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Calculus

Calculus is a branch of mathematics concerned with two types of functions: derivatives and integrals.

The derivative calculates the rate of change of the function at a point on a curved line. This formula also works for a straight line, as well. A derivative of a function is written by adding a apostrophe like this: f'(x). One of the applications of derivatives is to determine velocity and acceleration of an object in motion.

Integrals measure the area under a curved line graph, such as a half circle. The integral symbol looks like a flattened S.

Derivatives and integrals are related in that they are inverse functions of each other. That means the operations will cancel each other out, such as taking the square root of a squared number will give you the original number.

Applications of integrals include calculating areas of plane regions or surfaces, as well as calculating volumes of solids.

Both derivatives and integrals are defined by using the concept of a limit. An example of a limit is where you have the equation 1/x. If you take x to be very large, then 1/x gets closer to 0.

Items submitted should be about calculus as the main topic of the webpage. These can be presented as tutorials, quiz pages, resource, links, lists, forums and journals.

Math Analysis pages should be submitted in the Science/Math Analysis category.

Differential equations should be listed in the Science/Math/Differential_Equations category.

Differential Geometry should be submitted to the Science/Math/Geometry/Differential_Geometry/ subcategory.

Calculus of Variations

Calculus of variations is the study of finding minima and maxima of functions.

Submit sites that are beyond basic calculus that focuses on finding the minima and maxima of functions.

Fractional Calculus

Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers of the differential operator d/dx.

History

Development of calculus ideas began in ancient Greek times starting Archimedes in around 225 BC used the exhaustion method, that was previously developed by Zeno, Eudoxus and others, to prove that the area of a segment of parabola can be derived from knowing the area of circumscribed parallelogram. This finding relates to integral calculus. In the early 17th century, Descartes created a new method of finding the slope of a normal line. Next, Barrow was working on how to find the slope of a tangent line to the circle by shortening the two sets of points on a chord in a circle. This was known as Barrow's differential triangle. Barrow also may have understood about the inverse relationship between differentiation and calculus. The development of integral and derivative calculus was fairly separate until the 17th century that Barrow, Isaac Newton and Gottfried Leibniz discovered the relationship between the two branches of the field and were able to write a proof for this theorem. Knowing this relationship is extremely helpful in finding the integral formulas that we use to find curved areas. There were many other people not listed here or as well known as Archimedes, Leibniz, and Newton, but they all created a progression of events to create this enormously useful and elegant mathematical tool. Applications of calculus have expanded from finding areas of curved shapes to biology to profit optimization and on to engineering applications.

Please submit sites that deal with the history of calculus or the two branches of calculus: 1) Derivatives and 2) Integration.

Derivatives measure the rate of change on a curve as opposed to simple, straight line.

Integrals measure the area under a curved surfaces, such as half circle. This half circle area can easily be doubled to yield the area of the complete circle.

Please, submit history sites that deal with more than one math topic or is broader in scope than calculus to Science/Math/History/.

Calculus of Variations

Fractional Calculus

History

Integral Tables

Multivariable Calculus

Software