Assume, that Fourier transform of and  do exist, that are denoted by and respectively.

We know, that and

.

Choose the true statements from the below list.

In the following initial value problems we would like to apply Euler method with step size . We would like to get the approximation of the solution function at .

Match the initial value problems with the corresponding esimation values. (Applying previous notation: Determine the value of .) 

Assume that the radius of convergence of  is 2. 

Then, the previous power series is necessarily convergent at 2. 

Select even functions from the foloowing ones.

We know that can be expressed in the following Fourier-serie:

Match up , and with the correct expressions that define them!

Select the odd functions from the below list!

We know that the Fourier serie of can be written as follows

The period of is 1.

We know that the Fourier serie of can be written as follows

The period of is 3.

We know that can be expressed in the following Fourier-serie:

Match up , and with the correct expressions that define them!

Select which of the following functions are odd.