Основные математические понятия в английском языке. Прокошева И.И. - 29 стр.

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()
(
)
1
2
0
1
1
−
=
−
−Π=
ε
s
n
s
n
xxD
D sub n minus one prime of x is equal to the product from s equal zero to n of,
parenthesis, one minus x sub s squared, close parentheses, to the power epsilon minus
one.
()
(
)
()
dw
kww
ztK
Пi
xt
w
−
=Κ
∫
=−
,
2
1
,
2
1
ρ
K of t and x is equal to one over two
π
i times the integral of K of t and z, over w
minus w of x, with respect to w along curve of the modulus of w minus one half, is
equal to rho.
()
0;0
4
2
2
>=∆∆+ aua
dt
ud
the second partial (derivative) of u with respect to t plus a to the fourth power, times
the Laplacian of the Laplacian of u, is equal to zero, where a is positive
() () ()
1;
2
1
>=
∫
∞+
∞−
cdw
w
x
w
Пi
xD
n
ic
ic
k
k
ζ
D sub k of x is equal to one over two
πι
times integral from c minus
ι
infinity to c
plus i infinity of dzeta to the k of w, x to the w over (or: divided by) w, with
respect to w, where c is greater than one.
2. Practice reading the following expressions by yourself, check your answer
using the keys
a.
()
xx
4
3
3
2
523
2
1
715
7
2
+=
−++
b.
()
Lxf
x
=
→
lim
1
c.
()
()
(
)
Sx
xfxSxf
xf
s
−+
=
→
lim
0
'
d.
dt
ds
S =
29
                                                                          (       )
                                                                   n
                                                 Dn−1 ( x ) = Π 1 − x s2
                                                                                   ε −1
                                                                  s =0



D sub n minus one prime of x is equal to the product from s equal zero to n of,
parenthesis, one minus x sub s squared, close parentheses, to the power epsilon minus
one.

                                                        1                      K (t , z )
                                        Κ (t , x ) =              ∫                       dw
                                                       2 Пi     1             w − w(k )
                                                              w− = ρ
                                                                2



K of t and x is equal to one over two πi times the integral of K of t and z, over w
minus w of x, with respect to w along curve of the modulus of w minus one half, is
equal to rho.


                                              d 2u
                                                   + a 4 ∆∆u = 0; (a > 0)
                                              dt 2

the second partial (derivative) of u with respect to t plus a to the fourth power, times
the Laplacian of the Laplacian of u, is equal to zero, where a is positive


                                                         c + i∞
                                                    1                 k      xn
                                       Dk ( x ) =                         (w) dw; (c > 1)
                                                  2 Пi c −∫i∞
                                                              ζ
                                                                             w


   D sub k of x is equal to one over two πι times integral from c minus ι infinity to c
   plus i infinity of dzeta to the k of w, x to the w over (or: divided by) w, with
   respect to w, where c is greater than one.


       2. Practice reading the following expressions by yourself, check your answer
                                    using the keys
               2       1               2 3
          a.    15 + 7  + 3(x − 2)  = 5 + x
               7       2               3 4

          b.   lim f (x ) = L
                x →1



                                   f ( x + S )x − f ( x )
          c. f ' (x ) = lim
                            s →0            Sx

                       ds
          d. S =
                       dt


                                                                                               29

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