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Calculus? Can You Think of a Problem Calculus Could Be Used to Solve?

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Calculus? Can You Think of a Problem Calculus Could Be Used to Solve? Mathematics Before you read Discuss these questions with your partner. What do you know about calculus? Can you think of a problem calculus could be used to solve? В A Vocabulary Complete the definitions below with words from the box. slope approximation embrace acceleration diverse indispensable sphere cube rectangle 1 If something is a(n) it В Reading 1 isn't exact. 2 An increase in speed is called Calculus 3 If something is you can't Calculus is the branch of mathematics that deals manage without it. with the rates of change of quantities as well as the length, area and volume of objects. It grew 4 If you an idea, you accept it. out of geometry and algebra. There are two 5 A is a three-dimensional, divisions of calculus - differential calculus and square shape. integral calculus. Differential calculus is the form 6 Something which is is concerned with the rate of change of quantities. different or of many kinds. This can be illustrated by slopes of curves. Integral calculus is used to study length, area 7 If you place two squares side by side, you and volume. form a(n) The earliest examples of a form of calculus date 8 A is a three-dimensional back to the ancient Greeks, with Eudoxus surface, all the points of which are the same developing a mathematical method to work out distance from a fixed point. area and volume. Other important contributions 9 A is also known as a fall. were made by the famous scientist and mathematician, Archimedes. In India, over the 98 Macmillan Guide to Science Unit 21 Mathematics 4 course of many years - from 500 AD to the 14th Pronunciation guide century - calculus was studied by a number of mathematicians. In fact, the first text on calculus Archimedes /a:ki'mi:di:z/ was written in India. However, it was not until embrace /imbreis/ the end of the 1600s that calculus was taken up Eudoxus /ju'doksss/ ^indispensable /mdi spensab l/ in Europe. There was much scientific activity at У the time, and calculus was able to answer many questions, particularly in the field of physics. В В Comprehension Many great mathematicians of the time embraced Read the text and decide if the following calculus and furthered its development, including statements are true or false. Rene Descartes and Pierre de Fermat, but the most important contributions were made by 1 Calculus and geometry led to T • Gottfried Leibniz and Isaac Newton. Newton was the development of algebra. F • the first to use calculus in his studies of physics 2 India was using calculus T П and Leibniz developed many of the symbols that before Europe. F we use in calculus. • 3 In the 17th century, calculus was T • The starting point of calculus is the idea that you applied to physics. F • can use an approximation and keep increasing 4 Integral calculus can calculate the rate T •О the accuracy until an exact answer is found. An at which a population increases. F example of this would be to calculate the volume • or area of a sphere by using shapes such as 5 Differential calculus has to do with T • rectangles or cubes that become increasingly systems that are undergoing change. F • smaller until the exact volume or area is determined. In calculus, this final result is called Before you listen a limit. Discuss these questions with your partner. Differential calculus describes processes that are Do you know who coined the term calculus? in flux - which means they are constantly Can you think of another word that comes from changing. Examples of this are temperature the word calculus? variations or the speed of a moving object. By using differential calculus, it is possible to determine the rate at which the temperature И С Listening *))) changes and the rate of acceleration of the Listen to a teacher and students moving body. Integral calculus begins with a discussing some of the history of calculus. known rate of change and, working backwards, Then answer the questions in your finds certain values. For example, if you know the own words. rate of acceleration of a car, you can find out its 1 What was the original meaning of the speed at a given point. word calculus? Today, both forms are used in every area of 2 Who named the branch of mathematics science and knowledge. Fields as diverse as known as calculutf? engineering, medicine, business and economics make use of calculus. Calculus is such an 3 Why did Newton name it the science indispensable tool that it is applied whenever of fluxions? we have a problem that can be solved 4 What did Newton accuse Leibniz of doing? by mathematics. 5 Leibniz and Newton had different starting points in their work on calculus - what were they? Macmillan Gui de to Science Unit 16 99 Mathematics Before you read Discuss these questions with your partner. Who do you think were the greatest mathematicians in history? Which kinds of mathematics were they involved in? What do you know about Pierre de Fermat? В D Vocabulary a. Match these words with their definitions. 1 devotion A don't pay attention to 2 astounding В somebody working in the same field 3 councillor С top judge 4 fellow D amazing 5 neglect E commitment 6 chief magistrate F member of an administrative body b. Complete the sentences below with words from the box. с N • devotion • astounding v • fellow • neglect • councillor В Reading 2 V 1 She shows great to her family. Pierre de Fermat 2 Please don't to pay the phone bill. Pierre de Fermat was born in Toulouse, France th th 3 Meet Peter. He's a(n) film on 17 August, 1601, and died on 12 January, enthusiast! We love watching films! 1665. lie came from a wealthy family, and he studied law in Orleans. After graduating, he 4 What a(n) speech he gave began to practise law and later he became a at the conference. It was amazing! councillor in parliament. By 1652, he had 5 He's been a town for over become the chief magistrate of the criminal five years now. court - a very important and highly respected position. c. Match the words to make phrases. In 17th century France, magistrates spent large 1 practise A theory amounts of time on their own. It was during this time that de Fermat worked in the field of 2 criminal В coordinates mathematics. In fact, his devotion to this 3 remarkable С law science was so great that he spent as much free 4 number D geometry time as he could working on mathematical 5 probability E achievements problems and solutions. Although de Fermat published very little in his lifetime, he is still 6 Cartesian F court considered to be one of the greatest 2 analytic G recognition mathematicians of all time. His achievements in 8 receive H theory mathematics are quite astounding. 100 Macmillan Guide to Science Unit 21 Mathematics De Fermat's most important work was done in Pronunciation guide the development of modern number theory, which was one of his favourite areas of magistrate Amaed3istreit/ mathematics, and which had an important Orleans hi\i?azl impact on the study of calculus. Sir Isaac Toulouse /tu:lu:z/ Newton said that his own invention of calculus - differential calculus in particular - was based BE Comprehension in large part on the work of de Fermat, who had Read the text and choose the done his studies on calculus well before Isaac correct answer. Newton and Gottfried Leibniz were born. In 1654, Blaise Pascal wrote a letter to de Fermat 1 Despite having little of his work published asking about the latter's views on probability. while alive, de Fermat Thus began a correspondence that became A had a successful career in law. the foundation of Probability Theory, with В is seen as a great mathematician. de Fermat and Pascal considered to be the С held an important position. founders of this theory. Rene Descartes is 2 De Fermat's work on modern numbers famous for his invention of Cartesian A was influenced by Newton's work. coordinates and his important work La В helped him develop a branch of calculus. Geometrie. De Fermat had independently come С had an effect on calculus. up with his own three-dimensional analytic geometry, which was more complicated and 3 Pascal and de Fermat advanced than Descartes'; Descartes' work A are recognised as the fathers of became more popular, however, because its Probabality Theory. notation was more convenient. Today, both В communicated about analytical geometry. scientists are seen as the fathers of С produced work more advanced analytic geometry. than Descartes'. 4 De Fermat's methods and results De Fermat also made contributions in the field A were never proven in his lifetime. of optics, formulating a law on the way light В were ahead of their time. travels. His methods were so advanced that С suffered as he never provided proof. many of his results were not proved for a century after his death, and de Fermat's Last 5 We know about de Fermat's work Theorem took more than three hundred years nowadays because to prove. De Fermat rarely provided his proofs, A his work was published. that is, evidence or procedures for reaching В learned people researched his claims. conclusions, to explain how he got his answers. С he left behind a correspondence. In his letters to fellow mathematicians, he stated theorems but neglected the proofs, which was very annoying for them.
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