“The Contribution of Calculus in the Social Progress”

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 an Egyptian successfully calculated the volume of a pyramidal frustum.[1][2] From the school of Greek mathematics, Eudoxus (c. 408−355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes while Archimedes (c. 287−212 BC) developed this idea further, inventing heuristics which resemble integral calculus.[3] The method of exhaustion was later used in China by Liu Hui in the 3rd century AD in order to find the area of a circle. It was also used by Zu Chongzhi in the 5th century AD, who used it to find the volume of a sphere.[2]

In AD 499 the Indian mathematician Aryabhata used the notion of infinitesimals and expressed an astronomical problem in the form of a basic differential equation.[4] This equation eventually led Bhāskara II in the 12th century to develop an early derivative representing infinitesimal change, and he described an early form of "Rolle's theorem".[5] Around AD 1000, the Islamic mathematician Ibn al-Haytham (Alhazen) was the first to derive the formula for the sum of the fourth powers, and using mathematical induction, he developed a method that is readily generalizable to finding the formula for the sum of any integral powers, which was fundamental to the development of integral calculus.[6] In the 12th century, the Persian mathematician Sharaf al-Din al-Tusi discovered the derivative of cubic polynomials, an important result in differential calculus.[7] In the 14th century, Madhava of Sangamagrama, along with other...

...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...

...Calculus
is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem of...

...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...

...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...

...input to the philosophy of mathematics came with his “Of the Geometric Spirit””.1 Blaise Pascal was also a major contributor to the founding of Statistics.
Blaise Pascal contributed to mathematics in many ways, but one of the most important contributions he made was the creation of Binomial Coefficients; now known as Pascal’s Triangle. “Pascal's triangle determines the coefficients which arise in binomial expansions”.1 Pascal’s Triangle has advanced dimension overviews. The...

...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...

...And garlic bulbs should be “moneybags,”
because their shape reminded her of the sacks of gold
10 coins in folktales.
Beginning in the 1780’s, novelist Charlotte Smith’s
explicit and implicit criticism of English life and laws,
of England’s social organization, earned her a reputation
Line as a “subversive.” Her novels contain some of the earliest
5 literary attacks on the English legal system. In comparison
to later exposés by nineteenth-century novelists such as...

...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...

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