What is calculus?
The branch of mathematics called calculus originates from describing the basic physical properties of our universe, such as the motion of planets, and molecules. Calculus approaches the paths of objects in motion as curves, or functions, and then determines the value of these functions to calculate their rate of change, area, or volume. In the 18th century, Sir Isaac Newton and Gottfried Leibniz simultaneously, yet separately, described calculus to help solve problems in physics. The two divisions of calculus, differential and integral, can solve problems like the velocity of a moving object at a certain moment in time, or the surface area of a complex object like a lampshade. All of calculus relies on the fundamental principle that you can always use approximations of increasing accuracy to find the exact answer. For instance, you can approximate a curve by a series of straight lines: the shorter the lines, the closer they are to resembling a curve.
Calculus is the branch of mathematics that defines and deals with limits, derivatives and integrals of functions. Often it is divided into two parts: Differential Calculus (dealing with derivatives, i.e., rates of change and tangents) and Integral Calculus (dealing with integrals, i.e., areas and volumes). Differential Equations that use methods from both grew into a separate discipline (actually more than just one), as did Calculus of Variations. As a way to illustrate the evolution of Calculus, I shall list several quotes plucked from Dunham’s book that demonstrate the attitude of various authors to the notion of infinitely small and the related notion of limit. Leibniz(p. 24) by infinitely small, we understand something … indefinitely small, so that each conducts itself as a sort of class, and not merely as the last thing of a class. If anyone wishes to understand these [the infinitely small] as the ultimate things …
While many people believe that calculus is supposed to be a hard math course, most don’t have any idea of what it is about. The good news is that if you remember your algebra and are reasonably good at it then calculus is not nearly as difficult as its reputation supposes. This article attempts to explain just what calculus is about–where it came from and why it is important. First, a little history leading up to the discovery of calculus, or its creation, depending on your philosophy. The word “calculus” comes from “rock”, and also means a stone formed in a body. People in ancient times did arithmetic with piles of stones, so a particular method of computation in mathematics came to be known as calculus. Arithmetic and geometry are the two branches of mathematics originating in ancient times. Mathematicians attempted to do algebra in those days but lacked the language of algebra, namely the symbols we take for granted such as +, -, X, รท and =.
Calculus, also known as tartar, is the hardened residue that forms on your teeth when plaque is not removed. Plaque can be removed by brushing twice a day and flossing daily. If tartar is allowed to remain on the teeth and below the gumline, it can lead to chronic infection and inflammation. The only way to remove tartar is to have your teeth professionally cleaned at your dental office.
