Leonhard Euler is one of the greatest mathematicians in the history, author of more than 800 works in mathematical analysis, graph theory, numbers theory, mechanics, infinitesimal calculus, music theory etc. Most of his works significantly influenced the development of mathematics. L. Euler was born in Basel, Switzerland 15 April 1707. He graduated from the University of Basel where he received a Master in Philosophy. Johann Bernoulli, one of the leading mathematicians of 18 century and Euler’s teacher, had a huge impact on the development of Euler, believing that he will be a great mathematician. He moved to St Petersburg, Russia in 1727 at the invitation of Peter the Great to work in the St Petersburg Academy of Science. He inspired everyone by his science …show more content…
This paper presents a development of mathematical analysis, illustrating the contribution of Euler to the development of calculus in the specific examples.
Mathematical analysis is a combination of divisions of mathematics that includes differentiation, integration, limits, infinite series and analytic function. First ideas of the concepts of mathematical analysis were established by the ancient Greek mathematicians. All the divisions of calculus, including analysis, had a similar idea: division on the infinitely small elements but the nature of analysis was unfamiliar to the authors of an idea. They developed the principle of infinity and established a method to calculate the area and volume of some plane figures and solids. Archimedes used infinite series, calculated a tangent to the Archimedean spiral. However, no general methods were established. Mathematical analysis was formally developed in the 17th century during the scientific revolution when Leibniz published his first article “New method for the maximum and minimum” in 1684, discussing differentials of powers and of radicals.(1) This article settled
...Great also created a well- structured police state that further legitimized and strengthened authoritarian rule in Russia. There are several testaments to this lasting influence, such as the increased public institution in the Soviet Union and the Russian federation. Places such as Moscow State University, date back to the time in which Peter the Great ruled. Peter the Great also founded Saint Petersburg, Russia in 1703. Additionally, in 1725 (the year of his death), an academy of the sciences was also established there.
Abstract—The transition to calculus was a remarkable period in the history of mathematics and witnessed great advancements in this field. The great minds of the 17th through the 19 Centuries worked rigorously on the theory and the application of calculus. One theory started another one, and details needed justifications. In turn, this started a new mathematical era developing the incredible field of calculus on the hands of the most intelligent people of ancient times. In this paper, we focus on an amazing mathematician who excelled in pure mathematics despite his physical inability of total blindness. This mathematician is Leonard Euler.
Born in the summer of September 17, 1826 in Breselenz, Kingdom of Hanover what’s now modern-day Germany the son of Friederich Riemann a Lutheran minister married to Charlotte Ebell was the second of six children of whom two were male and four female. Charlotte Ebell passed away before seeing any of her six children reach adult hood. As a child Riemann was a shy child who suffered of many nervous breakdowns impeding him from articulating in public speaking but he demonstrated exceptional skills in mathematics at an early age. At the age of four-teen Bernhard moved to Hanover to live with his grandmother and enter the third class at Lynceum two years later his grandmother also passed away he went on to move to the Johanneum Gymnasium in Lunberg and entered High School. During these years Riemann studied the Bible, Hebrew, and Theology but was often amused and side tracked by Mathematics. Showing such interests in mathematics the director of the gymnasium often time allowed Riemann to lend some mathemat...
...ibutions to analytic geometry, algebra, and calculus. In particular, he discovered the binomial theorem, original methods for expansion of never-ending series, and his “direct and inverse method of fluxions.”
The development of this mathematical system would lay the foundations for Descartes other philosophical discoveries in which his most significant contributions to the modern world would be made. In the year 1619, Descartes left his mentor Beeckman and joined the Emperor for the Holy Roman Empire Ferdinand V. During his time in the army Descartes had three distinct dreams in which he believed gave him a path to follow later on in life. The basis of these dreams was truly the break between the classics th...
...st important scientists in history. It is said that they both shaped the sciences and mathematics that we use and study today. Euclid’s postulates and Archimedes’ calculus are both important fundamentals and tools in mathematics, while discoveries, such Archimedes’ method of using water to measure the volume of an irregularly shaped object, helped shaped all of today’s physics and scientific principles. It is for these reasons that they are remembered for their contributions to the world of mathematics and sciences today, and will continue to be remembered for years to come.
No other scholar has affected more fields of learning than Blaise Pascal. Born in 1623 in Clermont, France, he was born into a family of respected mathematicians. Being the childhood prodigy that he was, he came up with a theory at the age of three that was Euclid’s book on the sum of the interior of triangles. At the age of sixteen, he was brought by his father Etienne to discuss about math with the greatest minds at the time. He spent his life working with math but also came up with a plethora of new discoveries in the physical sciences, religion, computers, and in math. He died at the ripe age of thirty nine in 1662(). Blaise Pascal has contributed to the fields of mathematics, physical science and computers in countless ways.
Born in the Netherlands, Daniel Bernoulli was one of the most well-known Bernoulli mathematicians. He contributed plenty to mathematics and advanced it, ahead of its time. His father, Johann, made him study medicine at first, as there was little money in mathematics, but eventually, Johann gave in and tutored Daniel in mathematics. Johann treated his son’s desire to lea...
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other. Eight different differential rules were established in order to assist with finding the derivative of a function. Those rules include chain rule, the differentiation of the sum and difference of equations, the constant rule, the product rule, the quotient rule, and more. In addition to these differential rules, optimization is an application of differential calculus used today to effectively help with efficiency. Also, partial differentiation and implicit differentiation are subgroups of differential calculus that allow derivatives to be taken to more challenging and difficult formulas. The mean value theorem is applied in differential calculus. This rule basically states that there is at least one tangent line that produces the same slope as the slope made by the endpoints found on a closed interval. Differential calculus began to develop due to Sir Isaac Newton’s biggest problem: navigation at sea. Shipwrecks were frequent all due to the captain being unaware of how the Earth, planets, and stars mov...
The abstractions can be anything from strings of numbers to geometric figures to sets of equations. In deriving, for instance, an expression for the change in the surface area of any regular solid as its volume approaches zero, mathematicians have no interest in any correspondence between geometric solids and physical objects in the real world. A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. Mathematicians are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest richness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof.