and in space. Stright line and planes in space.

5. Second order plain curves.

6. Function. Main elementary functions. Limit of the functions. Continuities and discontinuities of the functions.

7. Main rules and formulas of differential calculus. Partial cases of differentiability. Applicution of the derivatives to investigation of the functions.

8. Antiderivative. Main integration methods. Integration of the fractionally-rational expressions. Integration of some tregonometry expressions.

9. Defined integral.

10. Applicutions of the defined integrals.

11. Main theorems of probability theory.

12. Limit theorems of probability theory.

13. Discrete and continuous random variables and their characteristics.

14. Statistical (pointwise and interval) estimation of the distribution parameters. Elements of the correlation theory.

 

 

Ukrainian, English