Derivative: an expression that represents the rate of change of a function. At this level, it is usually denoted as y’ or f’(x) (read y prime and f prime at…
read moreOverview One of the biggest controversies in science in the early 18th century was around the development of a new mathematical tool called calculus. In Europe, the mathematician, philosopher, and scientist…
read moreOverview Using infinitesimal quantities to approximate measurement of any item is an ancient way to determine the size and shape of irregular objects. Although it was very controversial in the…
read moreOverview Finding integrals, or integration, is the opposite of finding the derivative in calculus. The concept is closely connected with functions, and was independently discussed by both Newton and Leibniz…
read moreOverview A derivative of a function describes its rate of change at a particular point on the function. The rate of change doesn’t have to be constant, so it can…
read moreOverview Real numbers are the rational and irrational numbers that people deal with in everyday life. Hyperreal numbers include numbers that are infinitely large, infinitely small, or infinitesimal, along with…
read moreOverview Thinking about sets of objects and numbers is as simple as counting and as complex as infinity and transfinite numbers. Sets are an essential underlying concept of mathematics and…
read moreOverview Suppose we have an integral which appears unsolvable by ordinary means, such as ∫xsin(x)dx In many cases, we can do what is called integration by parts, which is where…
read moreOverview Occasionally, you will have what are called composite functions; that is, functions that are composed of multiple functions and thus cannot be differentiated easily. In reality, although these may…
read moreOverview Sometimes, a derivative is done using the chain rule, and it leaves with an equation that, at first glance, can look intractable when we are attempting to integrate it.…
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