Bachelor
2022/2023

# Mathematics.Mathematical Analysis II

Category 'Best Course for New Knowledge and Skills'

Type:
Elective course (International Bachelor's in Business and Economics)

Area of studies:
Economics

Delivered by:
Department of Mathematics

When:
1 year, 3, 4 module

Mode of studies:
offline

Open to:
students of one campus

Instructors:
Якубсон Михаил Яковлевич,
Ксенофонтова Вера Алексеевна,
Yury Eliyashev,
Alexandra Grinikh,
Viktoria Litvinova,
Oleg Podkopaev,
Evgeniy Valentinovich Runev,
Кумачева Сурия Шакировна

Language:
English

ECTS credits:
6

Contact hours:
144

### Course Syllabus

#### Abstract

The goal of studying the discipline “Mathematical Analysis II is learning the topics “Integral Calculus”, “Series and function series”, “Elements of ordinary differential equations theory”, allowing the student to approach other disciplines such as “Probability Theory and Mathematical Statistics”, “Optimal Decisions Theory”, “Microeconomics”, “Macroeconomics”, “Game Theory”, and “Econometrics”. The material of the course can be used in development and applications of numerical methods of solving the problems in many areas of knowledge, and for creating and analyzing the mathematical models in various subjects, first and foremost in economics. The discipline is a model for studying of the mathematical component of “Economics” students’ education.

#### Learning Objectives

- The goal of studying the discipline “Mathematical Analysis 2” is learning the basic course of Mathematical Analysis, getting familiar with the terminology, theoretical principles and problem solving skills based on the fundamental notions of the course such as antiderivative, indefinite and definite integral, multiple integrals, convergent/divergent series, radius of convergence of a power series, differential equation, its general and partial solution, superposition principle for the linear ODEs and other principles, forming of the theoretical foundations and a set of mathematical tools for the disciplines of the Economics cycle.
- As the result of having finished the course the student must: 1. Be acquainted with the main notions, theorems and methods of integral calculus, the ways of studying function series, methods of solving differential equations. 2. Be able to apply the tools of mathematical analysis to the problems of computing and predicting economic indicators, use tools of differential equations for modeling simple economic processes. 3. Have the skills of interpreting the results obtained in mathematical research.

#### Expected Learning Outcomes

- demonstrate the knowledge of the notions of convergence and divergence of a number series, radius of convergence of a power series
- knows the methods of solving differential equations, demonstrates the ability to apply the theory for analyzing differential equations

#### Course Contents

- Part 1 “Integral Calculus” Topic I. Antiderivative,indefinite integral.
- Topic II. Definite integral
- Topic III. Multiple integrals
- Part 2 «Series» Topic IV. Number and function series
- Part 3 «Introduction to ordinary differential equations theory» Topic V. «Ordinary differential equations»

#### Assessment Elements

- Test 1The tests are being held in the auditorium or distance remotely (in case of distance learning format) in a written form, the duration is determined by the lecturer and the students are notified of it in advance. The possibility of the tests being held for all groups at the same time reserved. The requirements for the test procedure in distance format are being made available to the students via an instruction in SmartLMS (and or via the University email) in advance
- Test 2The tests are being held in the auditorium or distance remotely (in case of distance learning format) in a written form, the duration is determined by the lecturer and the students are notified of it in advance. The possibility of the tests being held for all groups at the same time reserved. The requirements for the test procedure in distance format are being made available to the students via an instruction in SmartLMS (and or via the University email) in advance
- Test 3The tests are being held in the auditorium or distance remotely (in case of distance learning format) in a written form, the duration is determined by the lecturer and the students are notified of it in advance. The possibility of the tests being held for all groups at the same time reserved. The requirements for the test procedure in distance format are being made available to the students via an instruction in SmartLMS (and or via the University email) in advance
- Self-studyThe discipline involves the following forms of ongoing monitoring: the student’s self-study throughout the semester, consisting of regular homeworks (practice on the seminar material), seminar work (including quizzes).
- Exam1)The exam tasks will coincide with the demo variant in structure 2)The types of functions, integrands, differential equations etc. will be different from the demo variant, also the methods of solution will differ. 3) The computational part will be graded according to the same criteria as the tests. 4) In the computational problems the student is required to write down the answer. The answer should contain the objects that one needed to find, their characteristics, if asked in the problem. In the problems on series: convergence/divergence, type of convergence (if asked), for differential equations; particular/general solution

#### Interim Assessment

- 2022/2023 4th module0.18 * Test 2 + 0.36 * Exam + 0.05 * Self-study + 0.18 * Test 1 + 0.18 * Test 3

#### Bibliography

#### Recommended Core Bibliography

- Ильин В.А., Садовничий В.А., Сендов Б.Х. - МАТЕМАТИЧЕСКИЙ АНАЛИЗ Ч. 1 4-е изд., пер. и доп. Учебник для бакалавров - М.:Издательство Юрайт - 2016 - 660с. - ISBN: 978-5-9916-2733-7 - Текст электронный // ЭБС ЮРАЙТ - URL: https://urait.ru/book/matematicheskiy-analiz-ch-1-389342
- Кудрявцев Л.Д. - КУРС МАТЕМАТИЧЕСКОГО АНАЛИЗА В 3 Т. ТОМ 2 В 2 КНИГАХ 6-е изд., пер. и доп. Учебник для бакалавров - М.:Издательство Юрайт - 2016 - 720с. - ISBN: 978-5-9916-6126-3 - Текст электронный // ЭБС ЮРАЙТ - URL: https://urait.ru/book/kurs-matematicheskogo-analiza-v-3-t-tom-2-v-2-knigah-387530

#### Recommended Additional Bibliography

- Высшая математика: Учебник / Шипачев В.С. - М.:НИЦ ИНФРА-М, 2015. - 479 с.: 60x90 1/16 (Переплёт 7БЦ) ISBN 978-5-16-010072-2 - Режим доступа: http://znanium.com/catalog/product/469720
- Путко Б.А., Тришин И.М., Кремер Н.Ш. - под ред. - МАТЕМАТИЧЕСКИЙ АНАЛИЗ В 2 Т. Учебник и практикум для академического бакалавриата - М.:Издательство Юрайт - 2016 - 634с. - ISBN: 978-5-9916-6238-3 - Текст электронный // ЭБС ЮРАЙТ - URL: https://urait.ru/book/matematicheskiy-analiz-v-2-t-388079