Course Information
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.
| Code | Φ-112 |
|---|---|
| Title | General Mathematics II |
| Category | A |
| ECTS | 7 |
| Hours | 6 |
| Level | Undergraduate |
| Semester | Spring |
| Teacher | A. Porfyriadis |
| Program |
Monday 9:00-11:00, Amphitheater ST Wednesday 09:00-11:00, Amphitheater ST Thursday, 9:00-11:00, Amphitheater ST |
| Course Webpage | https://eclass.physics.uoc.gr/courses/PH112/ |
| 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. |
| 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] |
| 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) |
