Calculus II (2ΚΠ01)
Instructor : Maria Adam
Course typeCompulsory
Semester2
TermSpring Semester
ECTS5
Teaching hours4
Laboratory hours
Description
• Euclidean space Rn. Neighborhoods. Classification of points of Rn . Open and closed sets. Sequences. Basic theorems. • Functions of several variables. Limit of a function. Operations with limits. Continuous function. Properties of continuous functions. Partial derivatives. Partial derivatives of higher order. Differentiable function. Total differentials. Differentials of higher orders. Differentiation of composite functions. Implicit functions. Jacobians. Transformations. Inverse transformations. Directional derivatives. The mean-valued theorem and Taylor’s theorem for several functions. Extreme values. Extreme values under constraints. • Double and triple integrals. •Scalar and vector fields. Gradient, Divergence and Curl. Line integral of first kind and second kind. Green’s formula. Surface integral of the first and second kind. Stokes’ theorem. Gauss’ theorem. Conservative field. Solenoidal field.
Course objectives

The course aims to teach theorems and rules, to develop critical and analytical thinking so that interdisciplinary problems could be modelled and solved with mathematical accuracy and discipline.

Upon successfully completing this course the student should:

  • understand the fundamental concepts of function of several variables, such as the limit, the continuity, the partial derivative, the differential, synthesise and apply the properties of these concepts in the study of the extreme points of a real function of several variables.
  • have knowledge of the theoretical background for the study of double, triple and generalized integral of a real function of several variables and be able to apply the methods for calculating these  integrals.
  • have knowledge of the theory and methodology so as to calculate one line and surface integral, which can apply to problems such as area of a surface, work along a curve, etc.

The course aims at the acquisition of knowledge, ideas and skills that are to be implemented in other courses related to Informatics and Biomedicine.

Textbooks/Bibliography
  • Καδιανάκης Ν., Καρανάσιος Σ., Φελλούρης Α., Ανάλυση ΙΙ – Συναρτήσεις Πολλών Μεταβλητών, Νικ. Καδιανάκης, έκδοση 8η, 2009, Αθήνα.
  • Τσίτσας Λ., Εφαρμοσμένος Διανυσματικός Απειροστικός Λογισμός - Β' Έκδοση, εκδόσεις  Μ. Αθανασοπούλου-Σ.Αθανασόπουλος Ο.Ε., έκδοση 2η, 2003, Αθήνα.
  • Κωνσταντινίδου Μ., Σεραφειμίδης Κ., Λογισμός Συναρτήσεων Πολλών Μεταβλητών και Διανυσματική Ανάλυση, "σοφία" Ανώνυμη Εκδοτική & Εμπορική Εταιρεία, έκδοση 1η , 2012, Θεσσαλονίκη.
  • Φιλιππάκης Μ., Εφαρμοσμένη Ανάλυση και Θεωρία Fourier, εκδόσεις Μιχ. Φιλιππάκης, έκδοση 1η, 2014, Αθήνα.
  • Finney R.L., Weir M.D., Giordano F.R., Απειροστικός Λογισμός (σε έναν τόμο), Πανεπιστημιακές Εκδόσεις Κρήτης, ΙΤΕ, έκδοση 1η, 2012, Ηράκλειο Κρήτης.
Assessment method
Mandatory written exams at the end of the semester.
Course material
http://eclass.uth.gr/eclass/courses/DIB124/