Математический анализ

Бакалавриат 2024/2025

Статус: Курс обязательный (Прикладной анализ данных)

Направление: 01.03.02. Прикладная математика и информатика

Кто читает: Департамент больших данных и информационного поиска

Где читается: Факультет компьютерных наук

Когда читается: 1-й курс, 1-4 модуль

Формат изучения: без онлайн-курса

Охват аудитории: для своего кампуса

Преподаватели: Башминова Дарья Александровна, Гончаренко Василий Михайлович, Жуков Павел Владимирович

Язык: английский

Кредиты: 10

Full Syllabus Ask Question

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

Exam 1
At the end of the second and fourth modules the students pass a written exam. If plagiarism is detected, the assessment element will be assigned a score of "0". If the student is suspected of preparing the task not on his own, the teacher has the right to initiate additional verification or defense of this particular assessment element. Then such an assessment element will be graded based on the additional verification or the defense. Duration of the exam is 120 minutes.
Midterm 1
At the end of the 1st and 3rd modules (or at the beginning of the 2nd and 4th modules) the students have a written control work (midterm). If plagiarism is detected, the assessment element will be assigned a score of "0". If the student is suspected of preparing the task not on his own, the teacher has the right to initiate additional verification or defense of this particular assessment element. Then such an assessment element will be graded based on the additional verification or the defense. Duration of the midterms is 80 minutes.
Homeworks 1
During the year students have to do regular homeworks. Professors can ask students to present their written solutions orally. If plagiarism is detected, the assessment element will be assigned a score of "0". If the student is suspected of preparing the task not on his own, the teacher has the right to initiate additional verification or defense of this particular assessment element. Then such an assessment element will be graded based on the additional verification or the defense.
Quiz 1
Quizzes are held regularly in classes and based on previous homeworks. Quizzes can also include theoretical questions and definitionds from the previous lectures.
Bonus 1
Exam 2
At the end of the second and fourth modules the students pass a written exam. If plagiarism is detected, the assessment element will be assigned a score of "0". If the student is suspected of preparing the task not on his own, the teacher has the right to initiate additional verification or defense of this particular assessment element. Then such an assessment element will be graded based on the additional verification or the defense. Duration of the exam is 120 minutes.
Modterm 2
At the end of the 1st and 3rd modules (or at the beginning of the 2nd and 4th modules) the students have a written control work (midterm). If plagiarism is detected, the assessment element will be assigned a score of "0". If the student is suspected of preparing the task not on his own, the teacher has the right to initiate additional verification or defense of this particular assessment element. Then such an assessment element will be graded based on the additional verification or the defense. Duration of the midterms is 80 minutes.
Homework 2
During the year students have to do regular homeworks. Professors can ask students to present their written solutions orally. If plagiarism is detected, the assessment element will be assigned a score of "0". If the student is suspected of preparing the task not on his own, the teacher has the right to initiate additional verification or defense of this particular assessment element. Then such an assessment element will be graded based on the additional verification or the defense.
Quiz 2
Quizzes are held regularly in classes and based on previous homeworks. Quizzes can also include theoretical questions and definitionds from the previous lectures.
Bonus 2

Interim Assessment

2024/2025 2nd module
G(rade)=min[Round(0.35*Exam1+0.25*Midterm1+0.2*Homework1+0.2*Quiz1+Bonus1),10]
2024/2025 4th module
G(rade)=min[Round(0.35*Exam2+0.25*Midterm2+0.2*Homework2+0.2*Quiz2+Bonus2),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

Authors

GONCHARENKO VASILIY MIKHAYLOVICH

Course Syllabus