A rod of length L coincides with the interval [0, L] on the x-axis. Set up the boundary-value problem for the temperature u(x,t). a)The left end is held at temperature u0 , and the right end is held at temperature u1. The initial temperature is f(x) throughout. b)The left end is held at temperature 100°C, and there is heat transfer from the right end into the surrounding medium at temperature zero. The initial temperature is f(x) throughout.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.