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Ɇɢɧɢɫɬɟɪɫɬɜɨ ɨɛɪɚɡɨɜɚɧɢɹ Ɋɟɫɩɭɛɥɢɤɢ Ȼɟɥɚɪɭɫɶ ȻȿɅɈɊɍɋɋɄɂɃ ɇȺɐɂɈɇȺɅɖɇɕɃ ɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼȿɊɋɂɌȿɌ

Ʉɚɮɟɞɪɚ «ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ ʋ 1»

Ɇɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɩɨ ɜɵɩɨɥɧɟɧɢɸ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ ʋ 2

ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɢɧɠɟɧɟɪɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ

ɡɚɨɱɧɨɣ ɮɨɪɦɵ ɨɛɭɱɟɧɢɹ

ɗɥɟɤɬɪɨɧɧɨɟ ɭɱɟɛɧɨɟ ɢɡɞɚɧɢɟ

Ɇɢɧɫɤ 2 0 1 1

ɍȾɄ 512.64(075.8)

ɋɨɫɬɚɜɢɬɟɥɢ:

Ⱥ.ɇ. Ⱥɧɞɪɢɹɧɱɢɤ, Ⱥ.ȼ. Ɇɟɬɟɥɶɫɤɢɣ, ɇ.Ⱥ. Ɇɢɤɭɥɢɤ, Ƚ.Ⱥ. Ɋɨɦɚɧɸɤ, ȼ.ɂ. ɘɪɢɧɨɤ

Ɋɟɰɟɧɡɟɧɬɵ:

Ʌ.ɂ. Ɇɚɣɫɟɧɹ, ɡɚɜ. ɤɚɮɟɞɪɨɣ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɞɢɫɰɢɩɥɢɧ ɂɂɌ ȻȽɍɂɊ;

Ⱥ.ɇ. Ɋɭɞɵɣ, ɞɨɰɟɧɬ ɤɚɮɟɞɪɵ «ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ ʋ 2» ȻɇɌɍ, ɤɚɧɞɢɞɚɬ ɮɢɡɢɤɨ-ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɧɚɭɤ

ɇɚɫɬɨɹɳɚɹ ɪɚɡɪɚɛɨɬɤɚ ɩɪɟɞɧɚɡɧɚɱɟɧɚ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɩɟɪɜɨɝɨ ɤɭɪɫɚ ɡɚɨɱɧɨɝɨ ɨɬɞɟɥɟɧɢɹ ɢɧɠɟɧɟɪɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ.

Ɋɚɛɨɬɚ ɫɨɞɟɪɠɢɬ ɨɫɧɨɜɧɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɫɜɟɞɟɧɢɹ ɢɡ ɩɪɨɝɪɚɦɦɧɨɝɨ ɦɚɬɟɪɢɚɥɚ, ɩɨɞɪɨɛɧɵɟ ɪɟɲɟɧɢɹ ɬɢɩɨɜɵɯ ɩɪɢɦɟɪɨɜ, ɜɨɩɪɨɫɵ ɞɥɹ ɫɚɦɨɤɨɧɬɪɨɥɹ, ɚ ɬɚɤɠɟ ɤɨɧɬɪɨɥɶɧɵɟ ɡɚɞɚɧɢɹ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɬɟɦɚɦ ɤɭɪɫɚ ɦɚɬɟɦɚɬɢɤɢ.

Ȼɟɥɨɪɭɫɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ ɩɪ-ɬ ɇɟɡɚɜɢɫɢɦɨɫɬɢ, 65, ɝ. Ɇɢɧɫɤ, Ɋɟɫɩɭɛɥɢɤɚ Ȼɟɥɚɪɭɫɶ Ɍɟɥ.(017)292-77-52 ɮɚɤɫ (017)292-91-37

Ɋɟɝɢɫɬɪɚɰɢɨɧɧɵɣ ʋ ȻɇɌɍ/ɎɂɌɊ48-2.2011

ɋɈȾȿɊɀȺɇɂȿ
ȼȼȿȾȿɇɂȿ..................................................................................................................	6
ɉɊɈȽɊȺɆɆȺ..............................................................................................................	7
1. ɇȿɈɉɊȿȾȿɅȿɇɇɕɃ ɂɇɌȿȽɊȺɅ.......................................................................	9
1.1. ɉɨɧɹɬɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ.............................................................	9
1.2. Ɉɫɧɨɜɧɵɟ ɦɟɬɨɞɵ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ..............................................................	11
1.2.1. ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɣ ɢ ɦɟɬɨɞ ɩɨɞɧɟɫɟɧɢɹ ɩɨɞ
ɡɧɚɤ ɞɢɮɮɟɪɟɧɰɢɚɥɚ .......................................................................................	11
1.2.2. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɡɚɦɟɧɨɣ ɩɟɪɟɦɟɧɧɨɣ (ɩɨɞɫɬɚɧɨɜɤɨɣ).....................	12
1.2.3. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɪɢ ɩɨɦɨɳɢ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɩɨɞɫɬɚɧɨɜɨɤ...	13
1.2.4. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ ɱɚɫɬɹɦ...................................................................	14
1.2.5. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɣ, ɫɨɞɟɪɠɚɳɢɯ ɤɜɚɞɪɚɬɧɵɣ ɬɪɟɯɱɥɟɧ ɜ
ɡɧɚɦɟɧɚɬɟɥɟ......................................................................................................	16
1.2.6. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɪɚɰɢɨɧɚɥɶɧɵɯ ɞɪɨɛɟɣ..............................................	16
1.2.7. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ................................	20
1.2.8. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɢɪɪɚɰɢɨɧɚɥɶɧɵɯ ɮɭɧɤɰɢɣ.......................................	23
1.2.9. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɛɢɧɨɦɨɜ..................................	23
2. ɈɉɊȿȾȿɅȿɇɇɕɃ ɂɇɌȿȽɊȺɅ..........................................................................	26
2.1. Ɏɨɪɦɭɥɚɇɶɸɬɨɧɚ–Ʌɟɣɛɧɢɰɚ. Ɂɚɦɟɧɚɩɟɪɟɦɟɧɧɨɣɜɨɩɪɟɞɟɥɟɧɧɨɦ
ɢɧɬɟɝɪɚɥɟ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟɩɨɱɚɫɬɹɦ. ȼɵɱɢɫɥɟɧɢɟɩɥɨɳɚɞɟɣɩɥɨɫɤɢɯɮɢɝɭɪ..	26
2.2. ȼɵɱɢɫɥɟɧɢɟ ɞɥɢɧ ɞɭɝ ɤɪɢɜɵɯ. ȼɵɱɢɫɥɟɧɢɟ ɨɛɴɟɦɨɜ................................	31
2.3. ɇɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ ............................................................................	35
2.3.1.ɂɧɬɟɝɪɚɥɵ ɫ ɛɟɫɤɨɧɟɱɧɵɦɢ ɩɪɟɞɟɥɚɦɢ (ɧɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ
ɩɟɪɜɨɝɨ ɪɨɞɚ) ...................................................................................................	35
2.3.2. ɂɧɬɟɝɪɚɥɵ ɨɬ ɧɟɨɝɪɚɧɢɱɟɧɧɵɯ ɮɭɧɤɰɢɣ (ɧɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ
ɜɬɨɪɨɝɨ ɪɨɞɚ) ...................................................................................................	36
3. ɎɍɇɄɐɂɂ ɇȿɋɄɈɅɖɄɂɏ ɉȿɊȿɆȿɇɇɕɏ...................................................	37
3.1. ɉɨɧɹɬɢɟ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ ................................................	37
3.2. ɉɪɟɞɟɥ ɢ ɧɟɩɪɟɪɵɜɧɨɫɬɶ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ....................	37
3.3. Ⱦɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ ɮɭɧɤɰɢɣ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ...........................	38
3.3.1. ɑɚɫɬɧɨɟ ɢ ɩɨɥɧɨɟ ɩɪɢɪɚɳɟɧɢɹ ɮɭɧɤɰɢɢ............................................	38

3.3.2. ɑɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ...........................................................................	40
3.3.3. ɉɨɥɧɵɣ ɞɢɮɮɟɪɟɧɰɢɚɥ ɮɭɧɤɰɢɢ ........................................................	42
3.3.4. Ⱦɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ ɫɥɨɠɧɵɯ ɢ ɧɟɹɜɧɵɯ ɮɭɧɤɰɢɣ..........................	44
3.4. Ʉɚɫɚɬɟɥɶɧɚɹ ɩɥɨɫɤɨɫɬɶ ɢ ɧɨɪɦɚɥɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ......................................	46
3.5. ɗɤɫɬɪɟɦɭɦ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ............................................	47
3.6. ɇɚɢɛɨɥɶɲɟɟ ɢ ɧɚɢɦɟɧɶɲɟɟ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ ɜ
ɡɚɦɤɧɭɬɨɣ ɨɛɥɚɫɬɢ.................................................................................................	48
4. ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕȿ ɍɊȺȼɇȿɇɂə ɉȿɊȼɈȽɈ ɉɈɊəȾɄȺ ...................	51
4.1. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ..........	52
4.2. Ɉɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ 1 ɩɨɪɹɞɤɚ.............................	53
4.3. Ʌɢɧɟɣɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ 1–ɝɨ ɩɨɪɹɞɤɚ...........................	55
4.4. ɍɪɚɜɧɟɧɢɹ Ȼɟɪɧɭɥɥɢ......................................................................................	57
4.5. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜ ɩɨɥɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɚɯ......................	58
4.6. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ
ɭɪɚɜɧɟɧɢɹ, ɞɨɩɭɫɤɚɸɳɢɟ ɩɨɧɢɠɟɧɢɟ ɩɨɪɹɞɤɚ...................................................	60
5. ɅɂɇȿɃɇɕȿ ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕȿ ɍɊȺȼɇȿɇɂə ȼɕɋɒɂɏ ɉɈɊəȾɄɈȼ
ɋ ɉɈɋɌɈəɇɇɕɆɂ ɄɈɗɎɎɂɐɂȿɇɌȺɆɂ ...................................................	62
5.1. Ʌɢɧɟɣɧɵɟ ɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ n–ɝɨ ɩɨɪɹɞɤɚ ɫ
ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ...........................................................................	62
5.2. Ʌɢɧɟɣɧɵɟ ɧɟɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɩɨɫɬɨɹɧɧɵɦɢ
ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ....................................................................................................	64

6.ɅɂɇȿɃɇɕȿ ɇȿɈȾɇɈɊɈȾɇɕȿ ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕȿ ɍɊȺȼɇȿɇɂə ȼɕɋɒɂɏ ɉɈɊəȾɄɈȼ ɋ ɉɈɋɌɈəɇɇɕɆɂ ɄɈɗɎɎɂɐɂȿɇɌȺɆɂ ɂ

ɋɉȿɐɂȺɅɖɇɈɃ ɉɊȺȼɈɃ ɑȺɋɌɖɘ...............................................................

7.ɋɂɋɌȿɆɕ ȾɂɎɎȿɊȿɇɐɂȺɅɖɇɕɏ ɍɊȺȼɇȿɇɂɃ. ɆȿɌɈȾ ɂɋɄɅɘɑȿɇɂə. ɆȿɌɈȾ ɗɃɅȿɊȺ Ɋȿɒȿɇɂə ɅɂɇȿɃɇɕɏ ɋɂɋɌȿɆ ɋ ɉɈɋɌɈəɇɇɕɆɂ

ɄɈɗɎɎɂɐɂȿɇɌȺɆɂ.........................................................................................	71
7.1 ɇɨɪɦɚɥɶɧɚɹ ɫɢɫɬɟɦɚ n–ɝɨ ɩɨɪɹɞɤɚ ɨɛɵɤɧɨɜɟɧɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ
ɭɪɚɜɧɟɧɢɣ...............................................................................................................	71
7.2. Ʌɢɧɟɣɧɚɹ ɨɞɧɨɪɨɞɧɚɹ ɫɢɫɬɟɦɚ n–ɝɨ ɩɨɪɹɞɤɚ ɫ ɩɨɫɬɨɹɧɧɵɦɢ
ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ....................................................................................................	74
7.3. Ɂɚɞɚɱɢɞɢɧɚɦɢɤɢ, ɩɪɢɜɨɞɹɳɢɟɤɪɟɲɟɧɢɸɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯɭɪɚɜɧɟɧɢɣ..	78

ȼɈɉɊɈɋɕ ȾɅə ɋȺɆɈɄɈɇɌɊɈɅə......................................................................	82
ɇɟɨɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ...................................................................................	82
Ɉɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ.......................................................................................	83
Ɏɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ.......................................................................	84
Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɢ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ...	86
ɄɈɇɌɊɈɅɖɇȺə ɊȺȻɈɌȺ ʋ 2 ...............................................................................	88
ɅɂɌȿɊȺɌɍɊȺ...........................................................................................................	95

ȼȼȿȾȿɇɂȿ

ɇɚɫɬɨɹɳɢɟ ɦɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɢ ɤɨɧɬɪɨɥɶɧɵɟ ɪɚɛɨɬɵ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɫɬɭɞɟɧɬɨɜ ɩɟɪɜɨɝɨ ɤɭɪɫɚ ɡɚɨɱɧɨɝɨ ɨɬɞɟɥɟɧɢɹ ɢɧɠɟɧɟɪɧɨ-ɬɟɯɧɢɱɟɫɤɢɯ ɫɩɟɰɢɚɥɶɧɨɫɬɟɣ ȻɇɌɍ.

ɉɨɫɨɛɢɟ ɫɨɞɟɪɠɢɬ ɨɫɧɨɜɧɵɟ ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɫɜɟɞɟɧɢɹ ɢɡ ɩɪɨɝɪɚɦɦɧɨɝɨ ɦɚɬɟɪɢɚɥɚ, ɬɢɩɨɜɵɟ ɩɪɢɦɟɪɵ ɢ ɤɨɧɬɪɨɥɶɧɵɟ ɡɚɞɚɧɢɹ ɩɨ ɬɟɦɚɦ ɤɭɪɫɚ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɢ (20 ɜɚɪɢɚɧɬɨɜ).

ɋɬɭɞɟɧɬ ɞɨɥɠɟɧ ɢɡɭɱɢɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ, ɪɚɡɨɛɪɚɬɶ ɩɪɢɜɟɞɟɧɧɵɟ ɨɛɪɚɡɰɵ ɪɟɲɟɧɢɹ ɬɢɩɨɜɵɯ ɩɪɢɦɟɪɨɜ ɢ ɡɚɞɚɱ, ɜɵɩɨɥɧɢɬɶ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɫɜɨɟɝɨ ɜɚɪɢɚɧɬɚ, ɧɨɦɟɪ ɤɨɬɨɪɨɝɨ ɫɨɜɩɚɞɚɟɬ ɫ ɞɜɭɦɹ ɩɨɫɥɟɞɧɢɦɢ ɰɢɮɪɚɦɢ ɡɚɱɟɬɧɨɣ ɤɧɢɠɤɢ (ɲɢɮɪɚ). ȿɫɥɢ ɧɨɦɟɪ ɲɢɮɪɚ ɛɨɥɶɲɟ ɞɜɚɞɰɚɬɢ, ɬɨ ɫɥɟɞɭɟɬ ɨɬɧɹɬɶ ɨɬ ɧɨɦɟɪɚ ɲɢɮɪɚ ɱɢɫɥɨ, ɤɪɚɬɧɨɟ 20, ɢ ɩɨɥɭɱɟɧɧɚɹ ɪɚɡɧɨɫɬɶ (ɞɜɟ ɩɨɫɥɟɞɧɢɟ ɰɢɮɪɵ)

ɛɭɞɟɬ ɧɨɦɟɪɨɦ ɜɚɪɢɚɧɬɚ.
ɇɚɩɪɢɦɟɪ:
ɇɨɦɟɪ ɡɚɱɟɬɧɨɣ ɤɧɢɠɤɢ	ɇɨɦɟɪ ɜɚɪɢɚɧɬɚ	ɇɨɦɟɪɚ ɡɚɞɚɱ
301789/148	8	8, 28, 48 ɢ ɬ. ɞ.
303700/194	14	14, 34, 54 ɢ ɬ. ɞ.
300120/100	20	20, 40, 80 ɢ ɬ. ɞ.

ɉɊɈȽɊȺɆɆȺ

Ɍɟɦɚ 1. ɇɟɨɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ

ɉɟɪɜɨɨɛɪɚɡɧɚɹ. ɇɟɨɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ ɢ ɟɝɨ ɫɜɨɣɫɬɜɚ. Ɍɚɛɥɢɰɚ ɨɫɧɨɜɧɵɯ ɢɧɬɟɝɪɚɥɨɜ. Ɂɚɦɟɧɚ ɩɟɪɟɦɟɧɧɨɣ ɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ ɱɚɫɬɹɦ ɜ ɧɟɨɩɪɟɞɟɥɟɧɧɨɦ ɢɧɬɟɝɪɚɥɟ.

ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɪɨɫɬɟɣɲɢɯ ɞɪɨɛɟɣ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɪɚɰɢɨɧɚɥɶɧɵɯ ɮɭɧɤɰɢɣ. Ɇɟɬɨɞ ɪɚɰɢɨɧɚɥɢɡɚɰɢɢ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɪɨɫɬɟɣɲɢɯ ɢɪɪɚɰɢɨɧɚɥɶɧɨɫɬɟɣ.

Ɍɟɦɚ 2. Ɉɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ

Ɂɚɞɚɱɢ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɨɧɹɬɢɸ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ. Ɉɩɪɟɞɟɥɟɧɧɵɣ ɢɧɬɟɝɪɚɥ ɢ ɟɝɨ ɫɜɨɣɫɬɜɚ. Ɏɨɪɦɭɥɚ ɇɶɸɬɨɧɚ–Ʌɟɣɛɧɢɰɚ.

Ɂɚɦɟɧɚ ɩɟɪɟɦɟɧɧɨɣ ɢ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟ ɩɨ ɱɚɫɬɹɦ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɢɧɬɟɝɪɚɥɟ. ɇɟɫɨɛɫɬɜɟɧɧɵɟ ɢɧɬɟɝɪɚɥɵ.

ɉɪɢɥɨɠɟɧɢɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ ɤ ɜɵɱɢɫɥɟɧɢɸ ɩɥɨɳɚɞɟɣ ɩɥɨɫɤɢɯ ɮɢɝɭɪ ɜ ɞɟɤɚɪɬɨɜɵɯ ɢ ɩɨɥɹɪɧɵɯ ɤɨɨɪɞɢɧɚɬɚɯ. ȼɵɱɢɫɥɟɧɢɟ ɨɛɴɟɦɨɜ ɢ ɞɥɢɧ ɞɭɝ. ɉɪɢɛɥɢɠɟɧɧɵɟ ɦɟɬɨɞɵ ɜɵɱɢɫɥɟɧɢɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ.

Ɍɟɦɚ 3. Ɏɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ

Ɏɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ. Ɉɛɥɚɫɬɶ ɨɩɪɟɞɟɥɟɧɢɹ. ɉɪɟɞɟɥ. ɇɟɩɪɟɪɵɜɧɨɫɬɶ. ɑɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ.

Ⱦɢɮɮɟɪɟɧɰɢɪɭɟɦɨɫɬɶ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ, ɩɨɥɧɵɣ ɞɢɮɮɟɪɟɧɰɢɚɥ. ɉɪɨɢɡɜɨɞɧɵɟ ɨɬ ɫɥɨɠɧɨɣ ɮɭɧɤɰɢɢ. ɂɧɜɚɪɢɚɧɬɧɨɫɬɶ ɮɨɪɦɵ ɩɟɪɜɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɚ. ɇɟɹɜɧɵɟ ɮɭɧɤɰɢɢ ɢ ɢɯ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɟ.

Ʉɚɫɚɬɟɥɶɧɚɹ ɩɥɨɫɤɨɫɬɶ ɢ ɧɨɪɦɚɥɶ ɤ ɩɨɜɟɪɯɧɨɫɬɢ. Ƚɟɨɦɟɬɪɢɱɟɫɤɢɣ ɫɦɵɫɥ ɩɨɥɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɚ ɮɭɧɤɰɢɢ ɞɜɭɯ ɩɟɪɟɦɟɧɧɵɯ. ɑɚɫɬɧɵɟ ɩɪɨɢɡɜɨɞɧɵɟ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɵ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ɏɨɪɦɭɥɚ Ɍɟɣɥɨɪɚ.

ɗɤɫɬɪɟɦɭɦ ɮɭɧɤɰɢɢ ɧɟɫɤɨɥɶɤɢɯ ɩɟɪɟɦɟɧɧɵɯ. ɇɟɨɛɯɨɞɢɦɨɟ ɢ ɞɨɫɬɚɬɨɱɧɨɟ ɭɫɥɨɜɢɹ ɷɤɫɬɪɟɦɭɦɚ. ɍɫɥɨɜɧɵɣ ɷɤɫɬɪɟɦɭɦ. Ɇɟɬɨɞ ɦɧɨɠɢɬɟɥɟɣ Ʌɚɝɪɚɧɠɚ. Ɇɟɬɨɞ ɧɚɢɦɟɧɶɲɢɯ ɤɜɚɞɪɚɬɨɜ.

Ɍɟɦɚ 4. Ɉɛɵɤɧɨɜɟɧɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ

Ɂɚɞɚɱɢ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɦ ɭɪɚɜɧɟɧɢɹɦ. Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ 1–ɝɨ ɩɨɪɹɞɤɚ. Ɂɚɞɚɱɚ Ʉɨɲɢ. Ɍɟɨɪɟɦɚ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɢ ɟɞɢɧɫɬɜɟɧɧɨɫɬɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ Ʉɨɲɢ.

ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ 1–ɝɨ ɩɨɪɹɞɤɚ ɫ ɪɚɡɞɟɥɹɸɳɢɦɢɫɹ ɩɟɪɟɦɟɧɧɵɦɢ, ɨɞɧɨɪɨɞɧɵɯ, ɥɢɧɟɣɧɵɯ, ɭɪɚɜɧɟɧɢɹ Ȼɟɪɧɭɥɥɢ ɢ ɜ ɩɨɥɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɚɯ.

Ⱦɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. Ɂɚɞɚɱɚ Ʉɨɲɢ. Ɍɟɨɪɟɦɚ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɢ ɟɞɢɧɫɬɜɟɧɧɨɫɬɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ Ʉɨɲɢ. ɍɪɚɜɧɟɧɢɹ, ɞɨɩɭɫɤɚɸɳɢɟ ɩɨɧɢɠɟɧɢɟ ɩɨɪɹɞɤɚ.

Ʌɢɧɟɣɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɜɵɫɲɢɯ ɩɨɪɹɞɤɨɜ. ɋɜɨɣɫɬɜɚ ɥɢɧɟɣɧɨɝɨ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɨɝɨ ɨɩɟɪɚɬɨɪɚ. Ʌɢɧɟɣɧɨ–ɡɚɜɢɫɢɦɵɟ ɢ ɥɢɧɟɣɧɨ– ɧɟɡɚɜɢɫɢɦɵɟ ɫɢɫɬɟɦɵ ɮɭɧɤɰɢɣ. Ɉɩɪɟɞɟɥɢɬɟɥɶ ȼɪɨɧɫɤɨɝɨ.

Ʌɢɧɟɣɧɵɟ ɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ, ɭɫɥɨɜɢɟ ɥɢɧɟɣɧɨɣ ɧɟɡɚɜɢɫɢɦɨɫɬɢ ɢɯ ɪɟɲɟɧɢɣ. Ɏɭɧɞɚɦɟɧɬɚɥɶɧɚɹ ɫɢɫɬɟɦɚ ɪɟɲɟɧɢɣ. ɋɬɪɭɤɬɭɪɚ ɨɛɳɟɝɨ ɪɟɲɟɧɢɹ. Ʌɢɧɟɣɧɵɟ ɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ.

Ʌɢɧɟɣɧɵɟ ɧɟɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ. ɋɬɪɭɤɬɭɪɚ ɨɛɳɟɝɨ ɪɟɲɟɧɢɹ. Ɇɟɬɨɞ Ʌɚɝɪɚɧɠɚ ɜɚɪɢɚɰɢɢ ɩɪɨɢɡɜɨɥɶɧɵɯ ɩɨɫɬɨɹɧɧɵɯ. Ʌɢɧɟɣɧɵɟ ɧɟɨɞɧɨɪɨɞɧɵɟ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɟ ɭɪɚɜɧɟɧɢɹ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɫɨ ɫɩɟɰɢɚɥɶɧɨɣ ɩɪɚɜɨɣ ɱɚɫɬɶɸ.

ɇɨɪɦɚɥɶɧɵɟ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ. Ⱥɜɬɨɧɨɦɧɵɟ ɫɢɫɬɟɦɵ. Ƚɟɨɦɟɬɪɢɱɟɫɤɢɣ ɫɦɵɫɥ ɪɟɲɟɧɢɹ. Ɏɚɡɨɜɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ. Ɂɚɞɚɱɢ Ʉɨɲɢ ɞɥɹ ɧɨɪɦɚɥɶɧɨɣ ɫɢɫɬɟɦɵ. Ɍɟɨɪɟɦɚ ɫɭɳɟɫɬɜɨɜɚɧɢɹ ɢ ɟɞɢɧɫɬɜɟɧɧɨɫɬɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ

Ʉɨɲɢ. Ɇɟɬɨɞ ɢɫɤɥɸɱɟɧɢɹ ɞɥɹ ɪɟɲɟɧɢɹ ɧɨɪɦɚɥɶɧɵɯ ɫɢɫɬɟɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ.

ɋɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɫɜɨɣɫɬɜɚ ɪɟɲɟɧɢɣ. Ɋɟɲɟɧɢɟ ɫɢɫɬɟɦ ɥɢɧɟɣɧɵɯ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ.

ɉɨɧɹɬɢɟ ɨ ɤɚɱɟɫɬɜɟɧɧɵɯ ɦɟɬɨɞɚɯ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɢɫɬɟɦ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ.

1. ɇȿɈɉɊȿȾȿɅȿɇɇɕɃ ɂɇɌȿȽɊȺɅ

1.1. ɉɨɧɹɬɢɟ ɧɟɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢɧɬɟɝɪɚɥɚ

Ɉɩɪɟɞɟɥɟɧɢɟ 1. Ɏɭɧɤɰɢɹ F(x) ɧɚɡɵɜɚɟɬɫɹ ɩɟɪɜɨɨɛɪɚɡɧɨɣ ɞɥɹ ɮɭɧɤɰɢɢ f(x) ɧɚ ɢɧɬɟɪɜɚɥɟ (a, b), ɟɫɥɢ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɷɬɨɝɨ ɢɧɬɟɪɜɚɥɚ ɜɵɩɨɥɧɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨ

Fc(x)= f(x).

Ɉɩɪɟɞɟɥɟɧɢɟ 2. ɋɨɜɨɤɭɩɧɨɫɬɶ ɜɫɟɯ ɩɟɪɜɨɨɛɪɚɡɧɵɯ {F(x)+ɋ}, ɝɞɟ ɋ – ɩɪɨɢɡɜɨɥɶɧɚɹ ɩɨɫɬɨɹɧɧɚɹ, ɞɥɹ ɮɭɧɤɰɢɢ f(x) ɧɚɡɵɜɚɟɬɫɹ ɧɟɨɩɪɟɞɟɥɟɧɧɵɦ ɢɧɬɟɝɪɚɥɨɦ ɢ ɨɛɨɡɧɚɱɚɟɬɫɹ

³ f (x)dx F(x) C

Ɏɭɧɤɰɢɹ f(x) ɧɚɡɵɜɚɟɬɫɹ ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɣ ɮɭɧɤɰɢɟɣ, ɜɵɪɚɠɟɧɢɟ f(x) dx – ɩɨɞɵɧɬɟɝɪɚɥɶɧɵɦ ɜɵɪɚɠɟɧɢɟɦ.

Ɉɬɵɫɤɚɧɢɟ ɞɥɹ ɮɭɧɤɰɢɢ f(x) ɜɫɟɯ ɟɟ ɩɟɪɜɨɨɛɪɚɡɧɵɯ F(x) + ɋ ɧɚɡɵɜɚɟɬɫɹ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ. ɂɧɬɟɝɪɢɪɨɜɚɧɢɟ ɟɫɬɶ ɞɟɣɫɬɜɢɟ, ɨɛɪɚɬɧɨɟ ɞɢɮɮɟɪɟɧɰɢɪɨɜɚɧɢɸ.

Ɉɫɧɨɜɧɵɟ ɩɪɚɜɢɥɚ ɢɧɬɟɝɪɢɪɨɜɚɧɢɹ:

1) ³ f c(x )dx ³df (x ) f (x ) C ;

	³ f (x)dx d(F(x) C)	f (x)dx ;
2)	³( f (x ) r M(x ))dx ³ f (x )dx r ³M(x )dx ;
3)	³af (x )dx a³ f (x )dx,	(a const) ;

4)	ɟɫɥɢ ³ f (x )dx	F(x ) C , ɬɨ ³ f (ax b)dx		1	F(ax b) C , ɩɪɢ ɭɫɥɨɜɢɢ,
4)	ɟɫɥɢ ³ f (x )dx	F(x ) C , ɬɨ ³ f (ax b)dx		a	F(ax b) C , ɩɪɢ ɭɫɥɨɜɢɢ,
				a
ɱɬɨ a, b – ɩɨɫɬɨɹɧɧɵɟ ɱɢɫɥɚ, az0;
5)	ɟɫɥɢ ³ f (x )dx	F(x ) C	ɢ u=M (x) – ɥɸɛɚɹ ɞɢɮɮɟɪɟɧɰɢɪɭɟɦɚɹ ɮɭɧɤɰɢɹ,
ɬɨ ³ f (u)du F(u) C ;

Ɍɚɛɥɢɰɚ ɨɫɧɨɜɧɵɯ ɧɟɨɩɪɟɞɟɥɟɧɧɵɯ ɢɧɬɟɝɪɚɥɨɜ

1.	³du		u C ;
2.	³u	D	du		uD1		C , ɝɞɟ D z 1;
					D 1

3.	³du		ln \| u \| C ;
	u
4.	³audu				au	C ;

				ln a
5.	³eu du			eu C ;
6.	³sin udu				cosu C ;
7.	³cosudu				sin u C ;
8.	³tgudu ln \| cosu \| C ;

10.

C ;

sin u

§ u

S·

11.

tg¨

C ;

cos u

4¹

12.

ctgu C ;

sin 2 u

13.

tgu C ;

cos2 u

14.

arctg

C ;

a2 u2

15.

arcsin

C ;

a2 u2

a u

C ;

16.

a2 u2 2a

a u

u2 r D2

C .

17.

u2 r D2

9. ³ctg udu ln|sin u| C ;

ȼ ɩɪɢɜɟɞɟɧɧɨɣ ɬɚɛɥɢɰɟ ɛɭɤɜɚ u ɦɨɠɟɬ ɨɛɨɡɧɚɱɚɬɶ ɤɚɤ ɧɟɡɚɜɢɫɢɦɭɸ ɩɟɪɟɦɟɧɧɭɸ, ɬɚɤ ɢ ɧɟɩɪɟɪɵɜɧɨ ɞɢɮɮɟɪɟɧɰɢɪɭɟɦɭɸ ɮɭɧɤɰɢɸ u=M(x) ɚɪɝɭɦɟɧɬɚ x.

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