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Problem $4.$

a$)$ Conduction : Say we have a rod $1$ m long which is at steady state. One end is $100$ C $,$ and the other is at $120$ C $.$ What is the temperature in the center?

b$)$ OK again for a bar. The left hand temp To is $120$ C $.$ Then stepping to the right, the next "point" $T_1$ is $115,$ the next $T_2$ is $109,$ then $T_3=107$ and so on to the end. Delta $x$ is $0\mathrm{.}1$ m

c$)$ What is the forward entered derivative for $\frac{de{l}^{2}T}{del{x}^2}$ at the left end at $x=0?$ Show this algebraically and the number itself.

d$).$ What is the center difference derivative for $\frac{de{l}^{2}T}{del{x}^2}$ at $T_1?$ Show this algebraically and the number itself.

e$)$ What is the backward difference derivative for $\frac{de{l}^{2}T}{del{x}^2}$ at $T_2?$ Show this algebraically and the number itself.