Materials expand when heated. Consider a metal rod of length Lo at temperature To. If the temperature is changed by an amount t:,. T, then therod's length approximately changes by t:;.L = aLot:;.T, where a is the thermal expansion coefficient and t:,. T is not an extreme temperature change. For steel, a = 1.24 X 10- 5 0 c- 1.(a) A steel rod has length Lo = 40 cm at To = 40°C. Find its length at T = 90°C.(b) Find its length at T = 50°C if its length at To= 100°C is 65 cm.( c) Express length L as a function of T if Lo = 65 cm at To = 100°C.

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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.