Courses

Differential and Integral Calculus ΙΙ

General

Course Contents

Course content: 1. Introduction to functions of two real variables, examples of graphical
representations, sphere, ellipsoid, paraboloid, cone, intersection of surfaces and planes, domain and
definition of continuity for z=f(x, y). 2. The concept of partial derivative, physical and geometric
interpretation, types and theorems of partial derivatives. The concept of total differential, higherorder partial derivatives. 3. Study of extrema, the problem of least squares, constrained extrema 4.
Double Integrals, their physical and geometric interpretation, properties, and methods of
computation. Types of integration domains 5. Double integrals, change of variables. Polar
Coordinates. Generalization of the Change of Variables Problem, moment of Inertia of a Plane
Surface. 6. Triple Integrals. Physical Interpretation. Properties and Computation Methods 7-9.
Fundamental knowledge of vector analysis: scalar and vector fields, vector functions. Derivative of a
vector function. Angular velocity. Uniform circular motion. Arc length of a curve. Derivative of z=f(x,y)
in a given direction. Integration of vector functions. Gradient of scalar fields. Divergence and curl of
vector fields 10-11. Line integrals (definition, properties and calculation methods). Path-independent
line integrals. Conservative vector fields. 12. Surface integrals (definition, properties and calculation
methods). 13. Stokes’ theorem and Gauss’s Divergence theorem

Educational Goals

Upon completing this course students should be able to use: functions of most variables and
recognize their graphic representations 2. The concepts of partial derivative and total differential 3.
The solving of double and triple integrals 4. Basic concepts of Differential Geometry 5. Line integrals
and surface integrals. 6. Implement the above in 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

ActivitySemester workload
Lectures52
Individual study52
Practice/exercises26
TOTAL130
Total260

Students Evaluation

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

Recommended Bibliography

  • Τερζίδης Χαράλαμπος, Λογισμός Συναρτήσεων πολλών Μεταβλητών & Διαφορικές
    Εξισώσεις, Εκδόσεις Ανικούλα, Θεσσαλονίκη 2006 ISBN: 9789605160319
  • Hass J., Heil C., Weir M.D., Απειροστικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης,
    Κρήτη 2015, 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, Σημειώσεις, Ηλεκτρονική Διεύθυνση:
    http://pde.teiser.gr/papaioannou/Mathimatika_2.asp
  • [In Greek]. Τερζίδης Χαράλαμπος, Λογισμός συναρτήσεων μιας μεταβλητής με στοιχεία διανυσματικής
    γραμμικής άλγεβρας, Εκδόσεις Χριστοδουλίδης, Θεσσαλονίκη 2006
    [In greek]. Hass J., Heil C., Weir M.D., Απειροστικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης,
    Κρήτη 2005, ISBN 978-960-524-515-3, Κωδικός στον Εύδοξο: 77107082
    [In greek]. 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
    [In greek} 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