Просмотр исходного текста страницы Differential Equations 2021

== [https://www.hse.ru/en/ba/data/courses/301393255.html Syllabus] ==

=== or see [https://drive.google.com/file/d/1RH-GXDP9RjLk0mS7qcyjlRmu9TZa61rM/view?usp=sharing this version of the syllabus]===

“Differential Equations” is a spring semester course for second-year students studying at the Faculty of Computer Sciences. It is designed to suit the requirements of the Faculty of Computer Sciences curriculum as well as UoL where DE is a part of the mathematical curriculum. Besides the course on differential equations is included as a topic in “Mathematical methods for economists” external exam. 

This course is an important part of the bachelor stage in the education of the future applied mathematicians and computer scientists. It has to give students skills for the implementation of mathematical knowledge and expertise. Its prerequisite is the knowledge of the single variable calculus. 

In the spring semester, the course is split into two unequal parts: it is taught from January through the end of April and after the students finish with their UoL exams in May it will resume and will continue till mid-June. 

The assessment of the students will be done by setting mock exam by the end of the 3rd module, then later by the University of London (UoL) examinations in May and final exam will be set in late June. But the final grade will depend solely on mock, final exams performance and home assignments grades.

As a general policy, personal computing devices such as laptops, calculators etc. are ''' not supposed to be used in the course'''. They are ''' absolutely prohibited in all exams'''. Students are expected to do all necessary arithmetic computations by hand.

== Lecturers and Teachers==

{| class="wikitable" style="text-align:center"
|-
| Lecturer|| [https://www.hse.ru/en/org/persons/131777 K.A. Bukin] <br/> [mailto:kbukin@hse.ru kbukin@hse.ru]

|rowspan="2"| Assistants 
|rowspan="2"| 
|-
| Teacher || V.Goncharenko
|}

== Lectures ==

'''Lecture 10.01.2022'''. First order equations.
[https://zoom.us/rec/share/0sar-a1VH7rx6tE1bx_df6-cdHbSV-N17M6jF44aUwRuOPNUedMwP-Pngrlutdzo.m-6hHoOxWmU5mwn5 Passcode: $76B5rUc]

'''Lecture 17.01.2022'''.  Fundamental theorem of DE.
[https://zoom.us/rec/share/boxmeeft5NowW4yDXl-0xByyE7nK2DCFWGj0gZNSfNJVadEIVgKLIt0xXqG7ar1n.VN0fwJuRW0FVExxl Passcode: ^Ts*1y69]

'''Lecture 24.01.2022'''.  Solow's growth model. Linear DE of the 2nd order.
[https://zoom.us/rec/share/LaSmzZSXTW2p0nqohKBwd9MqxZ0Ab5DHaKF0aH7KevAb_bM8994Ft-ib48vBII4.QXnnVTzUwYD8XSyj Passcode: ECxmcT1# ], [https://youtu.be/HUdN1T_b5bo Youtube]

'''Lecture 31.01.2022'''. How to solve n-th order linear DE with constant coeffifcients.
[https://zoom.us/rec/share/srFmnGOLzDq31UdPzWm9Xgmmf0PLnWAqjlN4rR8SfDVbuWe4zm2WQABg6EYc9__T.Slp_GdVSw0ZIu1zJ Passcode: 9r*2cYy#], [https://youtu.be/S4901gdlvYQ Youtube]

'''Lecture 07.02.2022'''. Solutions of the nonhomogeneous equations with quasipolynomials.
[https://zoom.us/rec/share/0sTwSxwZfdRT_gAdUpOGbOOehTS_1DKREowEVRNDeVFGhln1QI5Us74a2LAmT4c.ytOxchVihKXby8tp Passcode: 5Pyyqf#J],
[https://youtu.be/4XJTK4T9vNU Youtube]

'''Lecture 14.02.2022'''. Variation of parameters method. 
[https://zoom.us/rec/share/80TTAi3jQRgpsKEBC94uhC5YK-W1LTcxkf1_mKXnYApFy2kHv2_DE8rnAtspC3I_.lmA7rDGGMTqjM6x6 Passcode: 48+rFgL^], [https://youtu.be/C811fCKcXnk Youtube]

'''Lecture 21.02.2022'''. Systems of linear DE.   
[https://zoom.us/rec/share/KtIzDL2TYRx8afVP20M_B83KDQQfDGAcjcQiYuYeX3uKoZQHGItKxVZ__MLYWv8Q.vfDrnJkEW9nxTstV Passcode: !p.Aunz9], [https://youtu.be/pL1Ik524CFQ Youtube]

'''Lecture 28.02.2022''' Solving systems using JNF.
[https://zoom.us/rec/share/Js0LCnC10rFhr3NVv5TxkJckdsgZauhAs_7MngECU2n_nIy869lURey1VR9V7lbG.wOBFAI6WSQlfj2un Passcode: Ftd?4B%g], [https://youtu.be/M1_otZetNSo Youtube]

'''Lecture 14.03.2022''' Laplace transform.
[https://zoom.us/rec/share/kaKg6rj3aV3aWiUnhkyR6E33qabWOgkKaHTXtTK96Xbq-pr0SoltLq1dlkMQJ5Rw.qZwNqlm_wytSMZ99 Passcode: 5!%Z1sfW], [https://youtu.be/BA8jng0SA6o Youtube]

'''Lecture 21.03.2022''' Matrix exponent.
[https://zoom.us/rec/share/4tndPQMEKzn54fx70P8Bt4FWRkEcSpUQrfZMBBKy5Q-q8boHnlrgH8Nz2WKLEwAX.h4Q6-C5pFEcCV1nh Passcode: #?q2#XjS], [https://youtu.be/71kE9UEQyzU Youtube]

'''Lecture 04.04.2022''' Liouville formula.
[https://us06web.zoom.us/rec/share/QRoMj8nQ-v9nGL60XSp3wnaeTVhlSgFsfbTU-4fELiaRUPkF8lf3pR3Li8WXD7mO.seS83H9FRQU4EOF9 Passcode: &p=h38l9], [https://youtu.be/5BRrrwC-mVY Youtube]

'''Lecture 11.04.2022''' Sturm theorem.
[https://us06web.zoom.us/rec/share/M5L0pV41BVRk_cz_ecipt015yTAzdoj3FzmK5GUaoJnfuWdMUWpaxabkcDdq7BTI.2ao2EE1BdH2G1xIO Passcode: 3pkAKW.7], [https://youtu.be/hurKr5VYng4 Youtube]


'''Lecture 18.04.2022''' Linear difference equations.
[https://us06web.zoom.us/rec/share/b0-ORv9PYcgGBKvCnJDDOqmKJfnFOLihYU-_a04be4f4nQXbQzAJWFXtAxjNfaZQ.kmcT4mj_sC4dBo4b
Passcode: #MZr=44M], [https://youtu.be/brOxsvjjs_k Youtube]

== Seminars ==

[https://drive.google.com/drive/folders/1473Qn9_xPo_va80ILq_i3tkCJPm7nz2W Materials]

== Midterm test ==
==== ''Date'April 6th, 2022'

'''Midterm will be held in R304 for the groups 201, 202, 203 and in R305 for the group 204.
Please come to test a bit earlier at 9.15. Calculators are not allowed.


==== Midterm lasts for 80 minutes ====

''Materials'': [https://eduhseru-my.sharepoint.com/:b:/g/personal/gmbuzilov_edu_hse_ru/ETmk0ehOD0JIqC35TRUf808BeWrG3qVQBuExjy3PJCOLvA?e=vKUENr Demo version]

== Final exam ==
''Exam demo version'': [https://eduhseru-my.sharepoint.com/:b:/g/personal/gmbuzilov_edu_hse_ru/Ea4NH5H4529NqTm1_WiaRoUBT0pPyaDKmdDArkIH5HRBVg?e=FTrzCx] (recommended to solve)
==== Final exam is set on Monday June 21 at 16.20 ====

It will last for 120 minutes. No calculators are allowed.

== UoL Materials ==

''Materials'': [[https://drive.google.com/open?id=191gsbdfPE4vP1x5gNommmqhOnrOS38DA Materials]]

''Tasks for preparation'': [[https://drive.google.com/file/d/1PoDsGe4GzvoS1iiUZYiFjok3Pu-1PfFs/view?usp=sharing Tasks]]

''Exam demo version'': [[https://drive.google.com/file/d/1emy7QlMwRRj-eUOf8gGKwHRlLOe73lkb/view?usp=sharing Demo version]]

''Exam assessment rules'': [[https://drive.google.com/file/d/1qOyXzYI5kw2f2nftmBwV3SUw26ZLT4Ux/view?usp=sharing Assessment rules]]

== Assignments ==

=== Home assignments ===

[https://eduhseru-my.sharepoint.com/:b:/g/personal/gmbuzilov_edu_hse_ru/EdDfMzW9a7ZMp3ltZDb7H3YB-IqTmxa_9GdtGC5166oyEQ?e=qPtTfA Home assignment 1], due on "February 3rd"

[https://eduhseru-my.sharepoint.com/:b:/g/personal/gmbuzilov_edu_hse_ru/EchLKX1UxHtPndsmPRG7MjYBKlq7yJABgOkqnNwg2ZjwpA?e=BB5naA Home assignment 2], due on "February 17th"

[https://eduhseru-my.sharepoint.com/:b:/g/personal/gmbuzilov_edu_hse_ru/EboBAdSRrvdPk3_lpkiSvekBy2OrM2pTzI40S9PC5l5nfg?e=CUnm8D Home assignment 3], due on "March 3rd"

[https://disk.yandex.ru/i/WMkCYoHwNuEJ8w Home assignment 4], due on "March 24th"

[https://disk.yandex.ru/i/CpnDxLgwxd46BQ Home assignment 5], due on "April 21st"

== Overall Results ==

== Grading System ==

The home assignments constitute 30% of the final grade. The final exam is 40% of the final grade. The rest of the grade is formed by Midterm test which is due in the end of the 3rd module.

''' The final grade on the course''' will be determined according to the formula:

'''Grade''' = 0.4 * Final Exam + 0.3 * Midterm test + 0.3 * Home assignments

All grades are given initially out of 100. The final grades are also transferred to 10- and 5-points grades in accordance with the table (to be posted).
3.	The scale of corresponding grades
3.1.	Total grades for a given course are converted from the 100-point scale to the 5-point
and 10-point scale.
3.2.	The following basic scale has been established to convert grades from the 100-point scale to the 10-point scale
100-point scale	10-point scale

0-19,99	 ->    1

20-29,99 ->	2

30-39,99 ->	3

40-46,99  ->	4

47-53,99 ->	5

54-61,99	   ->     6

62-69,99 ->	7

70-77,99	   ->   8

78-85,9 -> 9

86-100	->       10


Retakes are organized in accordance with the HSE Interim and [https://www.hse.ru/docs/231102058.html Ongoing  Assessment Regulations]

== Reading ==
'''Obligatory:'''<br/>
- Mathematics for economists, Simon C. P., Blume L., 1994 <br/>
'''Optional:'''<br/>
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions.<br/>
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions.<br/>
== Internet Resources ==
[http://www.londonexternal.ac.uk/current_students/programme_resources/lse/index.shtml University of London Exam papers and Examiners reports for the last three years].<br/>