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.

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