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 parametricallydefined
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.

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], HealLink/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών.
[6]
H. Anton, I. Bivens, S. Davis, Calculus – Early Transcendentals (9^{th}
ed), John Wiley & Sons, 2009.
