Бакалавриат
2019/2020
Методы математического анализа
Статус:
Курс по выбору (Программа двух дипломов по экономике НИУ ВШЭ и Лондонского университета)
Направление:
38.03.01. Экономика
Кто читает:
Международный институт экономики и финансов
Где читается:
Международный институт экономики и финансов
Когда читается:
3-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Преподаватели:
Букин Кирилл Александрович
Язык:
английский
Кредиты:
5
Контактные часы:
64
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
- Enable students to acquire further skills in the techniques of calculus
- Prepare students for further courses in mathematics and related subjects like econometrics and actuarial science
- Enable understanding of the principles underlying the subject of calculus
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
- The Riemann integral
- Improper integrals
- Double integrals
- Manipulation of integrals. An introduction to the Lebesgue integral
- Laplace transforms