When calculus was invented, has always been a question in Math. The first signs of calculus were done by Greek mathematicians. Zeno of Elea of about 450 B.C. gave a number of problems which were based on the infinite. His argument was that motion is impossible. Other Greek mathematicians that contributed to the method of exhaustion are Leucippus, Democritus and Antiphon. The method of exhaustion is so called because one thinks of the areas measured expanding so that they account for more and more of the required area. Archimedes made one of the greatest contributions of the Greek. One advancement he made was to show that the area of a segment of a parabola is 4/3 the area of a triangle with the same base and vertex and 2/3 of the area of the circumscribed parallelogram. Archimedes also “invented” the volume and surface area of a sphere, the volume and area of a cone, the surface area of an ellipse, and the volume of any segment of a parabolic. No progress or advancements were made in calculus until the 17th century. One great mathematician that was born in Barsa, Persia is Abu Ali-Hasan ibn al-Haytham. He integrated a fourth-degree polynomial. In the 3rd century AD Liu Hui of China used the method of exhaustion in order to fin the area of a circle. In the 5th century AD Zu Chongzhi also used it to find the volume of a sphere. In the 12th century Bhaskara II of India developed an early derivative representing infinitesimal change and described an early form of “Rolle’s theorem”. Seki Kowa expanded the method of exhaustion in the early 17th century in Japan. In AD 1668 James Gregory provided a special case of the second fundamental theorem of calculus.

Some applications of calculus are used by biologist, electrical engineers, architects, space flight engineers, statisticians, graphic artist and so much more. Biologists use differential calculus. They use it to determine the exact rate of growth in a bacterial culture when different variables are changed such as...

...“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...

...
Calculus in Medicine
Calculus in Medicine
Calculus is the mathematical study of changes (Definition). Calculus is also used as a method of calculation of highly systematic methods that treat problems through specialized notations such as those used in differential and integral calculus. Calculus is used on a variety of levels such as the field of banking, data analysis, and as I will explain, in the field of medicine. Medicine is defined as the science and/or practice of the prevention, diagnosis, and treatment of physical or mental illness (Definition). The term medicine can also mean a compound or a preparation applied in treatment or control of diseases, mostly in form of a drug that is usually taken orally (Definition). Calculus has been widely used in the medical field in order to better the outcomes of both the science of medicine as well as the use of medicine as treatment. (Luchko, Mainardi & Rogosin, 2011). There has been a strong movement towards the inclusion of additional mathematical training throughout the world for future researchers in biology and medicine. It can be hard to develop new courses as well as alter major requirements, but institutions should consider the importance of a clear understanding of the function of mathematics in science. However, scientists who have not had the level of mathematical training needed to work in...

...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 approximations. • Understand the relationship between integration and differentiation and continuity. Learning Outcomes: After completing this unit, students will be able to: 1. describe the basic ideas concerning functions, their graphs, and ways of transforming and combining them; 2. use the concepts of derivatives to solve problems involving rates of change and approximation of functions; 3. apply the differential calculus to solve optimization problems; 4. relate the integral to the derivative; 5. use the integral to solve problems concerning areas.
11.
12.
Subject Synopsis: This unit covers topics on Functions and Models, Limits and Derivatives, Differentiation Rules, Applications of Differentiation and Integrals.
13.
Subject Outline and Notional Hours: Topic Learning Outcomes 1 L 4 T 1.5 P SL 6.25 TLT 11.75
Topic 1: Functions and Models
• • • • • • Functions Models and curve fitting Transformations, combinations, composition and graphs of...

...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 published first (Nova methodus, 1684) and the whole subject was subsequently marred by a priority dispute between the two inventors of calculus.
Greek mathematicians are credited with a significant use of infinitesimals. Democritus is the first person recorded to consider seriously the division of objects into an infinite number of cross-sections, but his inability to rationalize discrete cross-sections with a cone's smooth slope prevented him from accepting the idea. At approximately the same time, Elea discredited infinitesimals further by his articulation of the paradoxes which they create.
Antiphon and later Eudoxus are generally credited with implementing the method of exhaustion, which made it possible to compute the area and volume of regions and solids by breaking them up into an infinite number of recognizable shapes.
Archimedes of Syracuse developed this method further, while also inventing heuristic methods which resemble modern day concepts somewhat. (See...

...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 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...

...History of Differential Calculus
Universidad Iberoamericana
September 20, 2013
Ever since men felt the need to count, the history of calculus begins, which together with Mathematics is one of the oldest and most useful science. Since men felt that need for counting objects, this need led to the creation of systems that allowed them to maintain control of their properties. They initially did it with the use of fingers, legs, or stones. But as humans continued developing intellectually, they achieved to implement systems or more advanced forms that allowed them to solve problems.
The Egyptians were the first civilization to develop mathematical knowledge. They devised numeral systems through hieroglyphs, representing the numbers 1, 10 and 100 through sticks and human figures. This system evolved into what we know today as the Roman system. Other important civilizations in history, such as the Babylonians, created other numeral systems, where the solution to the problem of counting the objects was solved with the implementation of a sexagesimal method. Civilizations as ancient China and ancient India used a hieroglyph decimal system, with the characteristic that these implemented the number zero.
The progress achieved ever since each culture implemented their numeral system are still used today. The algebraic advance of the Egyptians resulted in the resolution to significant equations. The correct...

...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 Newton - an English scientist - both developed calculus in the 1680s. Calculus is used in a wide variety of careers, from credit card companies to a physicist use calculus in their work. In general, it is a form of mathematics which was developed from algebra and geometry.
Integration and differentiation are an important concept in mathematics, and are the two main operations in calculus. Differential calculus is a subfield of calculus which concentrates over the study of how functions change when their inputs are changed. The main focus in a differential calculus is the derivative which can be thought of as how much one quantity is changing in response to changes in some other quantity. The process to find the derivative is called differentiation, the fundamental theorem of calculus states that the differentiation is the reverse process to integration. Derivatives are mainly...

...discoveries, calculus was the culmination of centuries of work rather than an instant epiphany. Mathematicians all over the world contributed to its development, but the two most recognized discoverers of calculus are Isaac Newton and Gottfried Wilhelm Leibniz. Although the credit is currently given to both men, there was a time when the debate over which of them truly deserved the recognition was both heated and widespread. Evidence also shows that Newton was the first to establish the general method called the "theory of fluxions" was the first to state the fundamental theorem of calculus and was also the first to explore applications of both integration and differentiation in a single work (Struik, 1948). However, since Leibniz was the first to publish a dissertation on calculus, he was given the total credit for the discovery for a number of years. This later led, of course, to accusations of plagiarism being hurled relentlessly in the direction of Leibniz. It is also known that Leibniz and Newton corresponded by letter quite regularly, and they most often discussed the subject of mathematics (Boyer, 1968). In fact, Newton first described his methods, formulas and concepts of calculus, including his binomial theorem, fluxions and tangents, in letters he wrote to Leibniz (Ball, 1908). However an examination of Leibniz' unpublished manuscripts provided evidence that despite his correspondence...