This course aims to provide to the students all those mathematical notions in order to develop and upgrade their mathematical way of thinking in understanding and problem solving. Following the successful completion of the course it is expected that the students are able to learn and to use mathematical tools such as differentiation and integration, sequences and series and basic elements of analytic and differential geometry in describing and problem solving.  

• Basic notions of functions (inverse function).
• Trigonometric and Hyperbolic functions and their inverse.
• Limit continuity and the differential of a function of one variable.
• Theorem L’ Hopital. Techniques of integration. Definite integral and its applications (plane area, length of a curve, volume of a solid of revolution).
• The improper integral. 
• The notion of  a sequence. Limit of a sequence. Infinite series.
• Criteria of series convergence.
• Power series and its radius of convergence. Taylor’s theorem.  Inner and outer product of vectors. Parametric equations of a line in 3‐dimensional space. Equation of plane.
• Polar coordinates.  Vector function and Curves. Velocity and acceleration. Curvature of a curve. Partial and directional derivative

Suggested Literature:
1. Απειροστικός Λογισμός, (ενιαίος Τόμος) Finney‐Weir‐Giordano, ΙΤΕ/Παν/κες Εκδόσεις Κρήτης.
2. Μ. Αδάμ, Ι. Χατζάρα, Ν. Ασημάκη, https://repository.kallipos.gr/handle/11419/6356.
3. Μαθηματική Ανάλυση Ι, Θ. Ρασσιάς, εκδόσεις Τσότρας
4. Μαθηματική Ανάλυση ΙΙ, Θ. Ρασσιάς, εκδόσεις Τσότρας

Greek

Lectures