Mathematics

Description: The discipline contains the following sections: elements of linear and vector algebra, elements of analytical geometry, introduction to mathematical analysis; differential calculus of the function of one variable and their applications, differential calculus of the function of several variables and their applications. Integration methods. Applications of a definite integral. The latest technical methods of calculations allow to use mathematical researches concerning any branch of science and to bring the decision to practical applications.

Amount of credits: 5

Пререквизиты:

• Математика. Школьный курс

Course Workload:

Component: University component

Cycle: Base disciplines

Goal

• The purpose of teaching the discipline is to present the basic concepts and methods that are the main basis for mastering disciplines that use mathematical models, the formation of students' theoretical knowledge and practical skills in applying mathematical methods in setting and solving applied problems.

Objective

• the student must acquire knowledge of the basic concepts of the discipline, understanding and ability to prove the theory, skills in solving practical problems using the mathematical apparatus of this course

Learning outcome: knowledge and understanding

• Knows formulas and properties, symbolism of the basic concepts of analysis, the theory of comparison of infinitesimals, as well as methods for solving problems of linear algebra and analytic geometry and differential and integral calculus of functions of one and several variables in the discipline "Mathematics ".

Learning outcome: applying knowledge and understanding

• The knowledge gained in the study of the discipline "Mathematics 1" is successfully applied in solving applied problems, compiling mathematical models of various problems and in comparative data analysis, as well as in complex engineering activities.

Learning outcome: formation of judgments

• Able to independently apply methods and means of cognition, training and self-control, to realize the prospects of intellectual, cultural, moral, physical and professional self-development and self-improvement, is able to critically assess their own strengths and weaknesses.

Learning outcome: communicative abilities

• Able to work effectively individually and as a member of a team, demonstrating the skills of managing separate groups of performers, including on interdisciplinary projects, is able to show personal responsibility, adherence to professional ethics and standards of professional conduct.

Learning outcome: learning skills or learning abilities

• Analyzes and develops independently existing technical documentation; clearly presents and defends the results of complex engineering activities in the field of automation and control. Owns analytical ways of presenting mathematical information to create a mathematical model of applied problems.

Teaching methods

interactive technologies (with active forms of learning: controlled conversation; moderation; brainstorming; motivational speech);

independent research work of students during the educational process;

solving educational problems.

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

The evaluating policy of learning outcomes by work type

Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

• 40% of the examination result;
• 60% of current control result.

The final grade is calculated by the formula:

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Topics of lectures

• Matrices and actions on them
• Vectors, linear operations on vectors
• Straight on a plane
• Function limit
• Problems of mechanics leading to the concept of derivative
• Derivatives of inverse, implicit, parametrically specified functions
• Conditions for increasing and decreasing functions
• Functions of several variables
• Directional derivative
• Derivatives and differentials of higher orders of functions of several variables Extremum of functions of several variables
• Primitive function
• Integration methods
• Decomposition of rational fractions into simple partial fractions
• Integration of radical and trigonometric functions
• Definite integral

Key reading

• Берман Г.Н. Сборник задач по курсу математического анализа. – Издательство: Лань, 2020 г.
• Бугров Я.С., Никольский С.М. Элементы линейной алгебры и аналитической геометрии. – М.: Физматлит, 2004
• Клетеник Д.В. Сборник задач по аналитической геометрии. – М.: Профессия, 2009.
• Письменный Д.Т. Конспект лекций по высшей математике. – М.: Айрис-Пресс, 2004, ч.1.
• Рябушко А.П., Бархатов В.В. и др. Индивидуальные задания по высшей математике.- Минск: Высшая школа, 20012, Т.1,2,3.
• Айдос Е.Ж. Жоғары математика-1,2,3: Оқулық. – 3 кітапта. /Е.Ж.Айдос. – Алматы: Бастау», 2015. 1-кітап. – 320 б
• Айдос Е.Ж. Жоғары математика-1,2,3: Оқулық. – 3 кітапта. /Е.Ж.Айдос. – Алматы: Бастау», 2015. 1-кітап. – 320 б

Further reading

• Хисамиев Н.Г., Тыныбекова С.Ж., Конырханова А.А. Математика. 1, 2 томдары.- Өскемен.- ШҚМТУ баспасы, 2012.
• Тыныбекова С.Ж., Рахметуллина Ж.Т. Математика.- Өскемен.- ШҚМТУ баспасы, 2011
• Горбаченко В.И. Вычислительная линейная алгебра с примерами на MATLAB. СПб. : БХВ-Петербург, 2011.
• Мещеряков В.В. Задачи по математике с Matlab & Simulink. — М.: Диалог-МИФИ, 2007.
• Тыныбекова С.Ж., Мухамедова Р.О. Математика.- Усть-Каменогорск.- издательство ВКГТУ, 2011