George Pólya - Equations Quotes

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Even if without the Scott's proverbial thrift, the difficulty of solving differential equations is an incentive to using them parsimoniously. Happily here is a commodity of which a little may be made to go a long way.... the equation of small oscillations of a pendulum also holds for other vibrational phenomena. In investigating swinging pendulums we were, albeit unwittingly, also investigating vibrating tuning forks.

George Pólya
We wish to see... the typical attitude of the scientist who uses mathematics to understand the world around us.... In the solution of a problem... there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude.

George Pólya
The differential equation of the first order

... prescribes the slope at each point of the plane (or at each point of a certain region of the plane we call the field").... a differential equation of the first order... can be conceived intuitively as a problem about the steady flow of a river: Being given the direction of the flow at each point, find the streamlines.... It leaves open the choice between the two possible directions in the line of a given slope. Thus... we should say specifically "direction of an unoriented straight line" and not merely "direction."

George Pólya
In order to solve a differential equation you look at it till a solution occurs to you.

George Pólya