Further Calculus

2020/2021

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. 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
• Midterm
• UoL exam

Interim Assessment

• Interim assessment (4 module)
  0.15 * home assignments + 0.35 * Midterm + 0.5 * UoL exam

Bibliography

Recommended Core Bibliography

• Advanced mathematical methods, Ostaszewski, A., 2002

Recommended Additional Bibliography

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