Mathematics.Mathematical Analysis I

2026/2027

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Департамент математики

Статус:

Курс обязательный

Когда читается:

1-й курс, 1, 2 модуль

Преподаватели

Гриних Александра Леонидовна

Подкопаев Олег Борисович

Course Syllabus

Abstract

Mathematical Analysis i is a basic discipline included in the mathematical cycle of fundamental training of students of the “International Bachelor's in Business and Economics” study program. In this discipline the students get acquainted with the topics “Limits of functions” and "Differential calculus of functions of one and several variables" that will be used in the theory and applications of disciplines of the mathematical cycle. 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 I 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 mapping/function, limit, derivative and several others, and forming of the theoretical foundations and a set of mathematical tools for the disciplines of the Economics cycle.

Expected Learning Outcomes

• Demonstrates the knowledge of basic notions of set theory: sets, functions, basic elementary functions, ability to sketch their graphs using basic substitutions.
• Demonstrates the knowledge of the notions of limit of a function, continuity, ability to compute the limits and tell whether a function is continuous.
• Demonstrates the ability to differentiate functions, find the limits using derivatives, study the functions and sketch their graphs using derivatives
• Demonstrates the ability to work with functions of several variables: find their domains of definition, level lines and surfaces
• Demonstrates the ability to work with functions of several variables: find first and second order partial derivatives, extrema, find the directional derivatives and the gradient of a function of several variables.

Course Contents

• Part 1. Functions of one variable Topic 1. Introduction. Elements of sets and functions theory
• Topic II. Limits and continuity of functions of one real variable
• Part 2 Differential calculus. Topic I. Differentiation of functions of one variable
• Topic II. Point sets and sequences in n-dimensional space
• Functions of two variables.
• Topic III. Differentiable functions of several variables

Assessment Elements

• Test 1
• In class participation
• Exam
  The exam is 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 exam being held for all groups at the same time reserved.
• Test 2

Interim Assessment

• 2026/2027 2nd module
  0.08 * In class participation + 0.38 * Exam + 0.27 * Test 2 + 0.27 * Test 1

Bibliography

Recommended Core Bibliography

• C. R. J. Clapham, Introduction to Mathematical Analysis, 1973, Routledge & Kegan Paul. ISBN: 978-94-011-6572-3. [electronic resource] link: https://link.springer.com/book/10.1007/978-94-011-6572-3
• Mangatiana A. Robdera, A Concise Approach to Mathematical Analysis, 2003, [electronic resource] link: https://link.springer.com/book/10.1007/978-0-85729-347-3
• Rudin, W. (1976). Principles of mathematical analysis.

Recommended Additional Bibliography

• V. A. Zorich. (2016). Mathematical Analysis I (Vol. 2nd ed. 2015). Springer.

Authors

• Brodskaia Natalia Nikolaevna