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Regular version of the site

# Further Calculus

2019/2020
ENG
Instruction in English
5
ECTS credits
Course type:
Elective course
When:
3 year, 1, 2 module

### 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

#### Assessment Elements

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

#### Interim Assessment

• Interim assessment (2 module)
0.25 * December exam + 0.25 * home assignments + 0.25 * Mid-term test + 0.25 * UOL exam in May

#### Recommended Core Bibliography

• Advanced mathematical methods, Ostaszewski A., 2002