Calculus

Taking Basic Derivatives

Taking Basic Derivatives 1024 538 Teaching Staff

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…

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Math Review of Leibniz, Newton, and the Development of Calculus

Math Review of Leibniz, Newton, and the Development of Calculus 150 150 Deborah

Overview 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…

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Math Introduction to Infinitesimals

Math Introduction to Infinitesimals 150 150 Deborah

Overview 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…

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Math Introduction to Integrals

Math Introduction to Integrals 150 150 Deborah

Overview 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…

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Math Introduction to Derivatives

Math Introduction to Derivatives 150 150 Deborah

Overview 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…

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Math Review of Real, Complex, and Hyperreal Numbers

Math Review of Real, Complex, and Hyperreal Numbers 150 150 Deborah

Overview 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…

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Math Introduction to Sets and Logic

Math Introduction to Sets and Logic 150 150 Deborah

Overview 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…

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Solving Integrals Through the Use of Integration by Parts

Solving Integrals Through the Use of Integration by Parts 150 150 oren

Overview 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…

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How to Use the Chain Rule to Find Derivatives

How to Use the Chain Rule to Find Derivatives 150 150 oren

Overview 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…

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U Substitution as a Method of Solving Integrals

U Substitution as a Method of Solving Integrals 150 150 oren

Overview 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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