Mathematics 2

Description: The discipline contains sections: integral calculus; differential equations, which allows students to deepen their mathematical knowledge and master methods of mathematical modeling of various physical processes (to describe the movement of a body, the propagation of heat or sound, electromagnetic waves and other physical phenomena); numerical and functional series also allow solving a variety of practical problems, for example, to approximate functions or investigate the behavior of a system in time.

Amount of credits: 5

Пререквизиты:

• Mathematics 1

Course Workload:

Component: University component

Cycle: Base disciplines

Goal

• The purpose of studying the discipline is the formation of students' scientific and practical ideas about mathematical methods for describing and solving practical problems in engineering, technology, and economics.

Objective

• The tasks of studying the discipline are the assimilation of the basic concepts, methods and tasks of sections: the integral calculus of the function of one variable; numerical and functional series used in approximate methods for solving various applied problems; differential equations to which many problems of geometry, mechanics, physics, hydraulics are brought.

Learning outcome: knowledge and understanding

• To organize, formulate and reproduce the basic definitions, theorems, formulas for the studied sections of the discipline and give examples of applied problems

Learning outcome: applying knowledge and understanding

• The ability to apply basic and special knowledge of mathematical sciences in the field of engineering and technology in professional activities, apply methods of mathematical analysis and modeling, theoretical and experimental research.

Learning outcome: formation of judgments

• To study and apply additional literature on the discipline to solve applied problems; to form an idea of the process or phenomenon under study by mathematical methods.

Learning outcome: communicative abilities

• To be able to work in a team for assimilation, consolidation and transfer of acquired knowledge by mathematical methods in solving applied problems

Learning outcome: learning skills or learning abilities

• To acquire skills to obtain new knowledge necessary for the development of special disciplines and continuing education in the specialty; strive for professional and personal growth.

Teaching methods

interactive technologies (with active forms of learning: executive (supervised) 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

• Primitive function
• Integration methods
• Decomposition of rational fractions into simple partial fractions
• Integration of radical and trigonometric functions
• Definite integral
• Differential equations
• First-order differential equations
• Differential equations of higher orders
• Linear homogeneous equations of second and higher orders with constant coefficients
• Linear non-homogeneous equations of second and higher orders with constant coefficients
• Числовые ряды
• Признак Даламбера
• Знакочередующиеся ряды
• Функциональные ряды
• Ряды Тейлора и Маклорена

Key reading

• Берман Г.Н. Сборник задач по курсу математического анализа. – Издательство: Лань, 2020 г.
• Письменный Д.Т. Конспект лекций по высшей математике. – М.: Айрис-Пресс, 2012, Ч. 2,3.
• Рябушко А.П., Бархатов В.В. и др. Индивидуальные задания по высшей математике. – Минск: Высшая школа, 2013. – Т. 2,3,4.
• Шипачев В.С. Высшая математика. – М.: Высшая школа, 2012.
• Шнарева Г.В., Высшая математика. Учебник. 2023, Ай Пи Ар Медиа
• Конюхов А.Н., Машнина С.Н., Ципоркова К.А., Введение в математический анализ. Учебное пособие, 2023, Рязанский государственный радиотехнический университет
• Жуковская, Т. В. Высшая математика в примерах и задачах в 2 частях. Ч.2 : учебное пособие / Т. В. Жуковская, Е. А. Молоканова, А. И. Урусов. — Тамбов : Тамбовский государственный технический университет, ЭБС АСВ, 2018. — 160 c. — ISBN 978-5-8265-1885-4 (ч.2), 978-5-8265-1709-3. — Текст : электронный // Цифровой образовательный ресурс IPR SMART : [сайт]. — URL: https://www.iprbookshop.ru/92664.html (дата обращения: 26.12.2024). — Режим доступа: для авторизир. пользователей
• Двойцова, И. Н. Высшая математика. Интегральное исчисление функции одной переменной. Неопределенный интеграл. Сборник контрольных заданий с примерами решений : учебное пособие / И. Н. Двойцова. — Железногорск : Сибирская пожарно-спасательная академия ГПС МЧС России, 2018. — 53 c. — Текст : электронный // Цифровой образовательный ресурс IPR SMART : [сайт]. — URL: https://www.iprbookshop.ru/90180.html (дата обращения: 26.12.2024). — Режим доступа: для авторизир. пользователей
• Березина, Н. А. Высшая математика : учебное пособие / Н. А. Березина. — 2-е изд. — Саратов : Научная книга, 2019. — 158 c. — ISBN 978-5-9758-1888-1. — Текст : электронный // Цифровой образовательный ресурс IPR SMART : [сайт]. — URL: https://www.iprbookshop.ru/80978.html (дата обращения: 19.12.2024). — Режим доступа: для авторизир. Пользователей