1st semester

Course: Mathematical Analysis I

Description:

Course title

Mathematical Analysis Ι

Course code

ΜΚ1

Course type

Compulsory

Course level

Undergraduate (first cycle)

Year of studies

1st

Semester

1st

ECTS Credits

5

URL

eclass.uowm.gr/courses/ICTE108/

Hours per week

4

Course content

Sets. Real numbers. Sequences of real numbers. Series of real numbers. Real functions of a single variable. Limits and continuity. Derivatives. Application of derivatives. Indefinite and definite integrals, improper integrals. Applications of integration. Power series.

Expected 
learning outcomes and competences to be acquired

Upon successful completion of this course, students will be able:

  • to examine the convergence of real sequences, series, as well as power series,
  • to calculate infinite sums,
  • to study real functions of one variable,
  • to differentiate parametrically-defined and implicit functions,
  • to determine lines tangent to plane curves that are described in different ways,
  • to calculate indefinite, definite, and improper integrals,
  • to use polar coordinates,
  • to calculate the area between curves, and the length of plane curves,
  • to approximate functions with polynomials.

Prerequisites

None

Teaching methods

Lectures, exercises

Assessment methods

Written final exam (100%)

Language of instruction

Greek

Recommended bibliography

[1]     R. L. Finney, M. D. Weir, F. R. Giordano, Απειροστικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης, 2012.

[2]     F. Ayres, Διαφορικός και Ολοκληρωτικός Λογισμός, Κλειδάριθμος, 2008.

[3]     Θ. Ρασσιάς, Μαθηματική ανάλυση I, ΣΥΜΕΩΝ, 2011.

[4]     Brand, Louis Μαθηματική ανάλυση, Εκδόσεις Ι. Συμεών , 1984

[5]     Ghorpade, Sudhir R.Limaye, Balmohan V., A Course in Calculus and Real Analysis [electronic resource], Heal-Link/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών.

[6]     H. Anton, I. Bivens, S. Davis, Calculus – Early Transcendentals (9th ed), John Wiley & Sons, 2009.



Lecturer: Balassas Konstantinos