Calculus

2022/2023

Учебный год

ENG

Обучение ведется на английском языке

10

Кредиты

Кто читает:

Департамент больших данных и информационного поиска

Статус:

Курс обязательный

Когда читается:

1-й курс, 1-4 модуль

Преподаватели

Днестрян Андрей Игоревич

Орел Ольга Евгеньевна

Course Syllabus

Abstract

The discipline gives the fundamentals of mathematics, provides the foundation for mathematical modeling, and introduces the first concepts of data analysis. The prerequisites are high school algebra and trigonometry. Prior experience with calculus is helpful but not essential.

Learning Objectives

• Students will develop an understanding of fundamental concepts of the single and multi variable calculus and form a range of skills that help them work efficiently with these concepts.
• Students will gain knowledge of the derivatives of single-variable functions, their integral, and the derivatives of multi-variable functions.
• The course will give students an understanding of simple optimization problems.

Expected Learning Outcomes

• Analyze functions represented in a variety of ways: graphical, numerical, analytical, or verbal, and understand the relationships between these various representations
• Students should be able to understand and apply basic concepts of the theory of limits, continuous and differentiable single-variable functions, antiderivatives and integrals of single-variable functions, continuous and differentiable several-variable functions.
• Apply numerical algorithms that solve algebraic equations and compute derivatives and integrals, to model a written description of simple economic or physical phenomena with functions, differential equations, or an integral, use mathematical analysis to solve problems, interpret results, and verify conclusions, determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
• Compute derivatives and antiderivatives.
• Compute limits of sequences and functions
• Describe the space of several variables, convergence in the space, and properties of the distance.
• Determine the convergence of improper integrals.
• Estimate the asymptotical behavior of functions.
• Formulate and solve simple optimization problems.
• Represent a function as the Taylor polynomial and a remainder term.
• Apply basic concepts of the theory of limits, continuous and differentiable single-variable functions, antiderivatives and integrals of single-variable functions, continuous and differentiable several-variable functions.
• Determine basic principles of numerical algorithms that solve algebraic equations and compute derivatives and integrals.
• Define the relationship between the derivative and the definite integral, as expressed by the Fundamental Theorem of Calculus.
• Find the extrema of single- and several-variable functions.

Course Contents

• Sequences. Limit of a sequence
• Continuous functions
• Differentiable functions
• Integration
• Space of several variables and continuous functions on it
• Differentiation of functions of several variables

Assessment Elements

• 2nd module Exam
  The exam may be carried out online via distance learning platforms. At the end of the second and fourth modules the students pass a written exam.
• 4th module Exam
  The exam may be carried out online via distance learning platforms. At the end of the second and fourth modules the students pass a written exam.
• 1st semester Regular activity
  During the year students must also complete weekly home assignments. Professors can ask students to present their written solutions orally. Quizzes are held regularly in classes.
• 2nd semester Regular activity
  During the year students must also complete weekly home assignments. Professors can ask students to present their written solutions orally. Quizzes are held regularly in classes.
• 1st semester bonus activity
• 2nd semester bonus activity

Interim Assessment

• 2022/2023 2nd module
  G(rade)=roundoff (min (0.4*Regular activity + 0.6*Exam +Bonus points, 10))
• 2022/2023 4th module
  G(rade)=roundoff (min (0.4*Regular activity + 0.6*Exam +Bonus points, 10))

Bibliography

Recommended Core Bibliography

• Advanced calculus, Friedman, A., 2007
• Calculus early transcendentals, Stewart, J., 2012
• Numerical recipes : the art of scientific computing, Press, W. H., 2007

Recommended Additional Bibliography

• Курс дифференциального и интегрального исчисления. Т.1: ., Фихтенгольц, Г. М., 2001
• Сборник задач и упражнений по математическому анализу : учеб. пособие для вузов, Демидович, Б. П., 2003