лекц маткад

1.3.1& SYMBOLICS

Simplify. 0 )

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1.3.2, (, , )

df(x)

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1.4. & dF(x):

x:=	y:=
1.4.1 *	$ $ $ ,

$

1.4.2 * & , ,

dF(x):linterp(X,Y,x).

1.5 %

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1.6 , $)

& 1.63.

1.7 * $) #

Ot_Pogresh:= | df(0.63)-dF(1.63)| ·		,
113.175%.
1.8	%$ .

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2/ 2 &':

2.1%$ , 1 .

2.2( vs:=csplinc(X,Y);

2.3! dF(x):=interp(vs,X,Y,x);

2.4, $)

& 1.6.

#

39.023 %.

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3/ 3 :

3.1% .

3.2* & f(x):=3+sin(4+x2).

3.3 * $ $ $ X:=

Y:=

3.4 * & Fl(x):=linterp(X,Y,x), ( vs:=cspline(X,Y)

Fk(x):=interp(vs,X,Y,x).			( :
3.5	f(x),
	3.5.1	0 Calculus Definite Integral;
	3.5.2	* # # )
		# «=». – 4.792.
3.6	3 Fl(x) Fk(x).
– 4.926 – 5.146 .
3.7	* $) $ #:
	Ot_PogreshFl:= | - 4.792? (- 4.926)|		Ot_PogreshFl = 2.796,
	Ot_PogreshFk:= | - 4.792? (- 5.146)|		Ot_PogreshFk = 7.387.

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,	16.156			113.175		-2.796
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P:=Minimize(<( &+>,< ! ( />), P:=Maximize(<( &+>,< ! ( />),

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0 5.4 2 2

: f(x,y)= (x+2) +y +3.

	/			Mathcad		1
	1	* &		f(x,y):= x2+y2+3		f(x,y):(x+2)^2+y^2+3
	2	*		x:=1 y:=1		x:1 y:1
	$
	3	* &				P:Minimize(f,x,y)
				P:=Minimize(f,x,
				y)
	4
	$,					P =
	$
	5			f(-2,0)=3		f(-2,0)=
	(

! ( ! 5.5
0 z(x) =@x-5@-@x@-@7x+3@.
:
	/			Mathcad		1
	1	* &		z(x):=@x-5@-@x@-		z(x) :@x-5@-@x@-
		*		@7x+3@		@7*x+3@
	2			x:=0		x:0
	$
	3	* &		P:=Maximize(z,x)		P:Maximize(z,x)
	4
	,			P = -0.429		P =
	5			z (P) = 5		z(P) =
	(

! ( ! 5.6
0 f(x,y) = x2+y2 x [-10,10] y [10,20].
:
	/				Mathcad		1
	1	* &			f(x,y):= x2+y2		f(x,y):x^2+y^2
	2	*			x:=1 y:=1		x:1 y:1
	$
	3	* &			Given		Given
	#
	4	*			xA-10		x «Ctrl +0»-10
					xB10		x «Ctrl +9» 10
					yA10		y «Ctrl +0» 10
					yB20		y «Ctrl +9» 20

	5	* &		P:=Minimize(f,x,y)		P:Minimize(f,x,y)
	6
	$,					P =
	$
	7			f(0,10) = 100		f(0,10)=
	(

				, ! ( ! 5.7
1		/ f1(x), &' (, (;
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2		/		f2(x), &'	(,
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	f1(x)					f2(x)
	$ / (1+$4)					E
:

1 / 1 &':

1.1* & f(x):= .

1.2% .

1.3, $ $) ( ±2, ( ) $:= ±2.

1.4* & P:=Minimize(f,x).

1.5P:= ±0,76,

( f (0,76) = -0,57.

1.6* & P:=Maximize(f,x).

1.7P:= 0,76,

( f (0,76) = 0,57.

1.8%$ .

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2 / , &' (, )
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2.1	% .
2.2	* & f(x):= e
2.3	% .
2.4	, $) $ (
) $,				, , [-5;2], ( )
$:					$:=±5. * &
given	#; & $,
Evaluation: x ³-5				/ £ 2.
2.5	3	1.4…	1.7	$
			"= ±3.142
	P:=minimize(f,x)				f(P) =1
	P:=maximize(f,x)		P=0		f(P) = 4.113

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3.1% .

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3.2 * f1(x):= 1 + x 4 f2(x):= e 1+cos( x)

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