Courses Catalogue

Syllabus of the course: General Mathematics II


In this web page we provide the syllabus of the course General Mathematics II, offered by the Department of Physics.
The list of the courses offered during the current accademic year is available here.
The list of all courses offered by the Department of Physics is available here.

CodeΦ-112
TypeA
ECTS7
Hours6
SemesterSpring
InstructorG.Athanasiu
ProgramMonday 9:00-11:00, Amphitheater Α
Wednesday 09:00-11:00, Amphitheater Α
Thursday, 13:00-15:00, Room 1
Web page
Goal of the courseThe course is intended for first year undergraduate students and its purpose is to give a rather complete working knowledge of differential and integral calculus of functions of two and more variables.
SyllabusVector calculus: Vectors, Vector spaces, scalar, exterior and mixed product. Lines and planes in 3-dimensional Euclidean space. Vector fields.
Curves: Parametric representation of curves, in two and three dimensions, velocity and acceleration, moving frame, curvature, torsion.
Functions of many variables: Definition of functions of two or more variables, limits, continuity, level surfaces. Partial derivatives, differential, differentiability .Taylor’s expansion of functions of many variables, extrema, extrema under constraints. Coordinate transformation, transformation of partial derivatives, application to the Special Theory of Relativity.Parametric representation of surfaces, curvilinear coordinates.
Multiple Integrals: Double integrals, triple integrals, curvilinear integrals, surface integrals, Theorems of Green, Stokes, and Applications in Physics.
Bibliography«THOMAS, Απειροστικός Λογισµός» –R. L. Finney, M.D. Weir, F.R. Giordano, (Τόµοι Ι & ΙΙ) – Μετάφραση Μ. Αντωνογιαννάκης
«Ανώτερα Μαθηµατικά», M.R. Spiegel.
«Διαφορικός και Ολοκληρωτικός Λογισµός» - M. Spivak.

University of Crete - Department of Physics - P.O Box 2208 - GR-71003 Heraklion, Greece
phone: +30 2810 394300 - fax: +30 2810 394301