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Multivariable Calculus. This consists of 35 video lectures given by Professor Denis Auroux, covering vector and multi-variable calculus. Topics covered in this course include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.

from Foursquare

University of Minnesota - Twin Cities (University of Minnesota)

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.

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from Foursquare

University of Minnesota - Twin Cities (University of Minnesota)

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…

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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.

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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.

from Foursquare

University of Minnesota - Twin Cities (University of Minnesota)

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…

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