| Area of Mathematics: | Analysis | ||
| Semester: | 3ο | ||
| Course ID: | 31101 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 4 | Practice: 2 | Laboratory: 0 |
| ECTS : | 7 | ||
| Eclass: | For the course’s material, click here. | ||
| Instuctors: | Michail Markellos | ||
Description
- The Topology of Euclidean space: Sequences, open, closed, bounded and compact sets, set boundary.
- Convergence of vector functions of several variables: Limits , continuity, properties of continuous functions, polygonal connected and parametrized connected sets, the fundamental theorems of continuous functions, uniform continuity.
- Derivative of vector-valued functions, partial derivative, (total) derivative, tangent line, tangent plane.
- Basic Theorems of Differential Calculus.
- Function study. Critical,local maximum, minimum and saddle points. Absolute extremes of a real function, maximum-minimum theorem. Conditional extremes and Lagrange multipliers.
- Double and triple integral: Definitions and properties, area and volume calculations, integration techniques, change of variables with polar, cylindrical and spherical coordinates. Applications.
- Curvilinear integrals: parametrized curves, length of parametrized curve, definitions and properties of curvilinear integrals, calculations of curvilinear integrals, conditions of independence. Applications.
- Green’s Theorem.
Bibliography
- Marsden-A.Tromba , Vector Calculus , 3rd edition , Freeman and Company 1988
- Lang , Calculus of Several Variables , 3rd edition , Springer-Verlag 1987
