Guide to Science Unit 19
Calculus
Ex.1 Practice pronunciation of the following words:
1. differential
2. integral
3. a curve
4. a contribution
5. a sphere
6. a rectangle
7. to determine
Ex. 2 Find the following words and phrases in the texts p.98-99.
| темп; скорость | pace; speed |
| возникать из чего-л | spring from |
| кривая (линия); дуга | curve (line); arc |
| вести свое начало | to lead |
| 1) решать (задачу) 2) составлять, выражаться (в такой-то цифре) | 1) solve (problem) 2) compose, express (in such a figure) |
| вклад, ценные достижения | contribution, valuable achievements |
| включать, заключать в себе, содержать, охватывать | embrace |
| продвигать; поддерживать, содействовать, способствовать | promote; support |
| 1) приближённое значение 2) аппроксимация, приближение | 1) approximate value 2) approximation, approximation |
| нестабильный | unstable |
| прямоугольник | rectangle |
| изменение, варьирование; колебание | change, variation; wobble |
| заниматься | engage |
| отправная точка | a starting point |
| величина, значение | magnitude |
| незаменимый инструмент | indispensable tool |
Ex 3. Match the synonyms. Match the items on the right to the items on the left.
| 1. to describe |
| 2. to accept |
| 3. essential |
| 4. particular similarity, correlation, ratio |
| 5. to discover |
| 6. extraordinary |
| 7. to emerge |
| 8. to settle or decide by choice of alternative |
| 9. to be connected with |
| 10. to sort out |
| 11. to go on doing smth |
Ex. 4 Fill in the prepositions where necessary.
1. ___ the end ___ the 16-th century calculus was taken _____ ____ Europe.
2. A mathematical method to work ___ volume and area was developed.
3. Calculus grew ____ algebra and geometry.
4. The main contribution to science – calculus _____particular – was made ____ de Fermat.
5. Students of MIPT can’t spend time _____their own.
6. ____ fact, the first text _____ calculus was written ____ India.
7. This methodology resulted _____ the discovery _____ many important geometrical theorems and principles.
8. Einstein was born ____ Germany _____ 1879.
9. All right angles are equal _____ one another.
10. Pythagoras and Euclid laid the foundations ____ our understanding _____ space.
11. Percy's enchantment ______ Fibonacci numbers dates back _____ 1951.
Ex. 5 Complete the definitions with words from the box. (GS p.98 Ex A).
| acceleration approximation cube diverse embrace indispensable rectangle slope sphere |
1. If something is a(n)___ indispensable___, it isn't exact.
2. An increase in speed is called___ acceleration____.
3. If something is ____ approximation___, you can't manage without it.
4. If you ____ embrace___ an idea, you accept it.
5. A ____ cube___ is a three-dimensional, square shape.
6. Something which is ___ diverse___ is different or of many kinds.
7. If you place two squares side by side, you form a(n) ___ rectangle_____.
8. A ____ sphere___ is a three-dimensional surface, all points of which are the same distance from a fixed point.
9. A ____ slope__ is also known as a fall.
Ex. 6 Answer the questions on the text.
1. What does calculus deal with?
2. What is differential calculus concerned with?
3. Who was the first to develop a mathematical method to work out area and volume?
4. Where was the first text on calculus written?
5. Why was calculus taken up in Europe at the end of the 16-th century?
6. Who started to develop calculus in Europe?
7. What was the contribution of the European scientists in calculus?
8. What is the starting point of calculus? Can you give an example?
9. What does differential calculus describe?
10. What is the difference between differential and integral calculus?
11. Why is calculus so widely used today?
Ex. 7 Translate the sentences into Russian:
1. It was not until the 16th century that the system of mathematical notation that we use today finally developed.
2. It was not until the end of the 1600s that calculus was taken up in Europe.
3. Newton was the first to use calculus in his studies of physics.
4. It was during this time that de Fermat worked in the field of mathematics.
5. Although de Fermat published very little in his lifetime, he is considered to be one of the greatest mathematicians of all time.
6. Thus began a correspondence that became the foundation of Probability Theory, with de Fermat and Pascal considered to be the founders of this theory.
7. If the people he wrote to had not saved his papers and letters, we may never have heard of de Fermat and his remarkable achievements.
1. Лишь в XVI веке система математических обозначений, которую мы используем сегодня, наконец-то получила развитие.
2. Только в конце 1600-х годов исчисление было принято в Европе.
3. Ньютон был первым, кто использовал исчисление в своих исследованиях физики.
4. Именно в это время де Ферма работал в области математики.
5. Хотя де Ферма опубликовал очень мало за свою жизнь, он считается одним из величайших математиков всех времен.
6. Таким образом, началась переписка, которая стала основой теории вероятностей, и де Ферма и Паскаль считались основателями этой теории.
7. Если бы люди, которым он писал, не сохранили его бумаги и письма, мы, возможно, никогда не слышали о де Ферме и его замечательных достижениях.