Differential and Integral Calculus Ι

General

• Code: ΓΕΝ001
• Semester: 1st
• Study Level: Undergraduate
• Course type: General Background
• Teaching and exams language: Ελληνικά
• The course is offered to Erasmus students
• Teaching Methods (Hours/Week): Lectures (4)
• ECTS Units: 5
• Instructors: Papaioannou Stauros
• Coordinator: Papaioannou Stauros
• Exams Schedule:
  • 12/06/2026, 09:00 - 11:00:

Course Contents

Course presentations: 1. Sets of numbers (natural, real, integer). Complex numbers (definition,
complex plane, trigonometric form of a complex number, De Moivre’s theorem, exponential form,
Euler’s formula). 2. The cartesian coordinate system, functions of a real variable, polynomial
functions, properties. 3-4. Functions of a real variable, exponential and logarithmic functions,
hyperbolic functions, properties, periodic functions, trigonometric and inverse circular functions, the
concept of limit and the definition of a function of a real variable 5. The concept of derivative of a
number and the derivative of a real variable 6-7. Derivative of a composite function, derivative of
inverse functions, higher order derivatives, fundamental theorems, conclusions about f(x) derived
from the first and second derivatives, extrema. Taylor and Maclaurin series, vector functions and
their derivatives 8. Indefinite Integration, definition, basic types, and properties, methods of
integration. 9. Methods of indefinite integration 10. Definite integration 11. Generalized integrals,
integrals with variable limits and their differentiation, integration of functions defined on two
intervals, integrals in polar coordinates, volume of a solid of revolution 12-13. Application of definite
integration on the field of Civil Engineering.

Educational Goals

Upon completing this course students should be able to use: 1. Sets of numbers with an emphasis on
complex numbers 2. The real functions of a real variable (definition, limits, continuity) 3. Basic
concepts of calculus 4. Basic concepts of differential calculus 5. Their implementations on the field of
Civil Engineering.

General Skills

The course contributes to the following skills:
– Working independently
– Production of free, creative and inductive thinking

Teaching Methods

Face to face

Use of ICT means

Poweroint presentations, Excel, Matlab/Octave, E-learning
platform for educational material.

Teaching Organization

Students Evaluation

Final written examination
– open-ended questions (30-40%)
– problem – solving questions (70-60%)

Recommended Bibliography

• Τερζίδης Χαράλαμπος, Λογισμός συναρτήσεων μιας μεταβλητής με στοιχεία διανυσματικής & γραμμικής άλγεβρας, Εκδόσεις Χριστοδουλίδης, Θεσσαλονίκη 2006
• Hass J., Heil C., Weir M.D., Απειροστικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης, Κρήτη 2005, ISBN 978-960-524-515-3, Κωδικός στον Εύδοξο: 77107082
• Μπράτσος Αθανάσιος, Μαθήματα Ανώτερων Μαθηματικών, ISBN 978-960-603-030-7, [ηλεκτρ. βιβλ.] Αθήνα: Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, Ηλεκτρονική Διεύθυνση: https://repository.kallipos.gr/handle/11419/424
• Παπαϊωάννου Σταύρος, Βογιατζή, Δέσποινα, Μαθηματικά Ι, ISBN 978-960-603-427-5, [ηλεκτρ. βιβλ.] Αθήνα: Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, Ηλεκτρονική Διεύθυνση: https://repository.kallipos.gr/handle/11419/4551