Бакалавриат
2026/2027
Математический анализ
Статус:
Курс обязательный (Международный бизнес)
Где читается:
Высшая школа бизнеса
Когда читается:
1-й курс, 2, 3 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
6
Контактные часы:
96
Course Syllabus
Abstract
The course belongs to the core block of mathematical and natural sciences within bachelor training and introduces students to the foundations of calculus as a central discipline of modern mathematics. It is accessible to students with a standard secondary school background, yet systematically expands their mathematical culture and strengthens the ability to work with abstract concepts and precise formal reasoning. The ideas and methods studied here constitute the groundwork for a number of advanced subjects, including Probability Theory and Mathematical Statistics, Econometrics, Modeling in Management, Optimization Techniques, as well as Quantitative and Qualitative Approaches to Decision-Making. At the same time, calculus itself is not only an auxiliary tool but also a universal framework for describing variability, modeling continuous processes, and solving optimization problems in economics, engineering, and the natural sciences. A distinctive feature of the discipline is its dual orientation: on the one hand, it develops conceptual understanding and rigorous proofs, while on the other, it trains practical application of differential and integral methods. Special emphasis is placed on forming mathematical intuition, the ability to reformulate real-world problems in analytical terms, and the skill of applying calculus techniques to both theoretical and applied contexts.
Learning Objectives
- Know principles of mathematical models construction
- Ability to apply elements of mathematical analysis to problems of data analysis, economics, and management
Expected Learning Outcomes
- Ability to perform basic operations on sets
- Ability to determine the cardinality of sets
- Ability to work with elements of sets of natural, rational, and real numbers
- Ability to formulate and use Russell's paradox
- Ability to formulate the concept of a sequence
- Ability to perform basic operations on sequences
- Ability to determine and establish monotonicity of sequences
- Ability to determine and establish the boundedness of a sequence
- Ability to determine the existence of a limit of a sequence
- Ability to calculate the limit of a sequence
- Ability to conceptualize a function of a real argument
- Ability to conceptualize a continuous function
- Ability to conceptualize the composition of functions
- Ability to determine whether a function is monotonic
- Ability to determine whether a function is bounded
- Ability to calculate the limit of a function
- Ability to calculate the derivative of elementary functions and their compositions
- Ability to calculate indefinite integrals using various methods
- Ability to calculate definite integrals of continuous functions
- Ability to calculate the areas of plane figures using definite integrals
Bibliography
Recommended Core Bibliography
- Calculus, Stewart, J., 2012
- Calculus, Stewart, J., 2012
- Курс дифференциального и интегрального исчисления, Фихтенгольц, Г. М.,
Recommended Additional Bibliography
- Математический анализ (с экономическими приложениями). Функции одной переменной, [учебное пособие], Гос. ун-т - Высшая школа экономики, 194 с., Волкова, И. О., Крутицкая, Н. Ч., Шагин, В. Л., 1998
- Математический анализ. Т. 1: ., Зорич, В. А., 2015
- Математический анализ. Т. 2: ., Зорич, В. А., 2015