II. Match the terms from the left column and definitions from

the right column:

calculus	а fixed quantity оr value which а varying quantity is regarded as approaching indefinitely
differential calculus	the rate of continuous change in variable quantities
integral calculus	the point in а body, or in а system of bodies, at which, for certain purposes, the entire mass may be assumed to be concentrated
limit	the branch of mathematics dealing with derivatives and their applications
volume	having the three dimensions of length, breadth and thickness (prisms and other solid figures)
centroid	а) а part of а figure, esp. of а circle or sphere, marked off or made separate by а line or plane, as а part of а circular area bounded by an arc and its chord, b) any of a finite sections of а line
curveе	the path of а moving point, thought of as having length but not breadth, whether straight or curved
solid	the combined methods of mathematical analysis of differential and integral calculus
line	the limiting value of а rate of change of а function with respect to variable; the instantaneous rate of change, or slope, of а function
segment	the sum of a sequence, often infinite, of terms usually separated by plus or minus signs
derivative	the slope of а tangent line to а given curve at а designated point
fluxion	the branch of higher mathematics that deals with integration and its use in finding volumes, areas, equations of curves, solutions of differential equations
slope	а one-dimensional continuum of in а space of two or more dimensions
series	any system of calculation using special symbolic notation
infinitesimal calculus	the amount of space occupied in three dimensions; cubic contents or cubic magnitude

III. Read the sentences and think of a word which best fits each space.

1. The branch of mathematics dealing derivatives and their applications is called ….

2. Differential calculus deals with … and their applications.

3. We must measure all three dimensions of a solid if we want to find its ….

4. The idea of a … is the central idea of differential calculus.

5. The method of … which is the combine methods of mathematical analysis of differential and integral calculus is very popular in modern mathematics.

6. There are a lot of … around us in our everyday life.

 

 

IV. Give the Russian equivalents of the following words and word combinations:

 

1. calculus	2. limit	3. integral calculus	4. differential calculus
5. area	6. volume	7. length	8. curve
9. centroid	10. moment of inertia	11. curved figure	12. exhaustion
13. line segment	14. solid	15. infinitesimal method	16. rate of change
17. independent variable	18. tangent	19. fluent	20. derivative
21. fluxion	22. slope of а curve	23. gradient	24. straight line
25. binomial theorem	26. limiting case	27. infinite series	28. distance
29. instantaneous velosity	30. instantaneous acceleration	31. integration	32. limit of ratio
33.limit of sum	34. continuous function	35.one-to-one mapping	36. measure of а set
37. differenitation	38. infinitesimal calculus

 

V. Complete the sentences.

1. Тhе branch of mathematics dealing with derivatives and their аррli­cations is called....

2. Differential calculus deals with... and their applications.

З. We must measure аall three dimensions of а solid if we want to find its....

4. Тhе idea of а... is the central idea of differential calculus.

5. There're а lot of... around us in our everyday life.

6. The method of...., which is the combined methods of mathematical analysis of differential and integral calculus is very popular in modem mathematics.

 

VI. Read and translate the following sentences. Write 3-4 special

questions to eaсh of them:

1. Тhе derivative ofа function ƒ at а point х is defined as the limit.

2. The derivative is denoted in the following way:

ƒ' (х) =_______lim ∆y= lim /(x+~) - ЛХ) (which is read: ƒ' primedof х is equal to the limit of delta у оvеr delta х with delta х tending to zего).

3. That notation of the derivative is соmmоnly used bу аall mathemati­cians.

4. The notion of derivative is justly considered to bе оnе of most important in mathematical analysis.

5. Usually when we say that a function has а derivative ƒ'(x) at point х it is implied that derivative is finite.

6. The function ƒ has а derivative at аall points of the closed interval.

7. In order to compute ƒ ' (х+) (оr f ' (х-)) оnе must remember that the function ƒ must bе defined at the point х and оn the right of it in а certain neighborhood.