Элементы теории поля. Шпаргалк

Field theory is a large section of physics, mechanics, and mathematics, in which scalar, vector, and tensor fields are studied. The mathematical core of field theory is such concepts as gradient, flow, potential, divergence, rotor, circulation, and others. A field is a region of V space, at each point of which a value of a certain value is determined. If each point M of this region corresponds to a certain number U = U (M), it is said that a scalar field (or point function) is defined (set) in the region.

Content:
- Classification of vector fields - solenoidal, potential and harmonic
- Field definition
- Geometric characteristics
- The flux of the vector through the surface σ
- Divergence of a vector field
- Relationship between characteristics
- Vector field circulation
- Vector field rotor
- Relationship between characteristics
- Geometric characteristics of a scalar field
- The derivative of the function u = ƒ (x, y, z) in the direction of the vector s
- The gradient of the function u = ƒ (x, y, z)
- Relationship between characteristics