Your best source for free calculus help is undoubtedly Arithmetic.com, which has an array of helpful calculus lessons and a compilation of basic calculus answers. As a reference, the name calculus comes from the Latin word (the exact same word) meaning a small stone that was primarily used for counting; because the word is Latin, the plural is calculi. Calculus can be defined as the study and use of derivatives, integrals, limits, functions and infinite series. It is a huge component of most secondary and tertiary mathematical education concepts and it is widely used in various fields of science, as well as economics and engineering. Broadly encompassed within the larger field of mathematical analysis, calculus lessons can be considered more specifically as the study of mathematical change. Originally called the calculus of infinitesimals (but the name was later shortened to a colloquial format), this particular branch of mathematics has a number of specialty applications, including calculi that is variational, multi-variable, propositional, lambda or pi, join, integral, vector and differential, among many other types. The context of most basic calculus answers is almost always defined by specific limits and the understood continuum of real numbers, although newer calculi formats known as “non-standard analysis” employ infinitesimal numbers and numbers of infinite proportions in place of real numbers. Almost all major solutions within this particular branch of mathematics will be found using proofs, a systematic selection of steps where each movement that progresses forward is defined by a specified “rule” from a long but limited list of rules.
There are a few basic definitions that must be understood in order to fully grasp the various forms of calculi and their applications in the real world. One is the idea of a limit, which is the value of a specified mathematical function at one specific input, which is defined in terms of its values at nearby input or similar functions. Another important concept of calculi is that of its differential application. This is the use of derivatives, which are generally notated in problems with an apostrophe mark read as “prime.” Differentials specify the derivative definitions, applications and properties. The final concept that is important to this study is that of integrals, which defines spaces within graphs formed by notating functions of real variables and intervals. Because the various applications of calculi are so widely different and often come with completely different sets of vocabulary, functions and formulas, they are generally taught starting with two generalized formats of this branch of mathematics and then are split up into more specified objectives. If you are interested in various applications of the principles of calculi in its specific uses or in everyday applications, check out Arithmetic.com for more information.