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…

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…

Learn everything you need to know to get through Partial Derivatives and prepare you to go into Multiple Integrals with a solid understanding of what’s .

Two ideas for introducing functions - nuggetizer video (meh) and an activity: Ss figure out what the log function does (the calculator is a function machine). What's the range?

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

Learn everything you need to know to get through Partial Derivatives and prepare you to go into Multiple Integrals with a solid understanding of what’s .