Further Calculus

2021/2022

Учебный год

ENG

Обучение ведется на английском языке

4

Кредиты

Кто читает:

Международный институт экономики и финансов

Статус:

Курс обязательный

Когда читается:

3-й курс, 3, 4 модуль

Преподаватели

Букин Кирилл Александрович

Галыбин Александр Николаевич

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

• - 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

• 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

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

Assessment Elements

• home assignments
• Mid-term test
• UOL exam in May

Interim Assessment

• 2021/2022 4th module
  0.15 * home assignments + 0.5 * UOL exam in May + 0.35 * Mid-term test

Bibliography

Recommended Core Bibliography

• Advanced mathematical methods, Ostaszewski, A., 2002

Recommended Additional Bibliography

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