Chapter 2
Vectors and Scalars
Introduzione agli scalari
Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts ...
Introduzione ai vettori
To define some physical quantities, there is a need to specify both magnitude as well as direction. For example, when the U.S. Coast Guard dispatches a ...
Componenti vettoriali nel sistema di coordinate cartesiane
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal ...
Coordinate polari e cilindriche
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on ...
Coordinate sferiche
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe ...
Algebra vettoriale: metodo grafico
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the ...
Algebra vettoriale: metodo dei componenti
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like ...
Prodotto scalare (prodotto scalare )
The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a ...
Prodotto vettoriale (prodotto incrociato)
Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of ...
Prodotti Scalari e Tripli Vettoriali
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the ...
Operatore Gradiente e Del
In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The ...
Divergenza e ricciolo
The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as ...
Derivate seconde e operatore di Laplace
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or ...
Integrali di linea, superficie e volume
A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a ...
Divergenza e teoremi di Stokes
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental ...
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