Analysis II

Semester:
3rd
Course Type:
Compulsory courses (YM)
Track:
-
Code:
Κ06
ECTS:
8
TEACHING HOURS per week
Theory:
4
Seminar:
2
Laboratory:
-
Specializations
Foundations of Computer Science (S1):
-
Data and Knowledge Management (S2):
-
Software (S3):
-
Hardware and Architecture (S4):
-
Communications and Networking (S5):
-
Signal and Information Processing (S6):
-
Related Courses
Prerequisites:
-
Expected Prior Knowledge:
Detailed Description
DIT_PPS_K06-CalculusII.pdf
Course Content
  • Vectors, vector functions, inner and outer product, lines, planes, surfaces, arc length, unit tangent vector, TNB frame, multivariable functions, derivatives, limit, continuity.
  • Partial derivatives, chain differentiation, directional derivative, tangent planes, linearization, differentials, extrema and saddle points.
  • Taylor's theorem for multivariable functions.
  • Curvilinear coordinate systems, norm, gradient, divergence and curl.
  • Double and triple integrals in Cartesian and other coordinates, applications to the evaluation of areas, moments of inertia and centers of mass, change of variables (Jacobian determinants).
  • Integration of vector fields, line and surface integrals, path independence, potential functions and conservative fields, Green, Gauss and Stokes theorems and applications.
LITERATURE AND STUDY MATERIALS - READING LIST
• Διανυσματικός Λογισμός, Marsden J., Α. Tromba, ΙΤΕ ΠΑΝ/ΚΕΣ ΕΚΔΟΣΕΙΣ ΚΡΗΤΗΣ, • Απειροστικός Λογισμός (σε έναν Τόμο), B. Tomas, ΙΤΕ ΠΑΝ/ΚΕΣ ΕΚΔΟΣΕΙΣ ΚΡΗΤΗΣ, • Απειροστικός Λογισμός σε πολλές μεταβλητές, Τ. Χατζηαφράτης, ΕΚΔΟΣΕΙΣ Σ.ΑΘΑΝΑΣΟΠΟΥΛΟΣ& ΣΙΑ Ο.Ε, • Εφαρμοσμένος Απειροστικός Λογισμός, Λ.Ν. Τσίτσας, ΕΚΔΟΣΕΙΣ Σ.ΑΘΑΝΑΣΟΠΟΥΛΟΣ& ΣΙΑ Ο.Ε, • Μαθηματικά ΙΙ, Β’ έκδοση, Θ. Μ. Ρασσίας, ΕΚΔΟΣΕΙΣ ΑΘ. ΤΣΟΤΡΑΣ
e-Class link
Ανάλυση ΙΙ - ECLASS