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• - excel 2003. .

. .

MSc (..../ )

e-mail: s_4goum@yahoo.com, My Blog

24/07/2010

,

excel. excel

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excel ,

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excel ,

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. excel (site mediafire).

http://econews-sg.blogspot.com/http://www.mediafire.com/?5lghwq0wyjyeqon

• --------------------- 1 ( )

( Math)

excel solver ( ).

.

.

. .

.

-------

- , .

:

-

f(x0) x0 f(x) ,

x0 .

1) . 0)( 0 >xfN

2) . 0)( 0 0, f x=1 f(1)=-8

• -------

excel.

f(x,y) .

:

fx fy (

)

fx=0 fy=0 (x0,y0)

.

:

(x0,y0)

1) 0 , f

(x0,y0)

0)(*)()( 0,00,00,02 yxf xx

2) 00)(*)()( 0,00,00,02 0, fyy=2>0 fxy=-4== yyxxxy fff

) (x0,y0)=(-2,-4) fxx=14>0, fyy=2>0 fxy=-4

• !!!:

,

.

.

.

,

.

(input),

( : (x1,x2,..))

.

.

solver excel. x,y

solver .

, .

f(x)

f

() [a.b].

(x0) ,

x1 x2. x2 ,

x1. , x0=

x2, .

• .

(/ ) .

, .

,

.

.

/ ,

,

.

, ( solver

excel) , f=-x3+x2+y2-4*x*y.

(x0,y0)=(-2,-4).

(-3,-5) .

(2,3) . (

solver )

• -------

.

.

:

x1+x2+3*x3=6

-x1+2*x2-x3=3

2*x1+7*x2-4*x3=1

log(x1)+x2+3*(x3)=6

x1+2*x2-x3=3

2*x1+7* x2 -4*x3=1

:

A*x=b. Anxn . xnx1

, bnx1 .

.

= , x= , b= x=A-1*b

462121

311

3

2

1

xxx

136

.

(

).

, . excel

.

• ------------------ excel------------------

-------

excel f(x)=x4- 4*x-5.

x (.. x0=3)

f .

.

.

.

: f ( C24)

.

: x0 ( C23).

.

(x,f)=(1,-8)

-------

excel

f(x,y)= 0,5*(x-2)4+6*(y-5)2-3*x*y-50, y-x=1.

x,y (.. x0=2, y0=-4)

f .

(y0-x0)

.

.

: f ( F33)

.

: x0,y0. ( F31:F32)

: y-x ( J31). .

( : J31, , : 1)

.

(x,y,f)=(4.32, 5.32,-103.48)

• -------

excel MDETERM,

MMULT, MINVERSE.

MDETERM:

MMULT:

MINVERSE: .

A*x=b

x=A-1*b.

.

2*x1+x2+x3=10,5

x1+4*x2+4*x3=32,9

x1+x2+6*x3=37,7

= , x= , b= x=A-1*b

611441112

3

2

1

xxx

7.379.325.10

MDETERM (det) . Det=35.

.

MINVERSE.

3x3, MINVERSE Array

. Ctrl Shift Enter

-1.

MMULT, .

3x1. MMULT. Array 1,

-1. Array 2,

b. Ctrl Shift Enter

, (x1,x2,x3)=(1.3, 2.2, 5.7)

• ( Area)

, ,

.

()

.

- .

,

,

. ,

, R,

,

: f

• ..

.

.

------------------ excel------------------

excel

6 [-2,2].

.

+x*3+x*4 =f(x) 23

1) [-2,2] .

70 , () h

[2-(-2)]/70=0,057. -2,

h . 70 xi (x1, x2,..x70)=

(-2,-2+h,-2+2*h,-2+3*h..)

2) xi f(xi)

3) f(xi)*h

i-

4) .

excel (Area)

• ( Revenue)

,

. :

(R) f(t)=14*t-t2.

t=10 ?

1) [0,10] .

50 , () h

[10-0)]/50=0,2. 0,

h . 50 ti (t1, t2,..t50)=(0,0+h,0+2*h,0+3*h..)

2) ti f(ti)

3) f(ti)*h

i-

4)

( ).

excel (Revenue)

--------------------- 2 ( )

( Economic)

.

,

(). .

()

.

, .

()

/ .

• ()

/

.

, .

,

.

:

.

: 10 100.000 .

3,5%, ?

: , 50.00 .

2%. 7 ?

():

, .. 300 . 4 ?

():

5.000 10 . ,

5.000 ?

:

: ..= X*(1+r)-t

: M.A= X*(1+r)t

(): M.A()=rrX

t 1)1(* +

(): ..()=r

rXt)1(

11* +

, t , r

• ()

().

() .

(),

.

:

, .

,

( ). .. ,

(r),

(r/12).

: 6 500 .

4%. 3 ?

6 ,

. 2% (4%/2)

3 3*2=6 .

(excel)

PV:

FV:

NPER: (t)

RATE: (r)

PMT: /

• ( Loan)

. :

150.000 4%

25 .

.

PMT excel. ,

, ..

,

.

excel.

,

( ), .

25 .

, .

.

4%-6% 0,25% .

. (4%-

6%). .

, D39.

C39:D47 ( ). excel

(4%) 5.

D40:D47.

.

• --------------------- 3 ( )

( Stats)

.

.

12

(, , ).

, :

1)

2)

3)

4) , / , /

: Sum, Average, Stdev, Var, Count, CountA, CountIf, SumIf, Min, Max,

And, Or, If ( ). excel

( , , ,

) . ,

,

.

, .

-

.

.

, .

: (0,900], (900,1100], (1100,1300],

(1300,1500], 1500+. , 200 (900-

1100], (1100-1300] ... .

,

. ..

[1500,1800], 200 .

• , 50 .

() .

Frequency. . ,

C41:C45 Frequency. Data Array

(3:B14), Bins Array,

(B41:B44). Ctrl Shift Enter

.

.

.

,

.

.

. :

1000 12

()

. MinMax , Max ,

Min

• .

( ).

( ).

excel (autofill), ,

,

.

(excel)

Sum:

Average:

Max, Min: /

Var, Stdev: /

Count: ()

CountA: (,

, )

SumIf:

CountIf:

And:

Or:

.

If:

Frequency: .

(..

: / , /

,

,

)