Applications of partial differentiation

Fluid mechanics, heat and mass transfer, and electromagnetic theory are all modeled by partial differential equations and all have plenty of real life applications.

For example,

• Fluid mechanics is used to understand how the circulatory system works, how to get rockets and planes to fly, and even to some extent how the weather behaves.

• Heat and mass transfer is used to understand how drug delivery devices work, how kidney dialysis works, and how to control heat for temperature-sensitive things. It probably also explains why thermoses work!

• Electromagnetism is used for all electricity out there, and everything that involves light at all, from X rays to pulse optometry and laser pointers.

• Consider the transverse vibrations in an elastic membrane. The membrane subjected to a transverse load (perpendicular to the plane of the frame) of magnitude q of (x, y), where (x, y) is a system of Cartesian coordinates in the plane of the unloaded membrane. We are interested in calculating the transverse deflection w at (x, y), corresponding to an equilibrium configuration. The transverse vibrations of a tensed membrane are given by solving the PDE equation w xx plus w yy equals to minus q upon T plus rho h upon T into wtt. Here, h is the thickness of the membrane

• Link for application of Engg Mathematics : https://studiousguy.com/examples-of-mathematics/