Calculus is not a just vocational training course. In part, students should study calculus for the same reasons that they study Darwin, Marx, Voltaire, or Dostoyevsky: These ideas are a basic part of our culture; these ideas have shaped how we perceive the world and how we perceive our place in the world.
[Steven Storgatz] sets out to examine love affairs "mathematically", suggesting that equations that summarise specific romantic behaviour can then be solved with calculus. The result is a way to "predict the course" of an affair.
The billions of dollars in losses that have accumulated through debacles experienced by the likes of Procter & Gamble, Gibson Greetings and Barings Bank have given derivatives the public image of speculative risk enhancers, not new types of insurance. Concerns have also focused on the integrity of the mathematical modeling techniques that make derivatives trading possible.
In 1664, the Great Plague struck England and [Cambridge University, which Newton attended,] closed for a period to allow students and professors return home to prevent an outbreak at school. From 1664 to 1666, Isaac made his greatest contributions to mathematics. Relying on the works of Galileo, Kepler, and Descartes, Newton invented calculus... The creation and development of his calculus was said to be the first achievement of mathematics, however, Newton would not publish his calculus until much later in his life.
A German mathematician named Leibiniz had created an identical mathematical work to calculus and published these results in Germany in 1684. As a result, Leibiniz was referred to as calculus' creator, and when this news came to England Newton was enraged. While the debate raged on and both sides about who honestly claimed the rights to calculus, all communications broke down between Germany's mathematicians and England's mathematicians. As a result France used the work done by Newton and Leibniz and perfected calculus and advanced mathematics in their country.
Every year about a million American students take calculus. But far fewer really understand what the subject is about or could tell you why they were learning it. It’s not their fault. There are so many techniques to master and so many new ideas to absorb that the overall framework is easy to miss.
alculus is the mathematics of change. It describes everything from the spread of epidemics to the zigs and zags of a well-thrown curveball. The subject is gargantuan — and so are its textbooks. Many exceed 1,000 pages and work nicely as doorstops. But within that bulk you’ll find two ideas shining through... Those two ideas are the “derivative” and the “integral.” Each dominates its own half of the subject, named in their honor as differential and integral calculus.
While Newton considered variables changing with time, Leibniz thought of the variables x and y as ranging over sequences of infinitely close values. He introduced dx and dy as differences between successive values of these sequences. Leibniz knew that dy/dx gives the tangent but he did not use it as a defining property. On the other hand, Newton used quantities x' and y', which were finite velocities, to compute the tangent. Of course neither Leibniz nor Newton thought in terms of functions, but both always thought in terms of graphs. For Newton the calculus was geometrical while Leibniz took it towards analysis.
Ultimately, Cauchy, Weierstrass, and Riemann reformulated Calculus in terms of limits rather than infinitesimals. Thus the need for these infinitely small (and nonexistent) quantities was removed, and replaced by a notion of quantities being "close" to others. The derivative and the integral were both reformulated in terms of limits.
In due precision, Mathematics must be divided into two great sciences, quite distinct from each other--Abstract Mathematics, or the Calculus... and Concrete Mathematics, which is composed of General Geometry and of Rational Mechanics. The Concrete part is necessarily founded on the Abstract, and it becomes in its turn the basis of all natural 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.