User:Eml4500.f08.jamama.justin/HW6

Rube Goldberg Device: This is a device that accomplishes a simple task through many unnecessary steps, and in a very indirect fashion.

An example of this type of device can be seen in the following youtube link: []

NOTE: Honesty, imagination, ethics. It is always very important to do your own work, and not plagiarize other people's work. Honesty is the best policy.

Cont PVW to discrete PVW.

Lagrangian Interpolation.


 * Motivation for form of Ni(x) and Ni+1(x)

1) Mi(x) and Mi+1(x) are linear (straight lines), thus any linear combination of Ni and Ni+1 are also linear and in the particular expression for U(x) on Page 31-3.

$$N_{i}(x)=\alpha _{i}+\beta _{i}x $$ with $$(\alpha _{i},\beta _{i})$$ being numbers.

$$N_{i+1}(x)=\alpha _{i+1}+\beta _{i+1}x$$ Linear combo of Ni and $$(\alpha _{i},\beta _{i})$$ numbers.

$$N_{i+1}$$: $$N_{i}d_{i}+N_{i+1}d_{i+1}=(\alpha _{i}+\beta _{i}x)d_{i}+(\alpha _{i+1}+\beta _{i+1}x)d_{i+1}$$ $$=(\alpha _{i}d_{i}+\alpha _{i+1}d_{i+1})+(\beta _{i}d_{i}+\beta _{i+1}d_{i+1})x$$ is clearly a function of x.

2) Recall equation for U(x) (interp of U(x)) on Page 31-3:

$$U(x_{i})=N_{i}(x_{i})d_{i}+N_{i+1}(x_{i})d_{i+1}=d_{i}$$

=1 =0