MV Resource Center

Download a complete formula sheet right here in PDF format! Five pages long, and every formula you should possibly need!

If you have a high-resolution printer, you might try these two 3x5 images with the complete formulas! (Side 1, Side 2) They look big on your screen because they are at 210 DPI; you need to print them out from Word or some program other than your browser for the proper sizing.

MV Suite 0.9 for the TI-89

Don't you wish you could do MV problems on your TI-89 calculator to “check your work” on tests? (Especially ones with some multiple-choice questions?) Well, now you can, thanks to my handy MV Suite!

Current features include:

• tvec(vectorfunc, variable) — Calculate unit tangent vector
• nvec(vectorfunc, variable) — Calculate unit normal vector
• bvec(vectorfunc, variable) — Calculate (unit) binormal vector
• grad(scalarfunc, variables) — Calculate the gradient of a scalar function
• div(vectorfunc, variables) — Calculate the divergence of a vector function
• curl(vectorfunc, variables) — Calculate the curl of a 2D or 3D vector function
• curv(vectorfunc, variable) — Calculate the curvature of a vector function
• curvfunc(scalarfunc, variable) — Calculate the curvature of a Cartesian equation
• laminacm(scalarfunc1, scalarfunc2, variable) — Calculate the center of mass of a planar lamina bounded by two Cartesian functions

Download MV Suite 0.9 here. Transfer it to your calculator with TI Connect software and the USB/Mini USB connector that came with your calculator. (Or use any USB/Mini USB connector; they often come with cameras too.) Move install() to a new folder called MV, and run it. It will create all the programs in the suite; you do not need to use it again.

Function Documentation:

tvec(vectorfunc, variable)

Returns the unit tangent vector to an any-dimensional vector function, with the specified variable as the parameter.

tvec([sin(t),cos(t),5],t) = [cos(t), -sin(t), 0]

nvec(vectorfunc, variable)

Returns the unit normal vector to an any-dimensional vector function,with the specified variable as the parameter.

nvec([sin(t),cos(t),5],t) = [-sin(t), -cos(t), 0]

bvec(vectorfunc, variable)

Returns the (unit) binormal vector to a three-dimensional vector function, with the specified variable as the parameter.

bvec([sin(t),cos(t),5],t) = [0, 0, -1]

grad(scalarfunc, variables)

Returns the gradient vector of a scalar function with respect to the specified variables.

grad(x*y*z,[x,y,z]) = [y*z, x*z, x*y]

div(vectorfunc, variables)

Returns the divergence scalar of an any-dimensional vector function with respect to the specified variables.

div([x*z,x*y*z,-y^2],[x,y,z]) = x*z + z

curl(vectorfunc, variables)

Returns the curl vector of a two- or three-dimensional vector function with respect to the specified variables.

curl([x*z,x*y*z,-y^2],[x,y,z]) = [-x*y-2y, x, yz]

curv(vectorfunc, variable)

Returns the curvature scalar of an any-dimensional vector function, with the specified variable as the parameter.

curv([cos(t),sin(t),t],t) = 1/2

curvfunc(scalarfunc, variable)

Returns the curvature scalar of a function in the Cartesian plane, with the specified variable as the independent variable.

curvfunc(x^2,x) = 2/(4x^2+1)^(3/2)

laminacm(scalarfunc1, scalarfunc2, variable)

Returns the (x,y) location of the center of mass of a planar lamina formed by the area in between the two Cartesian functions, with the specified variable as the independent variable. (Only works if the two functions have only two points of intersection.)

laminacm(0,4-x^2,x) = [0, 8/5]