Advanced Mathematics an der IUBH Internationale Hochschule

f(x)=f(x+T)

with T as one unit, e.g. one period

A vector field relates a vector to every point in a given area A.

OR

A vector field is a vector-valued function that associates a vector with each element in the domain of the function.

F[y]=$\int_{a}^{b} y(x)dx

i=(1,0) and j(0,1)

standard unit vectors

any vector in two-dimensional space can be expressed as a linear combination of i and j.

A*cos(ax)

-a*sin(ax)

Functionals are maps from a set of functions to the set of real numbers. In this sense, functionals are functions of functions.

ln(ax)=ln(a)+ln(x)

-> ln(ax)' = 1/x

f(u(x))=df/dx=df/du*du/dx

The main idea is to express the signal as a sum of sine and

cosine components of varying amplitude and frequency.

a/cos^2(ax)

...the same magnitude but opposite direction.