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Regular version of the site
Bachelor 2023/2024

# Calculus

Type: Compulsory course
When: 1 year, 3, 4 module
Mode of studies: offline
Open to: students of one campus
Instructors: Andrey Subochev
Language: English
ECTS credits: 5
Contact hours: 80

### Course Syllabus

#### Abstract

This course is designed to introduce students to the basic ideas and methods of mathematical analysis and their application in business management. This course serves as a basis for the entire block of quantitative disciplines studied at HSE, and it also provides some analytical tools required by advanced courses in information technologies. The course provides students with experience in the methods and applications of calculus to theoretical and practical problems. The course is taught in English.

#### Learning Objectives

• providing students basic knowledge in calculus and ordinary differential equations;
• familiarizing with the applied problems of calculus;
• developing skills to solve typical problems of calculus.

#### Expected Learning Outcomes

• analyze functions represented in a variety of ways: graphical, numerical, analytical, or verbal, and understand the relationships between these various representations.
• communicate mathematics in well-written sentences and to explain the solutions to problems.
• model a written description of a simple situation with a function, differential equation, or an integral.
• understand and explain the meaning of solutions, including sign, size, relative accuracy, and units of measurement.
• understand the meaning of the definite integral as the net accumulation of change, and use integrals to solve various problems.
• understand the meaning of the derivative in terms of a rate of change and marginal analysis, and use derivatives to solve various problems.
• use mathematical analysis to solve problems, interpret results, and verify conclusions.

#### Course Contents

• Introduction
• Limits and continuity
• The double integral
• The derivative
• Number series, power series, and Taylor expansions
• Applications of the derivative
• The indefinite integral
• The definite integral
• Applications of the definite integral
• Improper Integrals
• Functions of several variables
• Partial derivatives and related topics
• Optimizing functions of two variables.
• Differential equations and slope fields
• Cauchy initial value problem

#### Assessment Elements

• Class activity (Gca)
• Mid-term exam (Gmidterm)
• Examination (Gfinal)
• Tests (Gtest)

#### Interim Assessment

• 2023/2024 4th module
0.15 * Class activity (Gca) + 0.5 * Examination (Gfinal) + 0.25 * Mid-term exam (Gmidterm) + 0.1 * Tests (Gtest)

#### Recommended Core Bibliography

• Calculus early transcendentals, Stewart, J., 2012
• Fundamental methods of mathematical economics, Chiang, A. C., 1984
• Schaum's outline of theory and problems of introduction to mathematical economics, Dowling, E. T., 1992