Bachelor
2024/2025
Calculus
Type:
Compulsory course (Data Science and Business Analytics)
Area of studies:
Applied Mathematics and Information Science
Delivered by:
Big Data and Information Retrieval School
Where:
Faculty of Computer Science
When:
1 year, 1-4 module
Mode of studies:
offline
Open to:
students of one campus
Language:
English
ECTS credits:
10
Contact hours:
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
- Exam 1At 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 1At 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 1During 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 1Quizzes 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 2At 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 2At 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 2During 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 2Quizzes 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 moduleG(rade)=max[Round(0.35*Exam1+0.25*Midterm1+0.2*Homework1+0.2*Quiz1+Bonus1),10]
- 2024/2025 4th moduleG(rade)=max[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