Аналитическая геометрия и линейная алгебра. Учебное пособие
.pdfǨǯǨDzǯǵǪǷǧǻǯǾǬǸDZǯǰ ǸǶǯǸǵDZ
1.Ȼɟɤɥɟɦɢɲɟɜ Ⱦ ȼ Ʉɭɪɫ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɝɟɨɦɟɬɪɢɢ ɢ ɥɢɧɟɣɧɨɣ ɚɥɝɟɛɪɵ >Ȼɟɤɥɟ ɦɢɲɟɜ Ⱦ ȼ @ Ɇ Ɏɢɡɦɚɬɥɢɬ – ɫ
2.ȼɨɥɤɨɜ Ⱦ ɘ Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɝɟɨɦɟɬɪɢɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ ɉɪɚɤɬɢɤɭɦ >ȼɨɥ
ɤɨɜ Ⱦ ɘ Ƚɚɥɭɧɨɜɚ Ʉ ȼ Ʉɪɚɫɧɨɳɟɤɨɜ ȼ ȼ @ ɋɉɛ ɂɡɞ ɜɨ ɉɨɥɢɬɟɯɧ ɭɧ ɬɚ
2016. – ɫ
3.ȼɨɥɤɨɜ Ⱦ ɘ Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɝɟɨɦɟɬɪɢɹ ɩɥɨɫɤɨɫɬɢ ɉɪɚɤɬɢɤɭɦ >ȼɨɥɤɨɜ Ⱦ ɘ Ƚɚɥɭɧɨɜɚ Ʉ ȼ Ʉɪɚɫɧɨɳɟɤɨɜ ȼ ȼ @ ɋɉɛ ɂɡɞ ɜɨ ɉɨɥɢɬɟɯɧ ɭɧ ɬɚ – ɫ
4.ȼɨɥɤɨɜ Ⱦ ɘ Ʌɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ ɉɪɚɤɬɢɤɭɦ >ȼɨɥɤɨɜ Ⱦ ɘ Ƚɚɥɭɧɨɜɚ Ʉ ȼ Ʉɪɚɫɧɨɳɟɤɨɜ ȼ ȼ @ ɋɉɛ ɂɡɞ ɜɨ ɉɨɥɢɬɟɯɧ ɭɧ ɬɚ – ɫ
5.ȼɨɥɤɨɜ Ⱦ ɘ Ʌɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ ɞɥɹ ɷɤɨɧɨɦɢɫɬɨɜ / >ȼɨɥɤɨɜ Ⱦ ɘ Ƚɚɥɭɧɨɜɚ Ʉ ȼ Ʉɪɚɫɧɨɳɟɤɨɜ ȼ ȼ @ ɋɉɛ ɂɡɞ ɜɨ ɉɨɥɢɬɟɯɧ ɭɧ ɬɚ – c.
6.Ƚɚɥɭɧɨɜɚ Ʉ ȼ Ɉɫɧɨɜɵ ɥɢɧɟɣɧɨɣ ɚɥɝɟɛɪɵ / >Ƚɚɥɭɧɨɜɚ Ʉ ȼ Ʉɪɚɫɧɨɳɟɤɨɜ ȼ ȼ @ ɋɉɛ ɂɡɞ ɜɨ ɉɨɥɢɬɟɯɧ ɭɧ ɬɚ – ɫ
7.Ⱦɚɧɤɨ ɉ ȿ ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ ɜ ɭɩɪɚɠɧɟɧɢɹɯ ɢ ɡɚɞɚɱɚɯ Ɍ >ɉ ȿ Ⱦɚɧɤɨ Ⱥ Ƚ ɉɨɩɨɜ Ɍ ə Ʉɨɠɟɜɧɢɤɨɜɚ ɋ ɉ Ⱦɚɧɤɨ@ Ɇ Ⱥɫɬɪɟɥɶ – ɫ
8.ȿɮɢɦɨɜ Ⱥ ȼ ɋɛɨɪɧɢɤ ɡɚɞɚɱ ɩɨ ɦɚɬɟɦɚɬɢɤɟ ɑ >ȿɮɢɦɨɜ Ⱥ ȼ Ⱦɟɦɢɞɨ ɜɢɱ Ȼ ɉ @ Ɇ ɎɂɁɆȺɌɅɂɌ – ɫ
ȿɮɢɦɨɜ ɇ ȼ Ʉɪɚɬɤɢɣ ɤɭɪɫ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɝɟɨɦɟɬɪɢɢ >ȿɮɢɦɨɜ ɇ ȼ @ Ɇ Ɏɢɡ ɦɚɬɥɢɬ – ɫ
10.ɂɥɶɢɧ ȼ Ⱥ ɉɨɡɧɹɤ ɗ Ƚ Ʌɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ Ɇ ɎɂɁɆȺɌɅɂɌ – c.
11.Ʉɪɚɫɧɨɜ Ɇ Ʌ ȼɫɹ ɜɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ Ɍ >Ɇ Ʌ Ʉɪɚɫɧɨɜ Ⱥ ɂ Ʉɢɫɟɥɟɜ Ƚ ɂ Ɇɚɤɚɪɟɧɤɨ ȿ ȼ ɒɢɤɢɧ ȼ ɂ Ɂɚɥɹɩɢɧ@ Ɇ ɅɄɂ – 328 ɫ
12.Ʉɭɪɨɲ Ⱥ Ƚ Ʉɭɪɫ ɜɵɫɲɟɣ ɚɥɝɟɛɪɵ >Ʉɭɪɨɲ Ⱥ Ƚ @ ɋɉɛ Ʌɚɧɶ – ɫ
13.ɉɨɫɬɧɢɤɨɜ Ɇ Ɇ Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɝɟɨɦɟɬɪɢɹ >ɉɨɫɬɧɢɤɨɜ Ɇ Ɇ @ ɋɉɛ Ʌɚɧɶ– 416 ɫ
14.ɉɪɢɜɚɥɨɜ ɂ ɂ Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɝɟɨɦɟɬɪɢɹ >ɉɪɢɜɚɥɨɜ ɂ ɂ @ ɋɉɛ Ʌɚɧɶ –ɫ
15.Curtis C. Linear algebra: an introductory approach. Springer Science+Business Media, LLC, 2012. – 344 pp.
16.Dantzig G. B. Thapa M. N. Springer Science+Business Media, //& – 474 pp.
17.Smith L. Linear Algebra. Springer Science+Business Media, LLC, 2012. – 364 pp.
18.Shores T. S. Applied Linear Algebra and Matrix Analysis. Springer Science+Business Media, LLC, 2007. – 384 pp.
111
ǯǴǹǬǷǴǬǹ-ǷǬǸǺǷǸȂ
1.Ⱥɧɚɥɢɬɢɱɟɫɤɚɹ ɝɟɨɦɟɬɪɢɹ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://ru.onlinemschool.com/math/library/analytic_geometry/.
2.Ƚɟɨɦɟɬɪɢɹ ɧɚ ɩɥɨɫɤɨɫɬɢ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://www.matburo.ru/ex_ag.php?p1=aggeom.
3.Ʌɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ ɢ ɚɧɚɥɢɬɢɱɟɫɤɚɹ ɝɟɨɦɟɬɪɢɹ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.lektorium.tv/mooc2/26288.
4.Ⱦɟɤɚɪɬɨɜɚ ɫɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=mxmis3J4_OM.
5.ɐɢɥɢɧɞɪɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://mathhelpplanet.com/static.php?p=tsilindricheskie koordinaty.
6.ɋɮɟɪɢɱɟɫɤɚɹ ɫɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://mathhelpplanet.com/static.php?p=sfericheskie koordinaty.
7.ɍɪɚɜɧɟɧɢɟ ɩɥɨɫɤɨɫɬɢ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://LQWHU neturok.ru/ru/school/geometry/11 klass/bmetod koordinat v prostranstveb/uravnenie ploskosti.
8.ɉɪɹɦɚɹ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ
https://www.youtube.com/watch?v=yBuqIrv7hEM.
ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ Ⱦɢɫɬɚɧɰɢɨɧɧɨɟ ɨɛɭɱɟɧɢɟ Ƚɥ ɋɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɭɪɚɜ ɧɟɧɢɣ Ɉɩɪɟɞɟɥɢɬɟɥɢ Ɇɚɬɪɢɰɵ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://www.bgsha.com/ru/learning/course/print.php?COURSE_ID=1&CHAPTER_ID= 0656&LESSON_PATH=615.656.
10.ɂɡɭɱɟɧɢɟ ɦɚɬɟɦɚɬɢɤɢ ɨɧɥɚɣɧ Ɇɚɬɪɢɰɵ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨ ɫɬɭɩɚ http://ru.onlinemschool.com/math/library/matrix/.
11.ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ Ɇɚɬɪɢɰɵ ɢ ɞɟɣɫɬɜɢɹ ɧɚɞ ɧɢɦɢ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟ ɠɢɦ ɞɨɫɬɭɩɚ http://www.youtube.com/watch?v=Sad0Mjo T7o.
12.Ʉɚɤ ɧɚɯɨɞɢɬɶ ɨɛɪɚɬɧɭɸ ɦɚɬɪɢɰɭ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://www.youtube.com/watch?v= BlYPya uMc.
13.ɋɢɫɬɟɦɵ ɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ ɦɟɬɨɞ Ƚɚɭɫɫɚ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://www.youtube.com/watch?v=x4s7KqPB2yQ.
14.Ɇɚɬɪɢɰɚ ɥɢɧɟɣɧɨɝɨ ɨɩɟɪɚɬɨɪɚ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=GE7uAvAAwR0.
15.Ɇɚɬɪɢɰɚ ɥɢɧɟɣɧɨɝɨ ɨɩɟɪɚɬɨɪɚ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=L3T2kRbY_q8.
16.Ʌɢɧɟɣɧɵɟ ɨɩɟɪɚɬɨɪɵ ɢ ɮɭɧɤɰɢɨɧɚɥɵ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=zAwDPBV1o5k.
17.ɋɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɢ ɫɨɛɫɬɜɟɧɧɵɟ ɜɟɤɬɨɪɵ ɬɟɨɪɢɹ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=p6HEjf BfUE.
18.ɋɨɛɫɬɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɢ ɫɨɛɫɬɜɟɧɧɵɟ ɜɟɤɬɨɪɵ ɉɪɨɫɬɨɟ ɫɨɛɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v= U RD DW1eA.
Ʌɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ / ɉɪɚɤɬɢɤɚ / ɉɪɨɰɟɫɫ ɨɪɬɨɝɨɧɚɥɢɡɚɰɢɢ Ƚɪɚɦɚ – ɒɦɢɞɬɚ / Ɉɪɬɨɝɨɧɚɥɶɧɵɣ ɨɩɟɪɚɬɨɪ >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=f LPlwq Vk.
112
20.Analitic geometry >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.NKDQ academy.org/math/geometry/analytic geometry topic.
21.Plane analytical geometry >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://www.intmath.com/plane analytic geometry/intro.php.
22.Analitic geometry. Introduction >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ http://www.youtube.com/watch?v=Re0s1NPZ4ek.
23.Dot product >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/ watch?v=KDHuWxy53uM.
24.An Introduction to the Dot Product >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=X5DifJW0zek.
25.Dot vs. Cross Product >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=E34CftP455k.
26.Cross product >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/ watch?v=zA0fvwtvgvA.
27.Scalar triple product to verify the vectors are coplanar >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=FENmqu40jUc.
28.The Triple Scalar Product >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ
KWWSV ZZZ \RXWXEH FRP ZDWFK"Y PEH(/H=3 B<.
)LQG HTXDWLRQ RI D SODQH JLYHQ QRUPDO YHFWRU DQG D SRLQW LQ WKH SODQH >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=4tN2UCld3Qc.
30.'HILQLQJ D SODQH LQ 5 ZLWK D SRLQW DQG QRUPDO YHFWRU >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=UJxgcVaNTqY.
31.Minimum distance between the point and the plane >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ KWWSV ZZZ \RXWXEH FRP ZDWFK"Y 7N+9)M-- .
32.9HFWRU DQG 3DUDPHWULF (TXDWLRQV RI D /LQH /LQH LQ GLPHQVLRQV >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=PyPp4QvQY3Q.
33.Introduction to Eigenvalues and Eigenvectors >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=G4N8vJpf7hM&list=PLMIiGh1Rm KQXNPi6Jm0uy7ShQYMR26dAo.
34.Linear Transformations >ɗɥɟɤɬɪɨɧɧɵɣ ɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=a LcIKyuHQo.
35.Engineering mathematics – matrices quadratic form >ɗɥɟɤɬɪɨɧɧɵɣɪɟɫɭɪɫ@ – Ɋɟɠɢɦ ɞɨɫɬɭɩɚ https://www.youtube.com/watch?v=a0USeP6MSYA.
113
|
Ʉɧɢɝɢ ɩɨɱɬɨɣ |
|
|
Ɂɚɤɚɡ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɧɚ ɫɚɣɬɟ ɢɡɞɚɬɟɥɶɫɬɜɚ |
|
|
www.infra-e.ru |
|
|
|
|
ʋ |
ɇɚɢɦɟɧɨɜɚɧɢɟ ɤɧɢɝɢ |
|
ɩ ɩ |
||
|
||
1 |
Ⱥɫɬɪɨɧɨɦɢɹ |
|
2 |
Ȼɥɨɱɧɨ-ɦɚɬɪɢɱɧɵɣ ɦɟɬɨɞ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ |
|
3 |
ɩɨɜɟɪɯɧɨɫɬɟɣ -ɟ ɢɡɞ |
|
4 |
ȼɚɪɢɚɰɢɨɧɧɨɟ ɢɫɱɢɫɥɟɧɢɟ |
|
5 |
ȼɚɪɢɚɰɢɨɧɧɨɟ ɢɫɱɢɫɥɟɧɢɟ ɢ ɬɟɨɪɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ |
|
6 |
ȼɵɫɲɚɹ ɦɚɬɟɦɚɬɢɤɚ |
|
7 |
Ƚɢɞɪɨɝɚɡɨɞɢɧɚɦɢɤɚ ɫɛɨɪɧɢɤ ɡɚɞɚɱ ɫ ɪɟɲɟɧɢɹɦɢ |
|
8 |
Ƚɢɞɪɨɦɟɯɚɧɢɤɚ Ɍɟɨɪɢɹ ɢ ɩɪɚɤɬɢɤɚ |
|
9 |
Ⱦɢɫɤɪɟɬɧɚɹ ɦɚɬɟɦɚɬɢɤɚ |
|
10 |
Ʉɥɚɫɫɢɱɟɫɤɚɹ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɚ ɗɥɟɤɬɪɢɱɟɫɬɜɨ ɢ ɦɚɝɧɟɬɢɡɦ |
|
11 |
Ʉɥɚɫɫɢɱɟɫɤɚɹ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɚ ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ |
|
12 |
ɑɟɬɵɪɟɯɦɟɪɧɚɹ ɷɥɟɤɬɪɨɞɢɧɚɦɢɤɚ |
|
13 |
Ʉɭɪɫɨɜɨɟ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɩɨ ɩɪɢɤɥɚɞɧɨɣ ɦɟɯɚɧɢɤɟ |
|
14 |
Ʌɢɧɟɣɧɚɹ ɚɥɝɟɛɪɚ |
|
15 |
Ɇɚɬɟɦɚɬɢɤɚ ɱɢɫɥɨɜɵɟ ɢ ɮɭɧɤɰɢɨɧɚɥɶɧɵɟ ɪɹɞɵ |
|
16 |
Ɇɚɬɟɦɚɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ |
|
17 |
Ɇɟɬɨɞɵ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɨɛɪɚɛɨɬɤɢ ɞɚɧɧɵɯ |
|
18 |
Ɇɟɯɚɧɢɤɚ |
|
19 |
Ɇɟɯɚɧɢɤɚ ɠɢɞɤɨɫɬɢ ɢ ɝɚɡɚ |
|
20 |
Ɇɟɯɚɧɢɤɚ ɠɢɞɤɨɫɬɢ ɢ ɝɚɡɚ ɉɪɚɤɬɢɤɭɦ |
|
21 |
Ɇɟɯɚɧɢɤɚ ɉɪɚɤɬɢɤɭɦ |
|
22 |
Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ |
|
23 |
Ɉɛɳɚɹ ɮɢɡɢɤɚ Ɇɟɯɚɧɢɤɚ |
|
24 |
Ɉɫɧɨɜɵ ɦɟɬɨɞɚ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɜ ɩɪɨɱɧɨɫɬɧɵɯ ɪɚɫɱɟɬɚɯ |
|
25 |
Ɉɫɧɨɜɵ ɦɟɯɚɧɢɤɢ ɠɢɞɤɨɫɬɢ ɢ ɝɚɡɚ |
|
26 |
Ɉɫɧɨɜɵ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɦɟɯɚɧɢɤɢ |
|
27 |
ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɨɜ ɉɪɚɤɬɢɤɭɦ |
|
28 |
Ɍɟɨɪɟɬɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɩɥɚɧɢɪɨɜɚɧɢɹ ɢ ɨɛɪɚɛɨɬɤɢ ɮɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɢɯ |
|
|
ɷɤɫɩɟɪɢɦɟɧɬɨɜ |
|
|
|
|
29 |
Ɍɟɯɧɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ |
|
30 |
Ɏɢɡɢɤɨ-ɯɢɦɢɱɟɫɤɢɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɩɟɤɬɪɚɥɶɧɵɦɢ ɦɟɬɨɞɚɦɢ |
114
ɍɱɟɛɧɨɟ ɢɡɞɚɧɢɟ
Ⱦɦɢɬɪɢɣ ɘɪɶɟɜɢɱ ȼɨɥɤɨɜ Ʉɫɟɧɢɹ ȼɚɥɟɪɶɟɜɧɚ Ƚɚɥɭɧɨɜɚ
ǧǴǧDzǯǹǯǾǬǸDZǧȆ ǪǬǵdzǬǹǷǯȆ ǯ DzǯǴǬǰǴǧȆ ǧDzǪǬǨǷǧ
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ
ɂɡɨɛɪɚɠɟɧɢɟ ɧɚ ɨɛɥɨɠɤɟ )UHHSLN FRP
ɉɨɞɩɢɫɚɧɨ ɜ ɩɟɱɚɬɶ 9 Ɏɨɪɦɚɬ î Ȼɭɦɚɝɚ ɨɮɫɟɬɧɚɹ Ƚɚɪɧɢɬɭɪɚ ©7LPHV 1HZ 5RPDQª
ɂɡɞɚɬɟɥɶɫɬɜɨ ©ɂɧɮɪɚ-ɂɧɠɟɧɟɪɢɹªɝ ȼɨɥɨɝɞɚ ɭɥ Ʉɨɡɥɟɧɫɤɚɹ ɞ Ɍɟɥ - -01 E-PDLO ERRNLQJ#LQIUD-H UX KWWSV LQIUD-H UX
ɂɡɞɚɬɟɥɶɫɬɜɨ ɩɪɢɝɥɚɲɚɟɬ ɤ ɫɨɬɪɭɞɧɢɱɟɫɬɜɭ ɚɜɬɨɪɨɜ ɧɚɭɱɧɨ-ɬɟɯɧɢɱɟɫɤɨɣ ɥɢɬɟɪɚɬɭɪɵ
114