Unit 8.Some algebraic expressions and formulas

d 2 z

the second derivative of y with respect to x

dx2

d n z

the n-th derivative of y with respect to x

dxn

y = f (x)

y is a function of x ; or: y equals f of x

→

approaches; or: approaches the limit; or: tends to

x → a

x approaches the limit a

x → x0

x approaches x nought; or: x tends to x naught

∫nm

integral of … from n to m; or: integral of … between

limits n and m

∫2xdx = x2

the integral of 2x dx is x2

d

∫x lxdx

d over dx of the integral from x sub 0 (or: from x zero-

th) to x of capital Lxdx

dx x0

m = R1 x − P1 (x − a1 )

m equals R sub one multiplied by x minus P sub one

− P2 (x − a2 )

round brackets opened, x minus a sub one, round

brackets closed, minus P sub two round brackets opened,

x minus a sub two, round brackets closed; or: m equals R

first x minus P first multiplied by the difference between

x and a sub one minus P second multiplied by the

difference between x and a sub two

∑

the sum

n

Summing over x sub i from one to n

∑xi

l=n

a prime

[praIm]

штрих, со штрихом

a double prime

[`dAbl `praIm]

двойной штрих; два

[`trIpl `praIm]

штриха

a triple prime

тройной штрих; три

a first prime

[`fq:st `praIm]

штриха

modulus

[`mOdjulqs]

абсолютное значение

pl moduli

[`mOdjulaI]

(числа), модуль

derivative of

[dI`rIvqtIv qv]

производная;

[wID rIs`pekt tq]

производное число от

with respect to

что касается, по

approach

[q`prouC]YUU

приближаться,

подходить; достигать

[`IntIgrql ]

значения

integral of

интеграл от

limit

[`lImIt]

предел

8.1.2. Read the symbols.

1

x → a

a)

a double prime

2

∑

b)

second derivative of z

3

a2′′

c)

the sum

4

Z

d)

a second second prime

&

5

a′′

e)

x approaches the limit a