Unit 9 Theme: Analysis incarnate—Leonard Euler. Grammar:Prepositions.

Objectives: By the end of this unit, students should be able to use active vocabulary of this theme in different forms of speech exercises.

Students should know the rule of Prepositions and fulfill grammar exercises.

Methodical instructions: This theme must be worked out during two lessons a week according to timetable.

Lexical material: Introduce and fix new vocabulary on theme “Analysis incarnate—Leonard Euler.”.Define the important aspects of geometry. Discuss in groups. Speak about the history of geometry.

Grammar: Introduce and practice prepositions. Revise the use of prepositions.

Analysis incarnate—Leonard Euler.

Though P. Fermat and R. Descartes founded analytic geometry they did not advance the subject far enough and did not elaborate it purely analytically either. A century later L. Euler (1707-1783) a Swiss mathematician who lived the greater part of his life in Russia, engaged in scientific research, lecturing and textbook writing in St. Petersburg Academy, developed the subject matter of both Plane and Solid Analytic Geometry far beyond its elementary stages. Euler's mathematical career opened when Analytic Geometry (made public in 1637) was ninety years old, the calculus about fifty. In each of these fields a vast number of isolated problems were solved, but no systematic unification of the whole of the then mathematics, pure and applied, was made. In particular, the powerful analytic methods of Fermat, Descartes, Newton and Leibnitz were not exploited to the limit of what they were capable, especially in Calculus, Geometry and Mechanics, where Euler proved himself the master.

In the XVIII c. the Universities were not the principal centres of science in Europe. The lead in scientific research was taken by the various royal academies. In Euler's case St. Petersburg and Berlin furnished the sinews of mathematical creation. Both of these foci of creativity owed their inspiration to the restless ambition of Leibnitz. These academies were like some of these today: they were research organizations which paid their leading members to produce scientific research. Euler became famous for his great output of original mathematics and for the wide range of subjects he covered. He contributed new ideas to calculus, geometry, Algerba, Number Theory, Calculus of variations, probability and Topology. He also worked in many areas of applied mathematics, such as Acoustics, Optics, Meachanics, Astronomy, Ballistics, Navigation, Statistics and Finance. His industry was as remarkable as his genius. Euler was the most prolific mathematician in histoty; his scientific heritage is vast, a list of some 850, works of which 550 were published in the lifetime. Euler wrote his great memoirs quite easily and total blindness during the last seventeen years of his life did not regard his unparalleled productivity. He overcame the difficulty of blindness chiefly by means of his remarkable memory. Indeed, if anything, the loss of his eyesight sharpened Euler's perception of the inner world of his imagination.

Ex.1. Choose a,b,c or d.

1. Who founded analytic geometry?

a) Lagrange and Fermat b) P. Fermat and R. Descartes

c) Euler and Fermat d) Lagrange and Euler

2. Where did Euler live the greater part of his life?

a) in Russia b) Alexandria

c) Switzerland d) Greece

3. What did Euler become famous for … .

a) his great out put of original mathematics.

b) his great out put of analitic geometry.

c) his great out put of calculas.

d) his great out put of mechanics.

4. In what parts of mathematics did Euler especially prove himself as a master?

a) in differential equations.

b) in analytic geometry and caleulus.

c) in calculus, geometry and mechanics.

d) in arithmetics and physics.

Ex.2. Choose the title of the text according to summary.

a. New discovery in analytic geometry

b. Euler is innovator of mathematics

c. Euler’s genius and remarkablity of his industry

d. Euler is a swiss scientist

Ex.3. Translate the highlighted word correctly.

1. Euler engaged in scientific research lecturing many subjects.

a) читая лекцияb) читающий лекции

c) читать лекцииd) читал бы лекции

2. In each of the fields a vast number of isolated problems were solved.

a) решалисьb) решая

c) будут решатьсяd) решали бы

3. The powerful analytic methods were not exploited to the limit.

a) не будут разработаныb) не разрабатываются

c) не были разработаныd) не разрабатывались бы

4. These academies were research organizations which paid their leading members to produce scientific research..

a) чтобы проводить научно-исследовательскую работу.

b) проводя научно-исследовательскую работу.

c) проводящим научно-исследовательскую работу.

Ex.4.Listening

Follow the link: http://www.youtube.com/watch?v=NX9YbtYJZ8Y (Elementary Mathematics (K-6) Explained 0: Introduction)

Grammar: Prepositions

Do exercises from Units 121-128 p.242-257 ex.:121.1-128.6 (Raymond Murphy “English Grammar in Use” A self-study reference and practice book for intermediate students of English Third Edition. Cambridge).

БӨЖ тапсырмалар: 9

Speak about what you understood from the text “A modern view of geometry ” or write an essay.

Follow the link and pass the test:

http://www.study.ru/test/test.php?id=215