Math

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Cylindrical coordinate system diagram

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Cylindrical to rectangular coordinates

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Rectangular to cylindrical

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cos(2x)= ?

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cos(2x) = sin^2(x) - sin^(x)
cos(2x) = 2cos^2(x) - 1

cos(2x) = 1 - 2sin^2(x)

cos(2x) = ( 1 - tan^2(x) ) / ( 1 + tan^2(x) )

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Spherical coordinate system diagram

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Spherical to rectangular

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Rectangular to spherical

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Limit of a vector function

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cosh(x) = ?

sinh(x) = ?

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Derivative of Vector Function

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Differentiation of vector functions

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Integration of vector functions

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Rules of vector differentiation

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Unit tangent vector: T(t)

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Diagonal matrix

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Vector addition and scaling

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Matrix multiplication

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Row and column restriction on multiplying mxn and nxp

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n's must be equal. Columns of vector A must match rows of vector B.

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How many rows and columns will an mxn and nxp multiplication produce?

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mxp -> p rows and m columns

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Row column rule for computing vectors AxB

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Properties of vector multiplication

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Matrix multiplication warnings

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Matrix powers

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(A^0)x = identity

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Transpose of a matrix

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A^T = new matrix with rows and columns switched. Columns of A^T = rows of A.

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Transposed matrix examples

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Properties of transposed matrices

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Matrix inverse equality

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Singular vs nonsingular matrices

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Singular - not invertible

Nonsingular - invertible

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Formula for inverse of 2x2 matrix

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Linear ch.2.2 Theorem 5

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Linear ch.2.2 Theorem 6

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Product of nxn invertible matrices

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Elementary matrices from row operation

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Invertibility of elementary matrix

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Row equivalency of invertible matrices

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Finding A^(-1) -> (Inverse of matrix A)

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Invertible matrix theorem

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Invertible matrix theorem: a

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Invertible matrix theorem: b

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Invertible matrix theorem: c

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Invertible matrix theorem: d

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Invertible matrix theorem: e

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Invertible matrix theorem: f

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Invertible matrix theorem: g

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Invertible matrix theorem: h

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Invertible matrix theorem: i

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Invertible matrix theorem: j

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Invertible matrix theorem: k

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Invertible matrix theorem: l

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Invertible linear transformation

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Partial derivatives of z=f(x,y)

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How to do partial derivatives of z=f(x,y)

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Clairaut's theorem

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d/dx arctan(x)=?

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Differentiability of a function of 2 variables

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Chain rule for functions involving 1 independent variable.

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Chain rule for functions involving 2 independent variables.

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Implicit differentiation with 1 independent variable.

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Implicit differentiation with 2 independent variables.

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