THE HISTORY OF CALCULUS
The discovery of calculus is often attributed to two men, Isaac Newton and Gottfried Leibniz, who independently developed its foundations. Although they both were instrumental in its creation, they thought of the fundamental concepts in very different ways. 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.

It is interesting to note that Leibniz was very conscious of the importance of good notation and put a lot of thought into the symbols he used. Newton, on the other hand, wrote more for himself than anyone else. Consequently, he tended to use whatever notation he thought of on that day. This turned out to be important in later developments. Leibniz's notation was better suited to generalizing calculus to multiple variables and in addition it highlighted the operator aspect of the derivative and integral. As a result, much of the notation that is used in Calculus today is due to Leibniz.

The development of Calculus can roughly be described along a time line which goes through three periods: Anticipation, Development, and Rigorization. In the Anticipation stage techniques were being used by mathematicians that involved infinite processes to find areas under curves or maximize certain quantities. In the Development stage Newton and Leibniz created the foundations of Calculus and brought all of these techniques together under the umbrella of the derivative and integral....

...prominent figure in mathematics and was a major mathematician that greatly contributed to calculus.
Leibniz’s contribution to the invention of infinitesimal calculus was monumental and is widely recognized as modern mathematics starting point. Leibniz’s Nova Methodus pro Maximis et Minimis, itemque Tangentibus… in Acta Eruditorum, in 1684, published Leibniz’s details of his ideas of differential calculus. The paper contained the d notation, the...

...CALCULUSCalculus is the study of change which focuses on limits, functions, derivaties, integrals, and infinite series. There are two main branches of calculus: differential calculus and integral calculus, which are connected by the fundamental theorem of calculus. It was discovered by two different men in the seventeenth century. Gottfried Wilhelm Leibniz – a self taught German mathematician – and Isaac...

...N.E.D University of Engg. & Tech. CS-14
Integral Calculus:
Definition:
“The branch of mathematics that deals with integrals, especially the methods of
ascertaining indefinite integrals and applying them to the solution of differential
equations and the determining of areas, volumes, and lengths.”
History of Integral Calculus:
Pre-calculus integration:
The first documented systematic technique capable of determining integrals is
the method of...

...History and the Importance of CalculusCalculus can be summed up as "the study of mathematically defined change"5, or the study of infinity and the infinitesimal. The basic concepts of it include: limits, derivatives, differentiation and integrals. The word "calculus" means "rock"; the reason behind the naming of it is that rocks were used to used to carry out arithmetic. This branch of mathematics is able to be rooted all the way back to around 450...

...History of Calculus
The history of calculus falls into several distinct time periods, most notably the ancient, medieval, and modern periods. The ancient period introduced some of the ideas of integral calculus, but does not seem to have developed these ideas in a rigorous or systematic way. Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1800 BC), in which...

...How the calculus was invented?
Calculus, historically known as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Ideas leading up to the notions of function, derivative, and integral were developed throughout the 17th century, but the decisive step was made by Isaac Newton and Gottfried Leibniz. Publication of Newton's main treatises took many years, whereas Leibniz...

...No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught:
Information on Every Subject Name of Subject: Introduction to Calculus and Applications
Pre-requisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60%
9. 10.
Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear...