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Бакалавриат 2022/2023

Методы математического анализа

Направление: 38.03.01. Экономика
Когда читается: 3-й курс, 3, 4 модуль
Формат изучения: с онлайн-курсом
Онлайн-часы: 16
Охват аудитории: для своего кампуса
Язык: английский
Кредиты: 4
Контактные часы: 56

Course Syllabus

Abstract

This course is a continuation of Calculus MT1 174 which is taught for the second-year students. It lasts for one (spring) semester.
Learning Objectives

Learning Objectives

  • - to enable students to acquire skills in additional topics of calculus and help them to acquire math knowledge sufficient to apply for economic modeling, - to prepare students for further courses in mathematics.
Expected Learning Outcomes

Expected Learning Outcomes

  • apply Direct Comparison and Limit Comparison Test enabling to assess the convergence of such integrals
  • approximate the value of definite integral by the upper and lower estimates of sums
  • Appyly Laplace transform to the solution of differential equations
  • change the variables technique along with the change in order of integration in repeated integrals
  • check the uniform convergence of the improper integrals with parameter, manipulations include: differentiation and integration with respect to parameter along with the continuity of such integrals
  • handle the evaluation of the limits by performing changes of the variables/ employing Taylor; expansion and L’Hopitale rule
Course Contents

Course Contents

  • Limits
  • Improper integrals
  • Laplace transforms
  • Manipulation of integrals. An introduction to the Lebesgue integral
  • Double integrals
  • The Riemann integral
Assessment Elements

Assessment Elements

  • non-blocking Home assignments
  • non-blocking Exam
Interim Assessment

Interim Assessment

  • 2022/2023 4th module
    0.7 * Exam + 0.3 * Home assignments
Bibliography

Bibliography

Recommended Core Bibliography

  • Advanced mathematical methods, Ostaszewski, A., 2002

Recommended Additional Bibliography

  • Calculus : concepts and methods, Binmore, K., 2001

Authors

  • BUKIN KIRILL ALEKSANDROVICH