Mathematical Analysis I

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.

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.

None

Written intermediate exam (25%), written final exam (75%).

• R. L. Finney, M. D. Weir, F. R. Giordano, Απειροστικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης, 2012.
• F. Ayres, Διαφορικός και Ολοκληρωτικός Λογισμός, Κλειδάριθμος, 2008.
• Θ. Ρασσιάς, Μαθηματική ανάλυση I, ΣΥΜΕΩΝ, 2011.
• Brand, Louis Μαθηματική ανάλυση, Εκδόσεις Ι. Συμεών , 1984
• Ghorpade, Sudhir R.Limaye, Balmohan V., A Course in Calculus and Real Analysis [electronic resource], Heal-Link/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών.
• H. Anton, I. Bivens, S. Davis, Calculus – Early Transcendentals (9th ed), John Wiley & Sons, 2009.