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Бакалавриат 2020/2021

## Методы математического анализа

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

### Course Syllabus

#### Abstract

This course is a continuation of Calculus MT1 174 which is taught for the second-year students. It lasts for one (fall) semester. Upon completion of Further Calculus students will have to take the University of London (UoL) exam at the end of the fourth semester of their studies at ICEF.

#### 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

• handle the evaluation of the limits by performing changes of the variables/ employing Taylor; expansion and L’Hopitale rule
• approximate the value of definite integral by the upper and lower estimates of sums
• apply Direct Comparison and Limit Comparison Test enabling to assess the convergence of such integrals
• 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
• Appyly Laplace transform to the solution of differential equations

#### Course Contents

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

#### Assessment Elements

• home assignments
• mock
• December exam
• UoL exam

#### Interim Assessment

• Interim assessment (4 module)
0.3 * December exam + 0.15 * home assignments + 0.25 * mock + 0.3 * UoL exam

#### Recommended Core Bibliography

• Advanced mathematical methods, Ostaszewski A., 2002