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The differential equation of the first order <math>\frac {dy}{dx} = f(x,y)</math> ...prescribes the slope <math>\frac {dy}{dx}</math> at each point o… - George Pólya
" "The differential equation of the first order
<math>\frac {dy}{dx} = f(x,y)</math>
...prescribes the slope <math>\frac {dy}{dx}</math> 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."
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About George Pólya
George Pólya (December 13, 1887 – September 7, 1985) was a Hungarian mathematician and professor of mathematics at ETH Zürich and at Stanford University. His work on heuristics and pedagogy has had substantial and lasting influence on mathematical education, and has also been influential in artificial intelligence.
Biography information from Wikiquote
Also Known As
Native Name:
Pólya György
Alternative Names:
George Polya
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Georg Polya
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Georg Pólya
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Additional quotes by 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.
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