Mathematical Analysis

Description: The modern methods of mathematical analysis discussed in these sections form the basis for further study of the cycle of mathematical disciplines, and also make it possible to model and study the simplest applied problems in various branches of applied sciences. The discipline contains sections: introduction to mathematical analysis; differential and integral calculus of functions of one and several variables and their applications.

Amount of credits: 8

Пререквизиты:

• Математика. Школьный курс

Course Workload:

Component: University component

Cycle: Base disciplines

Goal

• The purpose of studying the discipline: The course of mathematical analysis is the foundation of mathematical education for a specialist in mathematical modeling, and within the framework of this course, orientation is carried out on the application of mathematical methods in professional activities.

Objective

• The tasks of studying the discipline: - mastering the main provisions of the classical sections of mathematical analysis, basic ideas and methods of mathematics, the system of basic mathematical structures and the culture of mathematical thinking, logical and algorithmic culture, understanding the general structure of mathematical knowledge, the relationship between various mathematical disciplines, the ability to implement the basic methods of mathematical reasoning based on common methods of scientific research and experience in solving educational and scientific problems

Learning outcome: knowledge and understanding

• Knowledge and understanding: knowledge and understanding of the basic mathematical definitions, theorems and other theoretical information of the course "Mathematical Analysis", as well as knowledge of the types of problems solved by certain mathematical methods;

Learning outcome: applying knowledge and understanding

• Application of knowledge and skills: application of knowledge and skills in the formulation of applied practical problems by mathematical methods, as well as the use of known methods to solve the formulated problems;

Learning outcome: formation of judgments

• Formation of judgments: the ability, based on the existing knowledge of the discipline "Mathematical Analysis", to draw conclusions about possible methods of analysis and solving practical problems in a special area;

Learning outcome: communicative abilities

• Communication skills: ability to work in a team to effectively solve the set practical problems based on knowledge of mathematical methods;

Learning outcome: learning skills or learning abilities

• Learning skills or learning abilities: the ability of independent or on the basis of educational educational programs for advanced training in the field of mathematical knowledge in order to meet the modern requirements of the specialty.

Teaching methods

интерактивные технологии обучения;

компьютерные технологии обучения;

самостоятельная исследовательская работа студентов во время учебного процесса.

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

• Функция, её области определения и значений
• Последовательность и её предел
• Предел функции в точке
• Непрерывность функции в точке
• Понятие производной
• Производные и дифференциалы высших порядков
• Функция нескольких переменных
• Частные производные и дифференциалы высших порядков
• Неопределенный интеграл
• Определенный интеграл
• Вычисление площади плоской фигуры в декартовой и в полярной системе координат
• Несобственные интегралы
• Теория рядов
• Знакочередующиеся числовые ряды
• Функциональные последовательности и функциональные ряды

Key reading

• Берман Г.Н. Сборник задач по курсу математического анализа. – СПб.: Лань, 2018.
• Бугров Я.С., Никольский С.М. Дифференциальное и интегральное исчисление. – М.: Дрофа, 2016.
• Сборник задач и упражнений по математическому анализу : учебное пособие для вузов, Б. П. Демидович, Москва: АСТ, 2014.
• Кудрявцев Л.Д. и др. Сборник задач по математическому анализу. – М. : Физматлит, 2018. – 496 с.
• Пискунов Н.С. Дифференциальное и интегральное исчисления для втузов. – М.: Интеграл - Пресс, 2015, Т.1.
• Фихтенгольц Г.М. Основы математического анализа.М.:Наука, 2019г.

Further reading

• Демидович Б.П. Краткий курс высшей математики. – М.: Астрель-АСТ, 2019.
• Китапбаев М.К., Сидоренко В.Н., Чи-Дун-Чи Ю.В. Высшая математика в вопросах и задачах. Дифференциальное и интегральное исчисление.- У-ка, ВКГТУ, 2002.
• иКузнецов Л.А. Сборник задач по высшей математике (типовые расчеты). – СПб.: Лань, 2015.
• Рябушко А.П., Бархатов В. В и др. Индивидуальные задания по высшей математике.- Алматы: Образование и наука, 2013, Ч 1.