Pronunciation guide

Aquinas

Cartesian

Constantinople

Poitiers

Psychology

Renaissance

E Comprehension

Read the text and decide if the following statements are true or false.

1 Descartes' time was one of major changes. T o F o

2 Descartes aimed to invent a new branch of mathematics and philosophy T o

F o

3 Descartes had not been influenced by earlier philosophers. T o

F o

4 Descartes' ideas often did not meet with the approval of church authorities. T o

F o

5 Descartes' major contribution was to calculus. T o

F o

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?

A Vocabulary

Complete the definitions below with words from the box.

N slope n approximation

N embrace n acceleration

N diverse nindispensable

N sphere n cube

nrectangle

1 If something is a(n)..........................it isn't exact.

2 An increase in speed is called.....................

3 If something is...........................you can't manage without it.

4 If you..........................an idea, you accept it.

5 A.........................is a three-dimensional, square shape.

6 Something which is.........................is different or of many kinds.

7 If you place two squares side by side, you form a(n)...........................

8 A.........................is a three-dimensional surface, all the points of which are the same distance from a fixed point.

9 A.........................is also known as a fall.

Reading

Calculus

Calculus is the branch of mathematics that deals with the rates of change of quantities as well as the length, area and volume of objects. It grew out of geometry and algebra. There are two divisions of calculus - differential calculus and integral calculus. Differential calculus is the form concerned with the rate of change of quantities. This can be illustrated by slopes of curves. Integral calculus is used to study length, area and volume.

The earliest examples of a form of calculus date back to the ancient Greeks, with Eudoxus developing a mathematical method to work out area and volume. Other important contributions were made by the famous scientist and mathematician, Archimedes. In India, over the course of many years - from 500 AD to the 14^th century - calculus was studied by a number of mathematicians. In fact, the first text on calculus was written in India. However, it was not until the end of the 1600s that calculus was taken up in Europe. There was much scientific activity at the time, and calculus was able to answer many questions, particularly in the field of physics. Many great mathematicians of the time embraced calculus and furthered its development, including Rene Descartes and Pierre de Fermat, but the most important contributions were made by Gottfried Leibniz and Isaac Newton. Newton was the first to use calculus in his studies of physics and Leibniz developed many of the symbols that we use in calculus.

The starting point of calculus is the idea that you can use an approximation and keep increasing the accuracy until an exact answer is found. An example of this would be to calculate the volume or area of a sphere by using shapes such as rectangles or cubes that become increasingly smaller until the exact volume or area is determined. In calculus, this final result is called a limit.

Differential calculus describes processes that are influx - which means they are constantly changing. Examples of this are temperature variations or the speed of a moving object. By using differential calculus, it is possible to determine the rate at which the temperature changes and the rate of acceleration of the moving body. Integral calculus begins with a known rate of change and, working backwards, finds certain values. For example, if you know the rate of acceleration of a car, you can find out its speed at a given point.

Today, both forms are used in every area of science and knowledge. Fields as diverse as engineering, medicine, business and economics make use of calculus. Calculus is such an indispensable tool that it is applied whenever we have a problem that can be solved by mathematics.

Date: 2016-01-14; view: 825