Math (quick) - still in progress

Quick tricks and identities for math (for quantum, math methods)

what is unit vector?

vector with length 1, indicates direction only

how to normalize a vector?

divide it by its magnitude

what does dot product measure?

what does ± signify

measures how much of one vector points in the direction of the other

positive means angle is <90,

negative means angle between 90 and 180 degrees

what does dot product = 0 mean?

vectors are orthogonal

even function: f(-x) = ____

f(x)

odd function: f(-x) = ____

-f(x)

even function: symmetry about which axis?

y -axis

odd function: symmetry about which axis?

the origin

x^n is even if ____, and odd if ____

n is even, n is odd

sin is ____(even or odd), cos is ____ (even or odd), tan is ____

sin is odd

cos is even

tan is

sum of two even functions is ____

sum of two odd functions is _____

even

odd

product: even * even =

odd * odd =

even * odd =

even

even

odd

derivative of even function is ____

derivative of odd function is ____

odd

even

gradient of function points in ____

steepest increase of function at that point

gradient is ____ to level curves and surfaces

perpendicular