Jacobian, Jacobian Determinant, Derivation of Jacobian Determinant, Jaco...

JACOBIAN


Let u, v are function of variables of x, y then the determinant ...

Maxima and Minima of Several Variables Example 2, Extrema of Functions o...

EXTREMA OF FUNCTIONS OF SEVERAL VARIABLES -- MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES

Let we have the function f(x,y) which have two variables x and y. We have to get the maxima and minima means either it is maxima or minima.

Maxima and Minima of Several Variables Example 1, Extrema of Functions o...

EXTREMA OF FUNCTIONS OF SEVERAL VARIABLES -- MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES

Let we have the function f(x,y) which have two variables x and y. We have to get the maxima and minima means either it is maxima or minima.

Maxima and Minima of Several Variables Example 3, Extrema of Functions o...

EXTREMA OF FUNCTIONS OF SEVERAL VARIABLES -- MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES

Let we have the function f(x,y) which have two variables x and y. We have to get the maxima and minima means either it is maxima or minima.

Approximation of Errors, Linear Approximation Errors

APPROXIMATION OF ERROR -- APPROXIMATION ERROR

Let x be a any physical quantity then ∂x is said to be say error in the present quantity x.or we can also say that ∂x is error which is known as Approximation Error. Now

∂x                                               Absolute Error
(∂x )/x                                         Relative Error
(∂x )/x  ×100                               Percentage Error

Jacobian Properties, Jacobian Chain Rule, Introduction to Jacobian Prope...

JACOBIAN PROPERTIES -- CHAIN RULE JACOBIAN

If u, v are the function of r, s and r, s be the functions of x, y then
(∂(u,v))/(∂(x,y))= (∂(u,v))/(∂(r,s))  ×  (∂(r,s))/(∂(x,y))

This is also called Chain Rule Property of Jacobian.

Langevin Theory of Diamagnetism, Langevin Theory, Langevin's Magnetism

LANGEVIN THEORY OF DIAMAGNETISM

Diamagnetic substances are those which placed in an external magnetic field become weekly magnetized in a direction opposite to the magnetic field direction. So, Diamagnetic material possesses a small value of negative susceptibility which is independent of temperature.
Let us consider the case of single electron of charge e moving in circular orbit in an atom so the equivalent current of a single electron will be
                            I = ev
V is the angular frequency of electron motion.