User:Eml4500.f08.RAMROD.A/MyContributionHW6

Ethics, Honesty and Imagination
It is always important to take a moment to remember the importance of being creative and imaginative. However, we must focus on our own creativity and not plagiarize the works of others. We cannot grow if we simply copy the imagination of others.

Rube Goldberg Device
Here is an impressive Rube Goldberg Device to inspire the creative mind in all. Rube Goldberg devices are impressive, complicated machines designed to do simple tasks - a show of human imagination.

Conversion of PVW to Discrete PVW
a look at Ni(x) and Ni+1(x)

Ni(x) and Ni+1(x) are linear functions and thus any linear conversion of Ni(x) to Ni+1(x) is also linear.

The following expressions illustrate the conversion:

$$ N_i(x)=\alpha_i+\beta_{i}x $$

$$ N_{i+1}(x)=\alpha _{i+1}+\beta_{i+1}x $$

we will use di to to create the following expression:

$$ N_id_i+N_{i+1}d_{i+1}=(\alpha_i+\beta_ix)d_i+(\alpha_{i+1}+\beta_{i+1}x)d_{i+1}

= (\alpha_id_i+\alpha_{i+1}d_{i+1}) + (\beta_id_i+\beta_{i+1}d_{i+1})x $$

The above is clearly a linear function in x

Images of Ni and Ni+1
images of Ni(x) and right: Ni+1(x)