Divergence Theorem: The value of the integral over the boundary ∂S of a simple, solid, outwardly oriented region S, whose components have continuous partial derivatives, is related to the volume that surface encloses. This theorem can be used to find the electric field strength at a certain point from a charged particle. The surface S must enclose the charge.

Stoke's Theorem: The value of the line integral along a simple, closed, piecewise-smooth, positively oriented curve C, is related to the area of the surface C encloses. F must have continuous partial derivatives on a region in ℝ³. Stoke's theorem can be used to find the magnetic field strength a given distance from a straight wire (Ampere's law). C would represent the circumference of an imaginary circle at a constant distance around the wire, and the right side of the equation would be…

Differential equations are those types of equations that have some derivatives of certain functions. The derivatives can either be ordinary derivatives or partial derivatives. If there are only ordinary derivatives in the equation then, the equation is defined as the ordinary type of differential equation and if the equation has all its terms as partial derivative then, such type of equation is called as partial differential equation.

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. #Glogster #PartialDerivatives

First Order Partial Derivatives of f(x, y) = ln(x^4 + y^4)

First Order Partial Derivatives of f(x,y) = x^4 + 6x^2y^2 + 2y^3 - 3x^2

Green's Theorem: The value of the integral along a simple, closed, positively oriented, and piecewise-smooth curve C is related to the area it encloses by this equation. For this to be true, P and Q must also have continuous partial derivatives. Green's Theorem is a special case of Stoke's Theorem and can be used to calculate the areas of complicated shapes i.e. lakes, bacteria cultures,... Planimeters are devices that engineers frequently use to find areas and they are built using the…

Partial derivatives are so called because they're the derivatives of multivariable functions. When a function is defined in terms of two or more variables, the function's derivative is actually a collection of partial derivative equations.