(Cadena; Travis; Norman, 77) It must be stated that Newton's mathematics that involved 'fluxions' was one of the first forms of the area defined as 'differential calculus'. Although Newton used and preferred to use geometrical methods to algebraic equations, calculus methods had come into importance. However, calculus was not widely accepted at the time, and there were several philosophical objections to the science, but the fact remains that these objections over the years have made no difference to the application of the science. This is mainly because of its abstract nature, and also the logically sufficient nature of the science. The mathematician, Karl Popper, has stated that scientific theories are definitely 'sufficient conditions', but are not 'necessary conditions', of the observation of scientific phenomena. (Philosophical problems with calculus)

This means that the metaphysics of mathematics belongs to the branch called meta-mathematics, and not to math proper. There have been numerous approaches to the question of infinitesimals over the years, but all the approaches have been replaced by talk about limits. When, for example, an individual talked about justifying the existence of these minute quantities, he was faced with a number of difficulties, and the solution to this was the theory of limits. This theory became so popular that most mathematicians felt that infinitesimals must be actually banished from their science. Infinitesimals had in fact addressed the originally made objections to calculus, and it was eventually discovered that calculus had in fact worked for several centuries before. When this is taken in a scientific context, it is a very good occurrence, and most physicists and scientists and mathematicians agree with the idea. (Philosophical problems with calculus)

The so called 'lambda calculus' that was invented during the 1930's was used to investigate the definition of 'function', the application of that function, and its recursion, and this means that it can clearly define what a 'computable function'...

Sometimes, the issue arises whether two lambda calculus expressions are similar or equivalent and a general algorithm cannot solve this issue; in fact the lambda calculus has served to influence functional programming languages to a great extent. According to the calculus, every expression stands for a single function with a single argument, and the argument of the function actually a function with a single argument. The value of the function would be another function with on single argument. (Lambda Calculus)
The importance of calculus cannot be underestimated, and the better it is understood, the better it would be for scientists and others in search of a solution to any problem involving derivative and integrals and limits.