Магистратура
2023/2024
Математический анализ
Статус:
Курс обязательный (Магистр по наукам о данных)
Направление:
01.04.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
1-й курс, 2 модуль
Формат изучения:
с онлайн-курсом
Онлайн-часы:
52
Охват аудитории:
для своего кампуса
Преподаватели:
Лукьяненко Никита Сергеевич
Прогр. обучения:
Магистр по наукам о данных
Язык:
английский
Кредиты:
3
Контактные часы:
10
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;
Course Contents
- 1: Introduction: Numerical Sets, Functions, Limits
- 2: Limits and Multivariate Functions
- 3: Derivatives and Linear Approximations: Single variate Functions
- 4: Derivatives and Linear Approximations: Multivariate Functions
- 5: Integrals: Anti-derivative, Area under Curve
- 6: Optimization: Directional derivative, Extrema and Gradient Descent
Assessment Elements
- Week Final Quizzes (weeks 1-5)Weekly Quizzes
- Practice Quizzes (week 6)
- SGA Open Question: Series
- First Week Extra Quiz
- SGA Open Question: Multivariate limit
- SGA Numerical Differentiation
- SGA Open Question: Extremum
- SGA Open Question: Chain Rule
- SGA Open Question: FTC
- SGA Numerical Integration
- Final Project
Interim Assessment
- 2023/2024 2nd module0.3 * Final Project + 0.02 * First Week Extra Quiz + 0.05 * Practice Quizzes (week 6) + 0.09 * SGA Numerical Differentiation + 0.09 * SGA Numerical Integration + 0.04 * SGA Open Question: Chain Rule + 0.04 * SGA Open Question: Extremum + 0.04 * SGA Open Question: FTC + 0.04 * SGA Open Question: Multivariate limit + 0.04 * SGA Open Question: Series + 0.25 * Week Final Quizzes (weeks 1-5)
Bibliography
Recommended Core Bibliography
- Friedman, A. (2007). Advanced Calculus (Vol. Dover edition). Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1153250
- James Stewart. (2016). Calculus, Early Transcendentals, International Metric Edition: Vol. Eighth edition, metric version. Cengage Learning.
- Jennifer F. Wood. (2015). Dowling, P. J., Festing, M., Engle Sr., A. D., International Human Resource Management (6th Edition), Cengage Learning EMEA, 2013. Management International Review, (4), 589. https://doi.org/10.1007/s11575-014-0236-1
Recommended Additional Bibliography
- William H. Press, Saul A. Teukolsky, William T. Vetterling, & Brian P. Flannery. (1992). Numerical Recipes in C: The Art of Scientific Computing. Second Edition. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.9CFCD6AE