Mathematics.Mathematical Analysis I

2021/2022

Academic Year

ENG

Instruction in English

7

ECTS credits

Delivered at:

Department of Mathematics

Course type:

Elective course

When:

1 year, 1, 2 module

Instructor

Podkopaev, Oleg

Course Syllabus

Abstract

“Mathematical Analysis 1” is a basic discipline included in the mathematical cycle of fundamental training of students of the “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 1” 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.As the result of having finished the course the student must: 1. Know the elementary functions, basic notions, theorems and methods of differential calculus 2. Have the skills of interpreting the results obtained in mathematical research.

Expected Learning Outcomes

• 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 first and second order partial derivatives, extrema, find the directional derivatives and the gradient of a function of several variables.
• Demonstrates the ability to work with functions of several variables: find their domains of definition, level lines and surfaces
• 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.

Course Contents

• Introduction. Elements of sets and functions theory
• Limits and continuity of functions of one real variable
• Differentiation of functions of one variable
• Point sets and sequences in n-dimensional space
• Functions of several variables
• Differentiable functions of several variables

Assessment Elements

• Test 1
  The 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 LMS (and or via the University email) in advance
• Test 2
  The 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 LMS (and or via the University email) in advance .
• Test 3
  The 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 LMS (and or via the University email) in advance.
• Self Work
  The teacher of the practical seminars evaluates the independent work of students and the completion of homework. The control can be carried out in the form of problem solving activities in the class.
• 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. The requirements for the exam procedure in distance format are being made available to the students via an instruction in LMS (and or via the University email) in advance.

Interim Assessment

• 2021/2022 2nd module
  0.39 * Exam + 0.17 * Test 2 + 0.1 * Self Work + 0.17 * Test 3 + 0.17 * Test 1

Bibliography

Recommended Core Bibliography

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

Recommended Additional 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
• Rudin, W. (1976). Principles of mathematical analysis.