Бакалавриат
2023/2024
Математический анализ
Статус:
Курс обязательный (Прикладной анализ данных)
Направление:
01.03.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
1-й курс, 1-4 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Преподаватели:
Голубев Максим Олегович,
Днестрян Андрей Игоревич,
Жуков Павел Владимирович,
Орел Ольга Евгеньевна
Язык:
английский
Кредиты:
10
Контактные часы:
136
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 ExamThe 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. 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.
- 4th module ExamThe 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. 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.
- 1st semester Regular activityDuring 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. 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.
- 2nd semester Regular activityDuring 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. 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.
- 1st semester bonus activityIf 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.
- 2nd semester bonus activityIf 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.
Interim Assessment
- 2023/2024 2nd moduleG(rade)=roundoff (min (0.4*Regular activity + 0.6*Exam +Bonus points, 10))
- 2023/2024 4th moduleG(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