Code
Φ-112
Level
Undergraduate
Category
A
Teacher
D. Antypas
ECTS
7
Hours
2
Semester
Winter
Display
Yes
Offered
Yes
Teacher Webpage
Goal of the course
The 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.
During the fall semester to course is offered in the form of selfstudy with only one two-hour lecture per week for the students that did not pass it during the spring semester. Emphasis is given in problem solving.
During the fall semester to course is offered in the form of selfstudy with only one two-hour lecture per week for the students that did not pass it during the spring semester. Emphasis is given in problem solving.
Program
Thuesday, 09:00-11:00, Room 3
Syllabus
Parametric equations and polar coordinates
Parametric representation of curves on the plane, calculus with parametric curves, polar coordinates, graphic representation of functions, areas and lengths or curves, conic sections. [1.5 weeks]
Vectors and the geometry of space
Coordinate systems in three dimensions, vectors, scalar and vector product, lines and planes, cylinders and surfaces of second order [1.5 weeks]
Vector functions and movement in space
Curves in space, integrals of vector functions, length of an arc, curvature and normal vectors of a curve, velocity and acceleration. [1 week]
Partial derivatives
Functions of many variables, limits, continuity, partial derivatives, chain rule, directional derivatives, gradient, tangent planes, extrema and saddle points, Lagrange multipliers, Taylor expansion, functions with constrained variables. [2 weeks]
Multiple integrals
Double and triple integrals and applications [3 weeks]
Integrals and vector fields
Line integrals, vector fields, work, circulation, flux, conservative fields, Green’s theorem on the plane, surface integrals, Stokes theorem, divergence theorem. [3 weeks]
Course review and in class problems
[1 week]
Parametric representation of curves on the plane, calculus with parametric curves, polar coordinates, graphic representation of functions, areas and lengths or curves, conic sections. [1.5 weeks]
Vectors and the geometry of space
Coordinate systems in three dimensions, vectors, scalar and vector product, lines and planes, cylinders and surfaces of second order [1.5 weeks]
Vector functions and movement in space
Curves in space, integrals of vector functions, length of an arc, curvature and normal vectors of a curve, velocity and acceleration. [1 week]
Partial derivatives
Functions of many variables, limits, continuity, partial derivatives, chain rule, directional derivatives, gradient, tangent planes, extrema and saddle points, Lagrange multipliers, Taylor expansion, functions with constrained variables. [2 weeks]
Multiple integrals
Double and triple integrals and applications [3 weeks]
Integrals and vector fields
Line integrals, vector fields, work, circulation, flux, conservative fields, Green’s theorem on the plane, surface integrals, Stokes theorem, divergence theorem. [3 weeks]
Course review and in class problems
[1 week]
Bibliography
«THOMAS, Απειροστικός Λογισµός» – J. Haas, Ch. Heil, M.D. Weir., (14η έκδοση 2018)
«Ανώτερα Μαθηµατικά» Spiegel, εκδόσεις ΕΣΠΙ (Shaum)
«Διανυσματικός Λογισμός» – J. E. Marsdern, A.J. Tromba, (6η έκδοση, ΠΕΚ)
«Ανώτερα Μαθηµατικά» Spiegel, εκδόσεις ΕΣΠΙ (Shaum)
«Διανυσματικός Λογισμός» – J. E. Marsdern, A.J. Tromba, (6η έκδοση, ΠΕΚ)
