Добавил:

Chupapi_Munyanya Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Национальный исследовательский университет «МЭИ»

Предмет:

Высшая математика

Файл:

УрМатФиз / УрМатФиз с теорией

.pdf

Скачиваний:

Добавлен:

16.05.2024

Размер:

4.39 Mб

Скачать

☆

<<< < Предыдущая 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3031 / 3631 32 33 34 35 36 > Следующая >>>

E | , K = jjKijjj C = C1 ::: Cn T = 0 ::: 0T :

K x t 7.1.1
jE Kj = 0	7:1:6

! " # $		K x t %
$	n
	n
	y x = X ai x Ci	7:1:7
	i=1

Ci i = 1 n | # & ' ()*+ 7.1.5 %.

- 7.1.1 .+ 7.3 , % -

()*+	n
	n
	Bi = X KjiBj i =	1 n	7:1:8
	j=1

& z x .+ 7.3 & ()*+ 7.1.8 Bi $'

n
z x = X bi x Bi:		7:1:9
i=1
7.1. 3	5 4	II
7.1 K x t % ' 4	f x :

1 K x t = 2x 1 cos t a = 0 b = f1 x = sin x f2 x = x8 2 K x t = x ch t + t a = 1 b = 1 f x = x:

: ' K x t - ! " # $.

" - , , & 4 .+.

- , , % 4 -& . : ' & .+, #% .

1: - $ 7.1.3 '

K11 = Z 2t 1 cos t dt = 4:

< ()*+ 7.1.5 ! ' :

1 + 4 C = 0:

7:1:10

301

, :

1 + 4 = 0 = 1=4:

!"# $7.1.10' = 1=4 C 6= :0() $7.1.7' * + , ,

- . :

y$x' = 2x 1:

*'	6= 1=4. 0			(# f$x' =
= f1$x' = sin x:		+ $7.1.3' 2
		f1 =	cos t sin t dt = 0:
		0
!"# $7.1.2'		C = 0:
- $7.1.4'			(# 6= 1=4
f1$x' = sin x
		y$x' = sin x:
0	f$x' = f2$x' = x:				+
$7.1.3' 2

		f1 =	cos t t dt = 2:
		0
!"# $7.1.2'
	$1 + 4' C = 2 C = 2=$1 + 4' :
	$7.1.4'				(#
6= 1=4 f2$x' = x
		y$x' =	2	$2x 1' + x:
		y$x' =	1 + 4	$2x 1' + x:
			1 + 4

' = 1=4. 0 *-+ , )- K$t x' = cos x$2t 1': 4 !"# $7.1.8'

$1 + 4 'B = 0:

302

		= 1=4
7.1.9!,		#-
% # & :
z x! = cos x:
( ) 7.4! *+ # =	1=4 # ,
f x! = f1 x! = sin x:

sin x cos x dx = 0:

+ .# , % , *+ - ) , 7.5!

y x! = C2x 1! + sin x

# | ) , | ) .

( ) 7.4! *+ # = 1=4 # ,f x! = f2 x! = x:

x cos x dx = 2 6= 0:

+ .# , % , *+ # , % f2 x! = x

# = 1=4 ) ,.
2: ! (		7.1.3! ,
	1			1
	K11 = ch t t dt = 0			K12 = ch t 1 dt = 2 sh 1
	1			1
		1		1
	K21 = t t dt = 2=3			K22 = t 1 dt = 0:
		1		1
	456+ 7.1.5! , :
	0	1	2 sh 1 1 0 C1 1 0 0 1
	@ 2 =3		1	A @ C2 A = @ 0 A	:	7:1:11!

303

, -

=2psh 1:

1 = p

=2psh 1

2 =

7.1.11 C1 C2 = p

3 sh 1

7.1.7

$ % &

y1 x = p

x + 1:

3 sh 1

2 =

=2p

sh 1

7.1.11

C1 C2 = p3 sh 1 1 , ( $

% &

y2 x = p3 sh 1 x 1:

6= 1 2:

7.1.3

f1 = Z ch t t dt = 0

f2 = Z t t dt = 2=3:

* +,-. 7.1.2

2 sh 1 1 0 C1 1 = 0 0 1

@ 23

A @ C2 A @ 2=3 A

C1 C2 =

2 sh 1 1:

3 4

2 sh 1

# 7.1.4

y x =

2 sh 1 x + 1 + x:

3 4 2 sh 1

1 2: *


% & 1 # K t x = ch x t + x: 2 +,-. 7.1.8
	0	1			2 =3 1 0 B1 1 = 0 0 1 :

	@ 2 sh 1				1 A @ B2 A @ 0 A
	,										-
		p		=2psh 1: 4
1 2 =			3								1 =
= p3=2psh 1 $ % &
		z1 x = ch x + p								x
							3 sh 1
		2 = p						=2psh 1 \| % &
						3
		z2 x = ch x p							x:
						3 sh 1

304

	7.4				=	2
f x = x:
1		1				2

Z f x z1 x dx = Z xch x + p3 sh 1 x dx = p3 sh 1							6= 0
Z f x z1 x dx = Z xch x + p3 sh 1 x dx = p3 sh 1						3	6= 0
1		1
	1		2


	Z	f x z2 x dx = p3 sh 1 3		6=:0
	1
" # " " , %" ,					=	1 2	"
" .

1 '

1 = 1=4 y1 x = 2x 1&

= 1=4

f1 x = sin x y x = sin x

f2 x = x y x =

2x 1 + x&

1 + 4

1 = 1=4

f1 x = sin x y x = C2x 1 + sin x

f2 x = x " " .

1 = p

= 2p

sh 1 y1 x = p3 sh 1

x + 1

2 = p3=2p

sh 1 y2 x = p3 sh

1 x 1&

2 sh 1 x + 1 + x&

6= 1 2 y x =

3 4 2 sh 1

6= 1 2

" " .

7.1. ( " " ) %" " " * ) % II 7.1 .

+ ,- - K x t .- 0 ' ""# 1 "-2 .

'	,	" " ,- - " " , % .
	,	" ,- - " " ., % -

"" ) . + " , #- " " .

# " , % % 1

sha b = sh a ch b ch a sh b	cha b = ch a ch b sh a sh b
2 sh2 a = ch 2a 1	2 ch2 a = ch 2a + 1:

305

K x t = x2 cos 2t

a = 0

b =

f1 x = sin 2x

f2 x = x2:

K x t = cos x + t

a = 0

b = 2 f x = x:

1 K x t = sin x t

a = 1

b = 1 f1 x = 3x2

f2 x = x:

K x t = sin x + t

a = 0

b = 2 f x = x:

2x2

K x t =sin x t a = 1 b = 1 f1 x =

f2 x = x

1 x2

K x t = cos x t

a = 0

b = 2 f x = x:

K x t = x2 sin 2t

a = 0

b =

f1 x = cos 2x

f2 x = x:

K x t = sin x t

a = 0

b = 2 f x = x:

1 K x t = cos x 3t2 1 a = 1 b = 1 f1 x = x f2 x = x2:

K x t = ch x + t a = 1 b = 1 f x = 1:

K x t =

2x2 1 2t2

a =

1 b = 1 f1 x = x + 1

f2 x = p

x2:

K x t = sh x

+ t a = 1 b = 1 f x = 1:

1 K x t = x+1 sin 2t a = 0 b = f1 x = cos 2x f2 x = x:

K x t = ch x t a = 1 b = 1 f x = 1:

8. 1 K x t = x2 t+1 a =

1 b = 1 f1 x = 5x3 3x f2 x = x2:

K x t = sh x t a = 1 b = 1 f x = 1:

9. 1 K x t = x 4t3 3t a = 1 b = 1 f1 x =

f2 x = x:

K x t = cos x + cos t

a = 0

b = 2

f x = x:

10.

1 K x t = x+1 cos t a = 0

b = f1 x = sin x

f2 x = x:

K x t = sin x + sin t

a = 0

b = 2

f x = x:

11.

K x t = x3 5t3 3t

a = 1

b = 1

f1 x = x

f2 x = x2:

K x t = ch x t + ch t a

= 1 b = 1 f x = x:

12.

K x t =

= 1

f1 x = 4x 3x

f2 x = x

+ sh t a = 1 b = 1 f x = x:

K x t = sh x

13.

K x t = 3x 1 sin 3t a = 0

b = =2

f1 x = sin 5x f2 x = 1:

306

K x t = cos x

t + x cos t

a = b =

f x = x:

14.

K x t = x2 3t2

1 a =

1 b = 1 f1 x = 5x3

3x f2 x = x2:

K x t = sin x

t + sin t

a =

b = f x = x:

15.

K x t = p1

t2 a = 1 b = 1

x = x

f2 x = p1

K x t = x sin t + sin x

a = b = f x = x:

16.

K x t = x + 1 cos t a = 0 b = =2 f1 x = cos 3x f2 x = 1:

K x t = sin x

t + x

a = b =

f x = x:

17.

1 K x t = x 5t3 3t a = 1 b = 1 f1 x = 3x2 1 f2 x = x2:

K x t = x sin t + t a =

b =

f x = x:

18.

1 K x t = x3

1 t a = 1 b = 1 f1 x =

f2 x = x2:

K x t = sh x t + sh t a = 1 b = 1 f x = x:

19.

K x t = x

1 sin t a = 0 b =

f1 x = sin 2x

f2 x = 1:

K x t = x sh t + sh x a = 1 b = 1 f x = x:

20.

K x t = p

a = 1

b = 1 f1 x = 2x

f2 x = x

K x t = sh x t + x a = 1 b = 1 f x = x:

21.

K x t = 3x2 1 3t2

1 a = 1

b = 1

f1 x = 1

f2 x = x:

K x t = x sh t + t a = 1 b = 1 f x = 1:

22.

1 K x t = 5x sin 5t a = 0

b = =2

f1 x = sin 3x

f2 x = 1:

K x t = cos x

t2 + x2 sin t a =

b =

f x = x:

23.

K x t = x t+1 a =

b = 1 f1 x = 3x2

f2 x = x2:

K x t = sin x

t + x sin t

a =

b =

f x = x:

24.

1 K x t = x2 2t2

1 a = 1 b = 1 f1 x =

f2 x = x2:

K x t = ch x t + x ch t a = 1 b = 1 f x = x:

25.

K x t = 3x + 1 cos 3t

a = 0 b = =2

f1 x = cos x

f2 x = 1:

307

K x t = x2 cos t + x sin t

a =

b =

f x = x2:

26.

1 K x t = x23t2

1 a =

b = 1

f1 x = x

f2 x = x:

K x t = cos x

t2 + sin x

a =

b =

f x = x:

27.

K x t =x4t3

3t a = 1

b =1 f1 x =

f2 x =x2:

K x t = cos x cos t + xt

a =

b =

f x = x:

28.

K x t = 2x sin 2t a = 0

b =

f1 x = sin x

f2 x = x:

2 K x t = ch x sh t + xt a = 1 b = 1 f x = x:

29.

K x t = x3 + 1t a = 1

b = 1

f1 x =35x4

30x2 + 3

f2 x = x:

2 K x t = x2 ch t + x sh t a = 1 b = 1 f x = x:

30.

K x t = p

a = 1

b = 1 f1 x =4x

f2 x =x

K x t = sin x t + cos x sin t a =

b = f x = x:

7.2.

! " # $% &-

& ( % 7.1

y0 x = f x yn x = Z K x t yn 1 t dt + f x n =

) " * + , - .					/( *-
0 # (12 # :
n	b
n	Z
y0 x = f x yn x = X i		Ki x t f t dt + f x n =
y0 x = f x yn x = X i		Ki x t f t dt + f x n =		1
i=1	a				1
&
b
K1 x t = K x t Ki x t = Z
K1 x t = K x t Ki x t = Z		K x s Ki 1 s t ds i =	2		7:2:1
a		1

| % .

308

jj		1	M	=	max	jK x t j:	:2:2

		M b a
					a b a b
	8f x 2 Ca			b ,

! ! " # $!% !a b & '

y x = X

i=1

. *

y x =

b
i Z Ki x t f t dt + f x :	:2:3
a
+ ,
Zb R x t- f t dt + f x	:2:4
a

				1
	R x t- =				i 1Ki x t		:2:5
				i=1
				X
\|					! .
7.2. 1 2 II
! K x t 3 4 # f x :
1 Kx t = arctg x		t + t2 a = 1 b = 1 f x = x-
2 K x t = ch x sh t + xt a = 1 b = 1 f x = x:
6 3 7 !					! ! K x t.
" 6 3 , ! R x t- % # !							3
, 7$ 8 ! $!.
9 % # , ! R x t-						3
. 1 &					$ 7 !
	K1 x t = arctg x t + t2 -
K2	x t = Z1		arctg x s + s2 arctg s t + t2 ds =
		1
= arctg x	t + t2 Z11	s + s2 arctg s ds = arctg x				t + t2 2 1! -

309

K3 x t =

arctg x s + s2 arctg s t + t2 ds =

= arctg x t + t2

1!2

:::

Ki x t = arctg x t + t2

1!i

i =

1 1

R x t 7.2.5 :

R x t =

i 1 arctg x t + t2

1!i 1 =

i=1

i 1

2 1 = arctg x t + t2

= arctg x t + t2 i=1

2=2j 1

j j 2=

2 f x = x

yx =

arctg x

t + t

t dt + x =

arctg x + x:

x t

! " , $!-

& " $" , ' . 6. ) *$ "

K11 =

ch s sh s ds = 0

K12 =

sh s s ds = 2

h 1 sh 1

K21 = s ch s ds = 0

K22 = s s ds = 2=3:

) . 6

K11 = K21 = 0 '

x t = t 2 h 1 sh 1 ch x + 3x! 3!

i = 2 1

310

<<< < Предыдущая 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3031 / 3631 32 33 34 35 36 > Следующая >>>

Соседние файлы в папке УрМатФиз

#
16.05.20249.25 Mб2Bilety_po_urmatfizu_v0_9.docx
#
16.05.202417.63 Mб1Kachestvennaya_podgotovka_k_ekzu_21_goda_1.docx
#
16.05.2024207.5 Кб1Задача Коши для ДУ 1-го пор.docx
#
16.05.2024416.66 Кб1Общ. реш. ДУ 1-го пор..docx
#
16.05.2024147.34 Кб2Программа по Матфизике.pdf
#
16.05.20244.39 Mб13УрМатФиз с теорией.pdf