Double integrals and Jacobis

By Roy Ernest Ballard

1. Lengths, surfaces and volumes

Ordinary words like 'curve' or 'region' have to take on specific meanings if they are to be used mathematically. As a first step, empty space is endowed with imaginary points or locations in space defined by coordinates x_i. A curve is a set of points, usually an infinite set, given by some rule. One type of rule is...
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STRESS

When a force is applied to an object the effect varies with direction. Take for instance a compressive force applied to an elastic cube like a rubber eraser. Between thumb and forefinger it can be squashed but then it bulges out sideways in directions perpendicular to the force. Not all substances bulge out sideways like this and  some even undergo a lateral contraction. . .
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