Master
2024/2025
Calculus
Type:
Compulsory course (Master of Data Science)
Delivered by:
Big Data and Information Retrieval School
When:
1 year, 2 module
Open to:
students of one campus
Instructors:
Andrey Subochev
Language:
English
Course Syllabus
Abstract
Mathematical analysis (differential and integral calculus of numerical functions of one and several numerical variables) is the study of the mutual influence of quantitative quantities that change continuously. By defining the operations of differentiation and integration, mathematical analysis provides researchers and practitioners with effective methods of working with continuous mathematical models that describe structures and processes in nature, man, or society in the language of functions. Since modern, rational management is unthinkable without the use of mathematical models, basic knowledge of mathematical analysis is necessary both for independent solution of economic, engineering and other tasks, and for understanding the methods and results of their application by other people. In addition, the study of mathematical analysis develops the ability to think logically, increases the intellectual level and expands the general cultural horizons of a person.
Learning Objectives
- • acquisition by students of basic knowledge on differential calculus of functions of one and several real variables; familiarization with a range of standard problems of mathematical analysis and basic methods of their solution;
- • formation of the ability to apply the methods of differential calculus to solve various problems, including those arising in other disciplines, as well as the ability to evaluate the results of their application;
- • formation of rigorous logical thinking skills through working with abstract concepts of higher mathematics; raising the intellectual level and expanding the general cultural horizons of students.
Expected Learning Outcomes
- Calculate discrete limit and the limit of sequences
- Learn asymptotic comparison of functions, Big- and little-o notations, famous important limits
- Calculate function's derivative
- Learn derivatives of single and multi-variate functions
- Learn indefinite and definite integration
- Learn principle differences of functions of several variables
- Construct machine learning models on the proposed data sets in Python.
- Evaluate performance of the models.
- Build features suitable for the selected machine learning models.
- Tune models to improve prediction and classification performance of the models.
- • find derivatives of elementary functions using differentiation formulas.
- • reproduce and apply the properties of degree, exponent, logarithm, as well as basic formulas of trigonometry in solving problems.;
- • plot basic elementary functions (degree, exponent, logarithm, sine, cosine, tangent, arcsin, arctangent);
- • solve linear and quadratic equations and inequalities, systems of equations and systems of inequalities;
- • independently perform arithmetic calculations with natural numbers within the first hundreds, perform arithmetic calculations with simple fractions;
- • solve standard problems of differential calculus of functions of one and several real variables using the specified method.
- • еxplain the statements of definitions and theorems by giving examples and counterexamples;
- • formulate definitions of basic concepts and basic theorems of differential calculus of functions of one and several real variables;
Interim Assessment
- 2024/2025 2nd moduleThe final grade in the discipline (TOTAL) is calculated as the weighted sum of the arithmetic average of 10 points for mini-control work (MCW) and 10 points for the exam paper (EXAM). TOTAL=0.08*MCW1+0.08*MCW2+0.08*MCW3+0.08*MCW4+0.08*MCW5+0.6*EXAM
Bibliography
Recommended Core Bibliography
- Демидович, Б. П. Сборник задач и упражнений по математическому анализу : учебное пособие для вузов / Б. П. Демидович. — 24-е изд., стер. — Санкт-Петербург : Лань, 2022. — 624 с. — ISBN 978-5-8114-9078-3. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/184105 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.
- Математический анализ в вопросах и задачах, учебное пособие, под ред. В. Ф. Бутузова, 4-е изд., испр., 480 с., Бутузов, В. Ф., Крутицкая, Н. Ч., Медведев, Г. Н., Шишкин, А. А., 2001