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Магистратура 2023/2024

Математический анализ

Статус: Курс обязательный (Магистр по наукам о данных)
Направление: 01.04.02. Прикладная математика и информатика
Когда читается: 1-й курс, 2 модуль
Формат изучения: с онлайн-курсом
Онлайн-часы: 52
Охват аудитории: для своего кампуса
Прогр. обучения: Магистр по наукам о данных (о)
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

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

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

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

Assessment Elements

  • non-blocking Quizzes
  • non-blocking Final Project
  • non-blocking Exam
Interim Assessment

Interim Assessment

  • 2023/2024 2nd module
    There are no blocking parts in the grading, but you have to get at least 40% to pass the course. The passing grade is 4/10. Please note that in order to get a grade of 9 or 10, students who have scored at least 7 points for the course will be invited to write a written test paper. Grading formula: IF (T*0.7+P*0.3 >=7; T*0.7+P*0.3+EX*0.2; T*0.7+P*0.3). T - tests P - project EX - exam (written test paper) Based on the results of all tasks the accumulated assessment is calculated: 0.7*tests + 0.3*project. The exam is counted with a weight of 0.2 only if the tests + project after graduation on the scale give at least 7. The connection between percents of completion and your grade will be found according to the following table: 1-10 1 2 3 4 5 6 7 8 min % 0 15 30 40 55 70 80 90
Bibliography

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

Authors

  • Боднарук Иван Иванович
  • Burova Margarita Borisovna