Теория функций комплексной переменной. Захаров Ю.В - 4 стр.

UptoLike

ВУЗ: 

СФУ | Красноярск

Составители: 

Рубрика: 

7
ɛ) ȼɵɩɨɥɧɟɧɢɟ ɢ ɫɞɚɱɚ ɬɪɟɬɶɟɝɨ ɤɨɧɬɪɨɥɶɧɨɝɨ ɡɚɞɚɧɢɹ, ɩɪɢɜɟɞɟɧɧɨɝɨ ɜ ɩɪɢɥɨɠɟɧɢɢ 3.
Ɉɰɟɧɤɚ 5 ɛɚɥɥɨɜ.
ɜ) ȼɵɩɨɥɧɟɧɢɟ ɞɨɦɚɲɧɢɯ ɡɚɞɚɧɢɣ ɢ ɭɫɩɟɲɧɚɹ ɪɚɛɨɬɚ ɧɚ ɡɚɧɹɬɢɹɯ ɨɰɟɧɢɜɚɟɬɫɹ 0,5 ɛɚɥɥɚ ɡɚ
ɡɚɧɹɬɢɟ. ȼɫɟɝɨ 5 ɛɚɥɥɨɜ.
Ɇɚɤɫɢɦɚɥɶɧɚɹ ɨɰɟɧɤɚ ɩɨ ɜɬɨɪɨɦɭ ɪɭɛɟɠɧɨɦɭ ɤɨɧɬɪɨɥɸ 25 ɛɚɥɥɨɜ.
ɉɊɂɅɈɀȿɇɂȿ 1
ɉɟɪɜɨɟ ɤɨɧɬɪɨɥɶɧɨɟ ɡɚɞɚɧɢɟ
1. ȼɵɱɢɫɥɢɬɶ
i
i
+
¸
¹
·
¨
©
§
−
1
2
1
.
2. ȼɵɱɢɫɥɢɬɶ
3
1Ln i− .
3. Ⱦɨɤɚɡɚɬɶ
xyz
22
sinch|cos| −= .
4. ȼɨɫɫɬɚɧɨɜɢɬɶ ɚɧɚɥɢɬɢɱɟɫɤɭɸ ɮɭɧɤɰɢɸ
)(z
f
ɩɨ ɟɟ ɞɟɣɫɬɜɢɬɟɥɶɧɨɣ ɱɚɫɬɢ
3223
236)(Re yxyyxxzf −−+= .
5. ȼɵɱɢɫɥɢɬɶ
³
=1||
3
z
dzz ɞɥɹ ɜɟɬɜɢ 11
3
= .
6. Ɋɚɡɥɨɠɢɬɶ ɜ ɪɹɞ Ʌɨɪɚɧɚ ɞɥɹ
az >|| ɮɭɧɤɰɢɸ
22
1
)(
az
zf
−
=
.
7. Ɋɚɡɥɨɠɢɬɶ ɜ ɪɹɞ Ʌɨɪɚɧɚ ɜ ɨɤɪɟɫɬɧɨɫɬɢ ɬɨɱɤɢ
2−=z ɮɭɧɤɰɢɸ
2
)2(
)(
+
=
z
z
zf
.
8. ɇɚɣɬɢ ɜɵɱɟɬ
»
¼
º
«
¬
ª
∞
+
,
2
sin
res
z
z
.
9. ȼɵɱɢɫɥɢɬɶ ɢɧɬɟɝɪɚɥ
dz
izzz
z
z
))(1(
sin
2
1
|1|
2
³
=−
−−
.
10. ȼɵɱɢɫɥɢɬɶ ɢɧɬɟɝɪɚɥ
³
=
+
4||
3
1
3
z
z
dz
z
z
e .
ɉɊɂɅɈɀȿɇɂȿ 2
ȼɚɪɢɚɧɬɵ ɜɬɨɪɨɝɨ ɤɨɧɬɪɨɥɶɧɨɝɨ ɡɚɞɚɧɢɹ
ɇɨɦɟɪɚ ɡɚɞɚɱ ɩɪɢɜɟɞɟɧɵ ɩɨ ɫɛɨɪɧɢɤɭ ɡɚɞɚɱ ȼɨɥɤɨɜɵɫɤɨɝɨ [3], ɝɨɞ ɢɡɞɚɧɢɹ 2002.
Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɜ ɩɪɢɥɨɠɟɧɢɢ 4 ɜɨɫɩɪɨɢɡɜɟɞɟɧɚ ɝɥɚɜɚ 4 ɷɬɨɝɨ ɡɚɞɚɱɧɢɤɚ. ɇɨɦɟɪɚ ɡɚɞɚɱ ɜ
ɫɛɨɪɧɢɤɟ 1975 ɝɨɞɚ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɦɟɬɨɞɢɱɟɫɤɢɯ ɩɨɫɨɛɢɹɯ [8], [9] ɢɥɢ ɪɚɫɫɱɢɬɚɬɶ ɩɪɢɛɚɜ-
ɥɟɧɢɟɦ ɤ ɧɨɦɟɪɭ ɡɚɞɚɱɢ ɢɡ ɫɛɨɪɧɢɤɚ 2002 ɝɨɞɚ (ɩɨɫɥɟ ɨɬɤɢɞɵɜɚɧɢɹ ɧɨɦɟɪɚ ɝɥɚɜɵ) ɱɢɫɥɚ
542.
8
ȼɚɪɢɚɧɬ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
ɇɨɦɟɪɚ ɡɚɞɚɱ
4.101, 4.133, 4.149.1
4.102, 4.134, 4.149.2
4.103, 4.135, 4.150
4.104.1, 4.136, 4.152
4.104.2, 4.137, 4.155
4.105.1, 4.142, 4.156
4.105.2, 4.143, 4.157
4.106, 4.145, 4.158
4.108, 4.146, 4.159
4.109, 4.177, 4.160
4.110, 4.178, 4.161
4.111, 4.179, 4.162
4.112, 4.180, 4.163
4.113, 4.181, 4.191
4.99, 4.182, 4.192
4.98, 4.201, 4.193
4.97, 4.202, 4.209
4.98, 4.203, 4.210
4.97, 4.204, 4.211.1
4.96, 4.205, 4.211.2
4.95, 4.206, 4.212
4.11, 4.118, 4.149.1
4.14, 4.120, 4.149.2
4.16, 4.121, 4.150
4.17, 4.122, 4.152
4.20.4, 4.123, 4.155
4.20.8, 4.124, 4.156
4.20.13, 4.125, 4.157
4.20.14, 4.126, 4.158
4.55, 4.127, 4.159
ȼɚɪɢɚɧɬ
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
ɇɨɦɟɪɚ ɡɚɞɚɱ
4.81, 4.128, 4.160
4.83, 4.129, 4.161
4.85, 4.130, 4.162
4.86, 4.133, 4.163
4.88, 4.134, 4.164
4.89, 4.135, 4.170
4.90.1, 4.136, 4.172
4.90.2, 4.137, 4.173
4.91, 4.142, 4.174
4.92, 4.143, 4.221
4.93, 4.145, 4.222
4.94, 4.146, 4.191
4.95, 4.177, 4.219
4.96, 4.178, 4.220
4.97, 4.179, 4.155
4.98, 4.180, 4.226
4.99, 4.181, 4.225
4.101, 4.182, 4.152
4.102, 4.191, 4.150
4.103, 4.193, 4.163
4.104.1, 4.194, 4.209
4.105.1, 4.197.1, 4.210
4.105.2, 4.197.2, 4.211.1
4.106, 4.201, 4.211.2
4.108, 4.202, 4.212
4.109, 4.203, 4.213
4.110, 4.204, 4.216.1
4.111, 4.205, 4.216.2
4.112, 4.206, 4.217
4.113, 4.192, 4.218
ɉɊɂɅɈɀȿɇɂȿ 3
Ɍɪɟɬɶɟ ɤɨɧɬɪɨɥɶɧɨɟ ɡɚɞɚɧɢɟ
Ɋɟɲɢɬɶ ɡɚɞɚɱɭ ʋ 1.21 ɢɡ [5]:
a) ɉɪɢɜɟɫɬɢ ɤ ɤɚɧɨɧɢɱɟɫɤɨɦɭ ɜɢɞɭ ɭɪɚɜɧɟɧɢɟ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ
04 =+++++ UcUbUaUaUaU
yxyyxyxx
,
b) ɍɩɪɨɫɬɢɬɶ ɩɨɥɭɱɢɜɲɟɟɫɹ ɭɪɚɜɧɟɧɢɟ ɫ ɩɨɦɨɳɶɸ ɡɚɦɟɧɵ
βζ
α
ξ
ζξζξ
+
= eVU ),(),( .
ɉɊɂɅɈɀȿɇɂȿ 4
ɇɢɠɟ ɩɪɢɜɨɞɢɬɫɹ ɱɚɫɬɶ ɝɥɚɜɵ 4, ɫɨɞɟɪɠɚɳɚɹ ɬɟɤɫɬɵ ɤɨɧɬɪɨɥɶɧɵɯ ɡɚɞɚɱ ɢɡ ɤɧɢɝɢ [3]
(ȼɨɥɤɨɜɵɫɤɢɣ Ʌ.ɂ. ɢɞɪ. ɋɛɨɪɧɢɤ ɡɚɞɚɱ ɩɨ ɬɟɨɪɢɢ ɮɭɧɤɰɢɣ ɤɨɦɩɥɟɤɫɧɨɝɨ ɩɟɪɟɦɟɧɧɨɝɨ
/Ʌ.ɂ. ȼɨɥɤɨɜɵɫɤɢɣ, Ƚ.Ʌ. Ʌɭɧɰ, ɂ.Ƚ. Ⱥɪɚɦɚɧɨɜɢɱ. – Ɇ.: ɇɚɭɤɚ, 2002).

Страницы