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Mathematics ΙΙ
Teaching Staff: To be announced
Course Code: ΤΠ-2002
Course Type: Compulsory
Course Level: Undergraduate
Course Language: Greek
Semester: 2nd
ECTS: 5
Teaching Units: 4
Teaching Hours: 4
Short Description:
- The simplest Differential Equations (DE).
- Practical examples and physical interpretation of DE solutions.
- Types and notation of Differential Equations. DEs of separated variables, linear DEs of 1st and 2nd
- An example application of DEs in some problems of increased environmental and technological significance (bodies free fall with resistance, the time evolution of pollutants concentration in a lake or a semi-enclosed basin, oscillations, mechanical sensors of 1st and 2nd order, time evolution of electrical charge production in a photovoltaic cell, R-L-C circuit behaviour).
- Vectors, practical use, definition, and designation. Vector components, coordinates, directional angles, and magnitudes. Vectors addition and difference.
- Multiplication of a scalar and a vector (and examples from Physics). Vectors dot (interior) product and physical interpretation.
- Vectors cross (exterior) product and applications. Scalar and Vector fields.
- Field mapping methods. The gradient of a scalar field and physical interpretation.
- Divergence of a vector field and physical interpretation.
- Gradient analytical computation and geometrical specification on a two-dimensional scalar field. Introduction to vector fields flows, the Stoke’s and Green’s theorems and their physical meaning.
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