The Riemann Integral

Mathematicians of the early eighteenth century completed much of what their predecessors began. The power of calculus to explain natural phenomena became a theme from which much new mathematics was created. This process continues to this day, with more and more complex problems using analysis in their solution. To name just a few, the mathematical theory of traffic is based on hyperbolic partial differential equations as studied two centuries ago. The use of analysis to resolve light reflections from fields of crops into predictions about yields used the same equations. The migration of hazardous substances through the soil into ground water is a problem so numerically complex that it requires the fastest computers together with the most sophisticated mathematics methods. Sophisticated animations, say of waves and the ocean, seen by us all "at the movies" has behind it very similar set of equations. No large jet aircraft can be built without complex mathematical modelling to determine its aerodynamics.

This is our legacy. The work begun two centuries ago is paying off today when we need it just to survive.

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