лекц маткад

" # ex = x3 .
&' # :
1	x:			x:=3
2	x:3 . ) , '
Mathcad ( ) ).
3	), ) ' . / (
#
	x3	- ex = 0.
( ) root.
4	& y . / (
	y: root(x^3 ± e^x,x)	y:=root(x3 ± eX,x)
5	0 y=, :			y=1.857
' root # #:
•
root.			x2 ± 1 = 0,
•	/ ) ,
,			Mathcad.	0 3

x3 ±10x + 2, $ )

root. X:= −10, -9.9..10

" 3

/ $) $ $ & $

):

X:=-2 root(x3−10x+2,x) = −3.258 X:= 0 root(x3−10x+2,x) = 0.201 X:= 3 root(x3−10x+2,x) = 3.057

Mathcad $ , ' . /
)
.		(
* # f(x)=g(x)
)	f(x) ± g(x) = 0 ./ (	root	)
&' :

root(f(x)-g(x),x).

/ ) ! , " (

/ $)
	nXn + ··· +A2X2		+ A1X + A0 =0
# & polyroots. root polyroots
). 1 , polyroots '
, ', .			0 )
polyroots.
Polyroots(v) ± '			n. 1 (
$ v n+1.		' n, '
.
! ( ! 6.1
X3-10·X+2	←" ( ( . . 3)

V:=

←6&& " (

polyroots(v)= ← -! 7 !-+

____________________________________________________________________

! ( ! 6.2

x3 + (3 + 2i)·x2 + (-4 + 6i)·x ± 8i ←! *+ , ! ( '$"

( " ( 6&& (

v:=

← ! 6&&

Polyroots(v) = ← -! 7 # !

% ( +! ,

/ # $ &' :

1 * ) $ $, $'$

. Mathcad # ' $ . 0

) , $' # &.

2 0 & Given. Mathcad,
.			Given ) & #,
. +,			( $
.
3	& ) & Given.
+, ) «=».
! # «[ctrl] =»		«=». )
) & : «<», «>»,				«£» «³».
4	& ), & &			Find.
Find ) # & , ,
.
∙	Find ( z1, z2, z3,	. . . ) − ' # ;
) $ .
Find ' # &' :
∙	5 Find	, ' #
, ) ) & Given Find.
∙	5 Find	, '
. 0, Find		(z1 , z2) ' , ) ' z1
z2, &' # .

1 & Given, , & , -

), ) ' & Find, & # .

) & Given Find #

) . 0 ) $

), # . ! $ ) . , ) &

. 5, ), x y '

), z w & ).

6.1
+		1
w = z		[ ctrl ] =	; ' 1 ,
			; 0
x > y		<	; #
x < y		>	#
x ³ y		[ ctrl ] 0	; #
x £ y		[ ctrl ] 9	#
w ¹ z		[ ctrl ] 3	0

% &' ) # : ∙ ¹;

∙ ), ) '

& ;

∙ a < b < c .

0 ) # ,

e#. " # & .

Find ) : x y, '

.

! ( ! 6.3

0 ) ( #
$
).
$". - $ :	x:=1
	y:=1
Given	x2+y2=6	←	!+) .
	x+y=6	←	! (
	x≤1	←	'!$ ! !
	y>2
	:= Find(x,y)
%:	xval = - 0.414
	yval = 2.414
! ! , ' ! %:
	xval2 + yval2 = 6		xval + = 2

" ., ' athcad ( ) , ! %?

∙5 # - # )

) # & &

' # , # ', Find

' # «( ! ».

∙5 # & ,

$&, . 3 ) ,

) $ #. , ) $'

).

∙!

.

, ! ( ! 6.4

" # & 0.00001.

:

% $ Mathcad ) #

# &'

(Solve block)

______________________

x:=0 y:=1 TOL:=1´10-5 .

1

2

3

4

* ) $ . * & Given.

* . + * & Find(x, )=.

Find(xylem)=

5 #

" Mathcad 6.1

" 6.1

7

5 8 3 0 9 3 1 2

! *" ) ! % * / && ! ". / +! , (

– ,

.

! # ,

# ) (

" -1) .

1 $ , # #

& #

. 5' ) # ($ $.

( # & # $

, &' $ $.

Mathcad ' 13 $ # $

$ $ $

. " $ – rkfixed –

" -1 4- # . ,

h5 (h – # ).

:

					Z:=rkfixed(y,x1,x2,npoints,D),
	y – $ $ #;
	x1 –	;
	x2 –	;
	npoints – # ;
	D – – $ .
"
Mathcad
			.
1 /						.
* #		D.			. ( ,
:								.	.
		. 0 &						,	.
2 /						.
(					, & ),
' .
3 /
						.
( ,						,
:					.
rkfixed ' Z ( +1) n ( –
). Z –								# :
–		( ,				, –
	,						– $
.

! ( ! 7.1

0 # . .

y′′=-y′+2y,

&'$ $ $: y(0)=1, y′(0)=3.

(

" rkfixed. (:

- ,

x1=0, x2=2 – ( ' #, npoints=400– # ,

. 0 ) Mathcad ) ' & # «[»

.

# Mathcad:

	,		– 400
	[0; 2],	– ($ $,			–
.		, (
( .7.1). & )				' &
.

" 7.1

% #, &

Z<0> ( $ ' & # Ctrl + 6),

– Z<1>. , ) #

.

, ! ( ! 7.2

/ $ $ ( &

f1, & f2) # [xn, xk]

#.

$ .

! $

$". + "

! "

f1

f2

Y(0)

y (0)

xn

xk

yn+9y

0

5(x+2)2

0

3

0

5

:

$) ) #

" -1 4- #

( rkfixed). #

&' :

Z:=rkfixed(y,x1,x2,npoints,D),

y – $ $ #; x1 – ; x2 – ; npoints – # ;

D – - $ . . (

( # ( 2).

rkfixed ' !+1 n ( –

). Z – # :

– ( , , –

, – $ $

.

1% .

2/ $) # &

f1 &':

2.1$ y:= .

2.2: $1:=0, $2:=5.

2.3* # : npoints:= 400

2.4	* &- $ : D(x,y):=	.
2.5	* & # :

	Z:= rkfixed(y,x1,x2,npoint,D).
2.6	%	#,
			Z1<0> ( $ ' & #
Ctrt + 6), –			Z1<1>.
3 / $) # &
f2 &':
3.1	* &- $ :			D(x,y):=	.
3.2	*	& #			:
Z:= rkfixed(y,x1,x2,npoint,D).
3.3	%	#,
			Z1<0> ( $ ' & #
«Ctrt + 6»), - Z1<1>.

" Mathcad 7.1.

" 7.2

8

: 1 0 13 3