Tag: easy calculus
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1.5 Symbolic versus numerical calculus
Calculus has a reputation for being difficult to learn, and with good reason. The traditional approach to teaching calculus is based on manipulating symbols (variables) in equations, learning how different types of mathematical functions become transformed by the calculus operations of differentiation and integration. For example, suppose a first-semester calculus student were given the following…
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1.4 How derivatives and integrals relate to one another
First, let us review some of the properties of differentials and derivatives, referencing the expression and graph shown below: A differential is an infinitesimal increment of change (difference) in some continuously-changing variable, represented either by a lower-case Roman letter d or a lower-case Greek letter “delta” (δ). Such a change in time would be represented as dt; a similar change in temperature as dT;…
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1.2 The concept of differentiation in Calculus
Suppose we wished to measure the rate of propane gas flow through a hose to a torch: Flowmeters appropriate for measuring low flow rates of any gas are typically very expensive, making it impractical to directly measure the flow rate of propane fuel gas consumed by this torch at any given moment. We could, however, indirectly measure…