The temperature T at (x,y,z) is given by T= 4x^2-y^2+16z^2.  Find the rate of change of T at P(4,-2,1) in the direction of 2i+6j-3k  In what direction does T increases most rapidly at P  In what direction does T decreases most rapidly at P  In what direction does T remains constant at P

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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.