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Differential Equations 2021

2023-01-19T10:59:24Z

Yavmaksimov:

== [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] [mailto:kbukin@hse.ru kbukin@hse.ru]

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

== Lectures ==

'''Lecture 10.01.2023'''. First order equations.

'''Lecture 17.01.2023'''. Fundamental theorem of DE. link: https://us06web.zoom.us/rec/share/oVMypYgrIpB08O7-PgSEWkGH6N3yM0wLjlY6e8GaL46KLU_OJHgwWKJi9ApRBBhw.BdVBhCdUWDk7b4u6
Пароль: *$5zSyLv

'''Lecture 24.01.2022'''. Solow's growth model. Linear DE of the 2nd order.

'''Lecture 31.01.2022'''. How to solve n-th order linear DE with constant coeffifcients.

'''Lecture 07.02.2022'''. Solutions of the nonhomogeneous equations with quasipolynomials.
[https://youtu.be/4XJTK4T9vNU Youtube]

'''Lecture 14.02.2022'''. Variation of parameters method.
[https://youtu.be/C811fCKcXnk Youtube]

'''Lecture 21.02.2022'''. Systems of linear DE.
[https://youtu.be/pL1Ik524CFQ Youtube]

'''Lecture 28.02.2022''' Solving systems using JNF.
[https://youtu.be/M1_otZetNSo Youtube]

'''Lecture 14.03.2022''' Laplace transform.
[https://youtu.be/BA8jng0SA6o Youtube]

'''Lecture 21.03.2022''' Matrix exponent.
[https://youtu.be/71kE9UEQyzU Youtube]

'''Lecture 04.04.2022''' Liouville formula.
[https://youtu.be/5BRrrwC-mVY Youtube]

'''Lecture 11.04.2022''' Sturm theorem.
[https://youtu.be/hurKr5VYng4 Youtube]

'''Lecture 18.04.2022''' Linear difference equations.
[https://youtu.be/brOxsvjjs_k Youtube]

'''Lecture 25.04.2022''' Systems of difference equations.
[https://youtu.be/3sR8sgsyfGw Youtube]

'''Lecture 30.05.2022''' Autonomous systems and types of equilibria.
[https://youtu.be/W6okCpU8Xbw Youtube]

'''Lecture 01.06.2022''' Equilibria of nonlinear systems.

'''Lecture 06.06.2022''' Liapounov's function.
[https://youtu.be/iKdT7ACv9ZE Youtube]

'''Lecture 08.06.2022''' Exam preparation.
[https://youtu.be/itPdn9xQx-o Youtube]

== Seminars ==

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

Whiteboard of the 1st seminar by V. Goncharenko
https://disk.yandex.ru/i/fKMmpf7Dg3VaYA

== Midterm test ==
==== 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)

''Last year exam'': [https://disk.yandex.ru/i/UCRJUw-KNVHicg]

== 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 2023 ===

[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"

[https://disk.yandex.ru/i/UbRyGmal5FvwcQ Home assignment 6], due on "June 13th"

== 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:''' 
- Mathematics for economists, Simon C. P., Blume L., 1994 
'''Optional:''' 
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions. 
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions. 
== 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].

Differential Equations 2021

2023-01-19T10:58:33Z

Yavmaksimov: 1

== [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] [mailto:kbukin@hse.ru kbukin@hse.ru]

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

== Lectures ==

'''Lecture 10.01.2023'''. First order equations.

'''Lecture 17.01.2023'''. Fundamental theorem of DE. link: https://us06web.zoom.us/rec/share/oVMypYgrIpB08O7-PgSEWkGH6N3yM0wLjlY6e8GaL46KLU_OJHgwWKJi9ApRBBhw.BdVBhCdUWDk7b4u6
Пароль: *$5zSyLv

'''Lecture 24.01.2022'''. Solow's growth model. Linear DE of the 2nd order.

'''Lecture 31.01.2022'''. How to solve n-th order linear DE with constant coeffifcients.

'''Lecture 07.02.2022'''. Solutions of the nonhomogeneous equations with quasipolynomials.
[https://youtu.be/4XJTK4T9vNU Youtube]

'''Lecture 14.02.2022'''. Variation of parameters method.
[https://youtu.be/C811fCKcXnk Youtube]

'''Lecture 21.02.2022'''. Systems of linear DE.
[https://youtu.be/pL1Ik524CFQ Youtube]

'''Lecture 28.02.2022''' Solving systems using JNF.
[https://youtu.be/M1_otZetNSo Youtube]

'''Lecture 14.03.2022''' Laplace transform.
[https://youtu.be/BA8jng0SA6o Youtube]

'''Lecture 21.03.2022''' Matrix exponent.
[https://youtu.be/71kE9UEQyzU Youtube]

'''Lecture 04.04.2022''' Liouville formula.
[https://youtu.be/5BRrrwC-mVY Youtube]

'''Lecture 11.04.2022''' Sturm theorem.
[https://youtu.be/hurKr5VYng4 Youtube]

'''Lecture 18.04.2022''' Linear difference equations.
[https://youtu.be/brOxsvjjs_k Youtube]

'''Lecture 25.04.2022''' Systems of difference equations.
[https://youtu.be/3sR8sgsyfGw Youtube]

'''Lecture 30.05.2022''' Autonomous systems and types of equilibria.
[https://youtu.be/W6okCpU8Xbw Youtube]

'''Lecture 01.06.2022''' Equilibria of nonlinear systems.

'''Lecture 06.06.2022''' Liapounov's function.
[https://youtu.be/iKdT7ACv9ZE Youtube]

'''Lecture 08.06.2022''' Exam preparation.
[https://youtu.be/itPdn9xQx-o Youtube]

== Seminars ==

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

Whiteboard of the 1st seminar by V. Goncharenko
https://disk.yandex.ru/i/fKMmpf7Dg3VaYA

== Midterm test ==
==== 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)

''Last year exam'': [https://disk.yandex.ru/i/UCRJUw-KNVHicg]

== 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 2023 ===

[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"

[https://disk.yandex.ru/i/UbRyGmal5FvwcQ Home assignment 6], due on "June 13th"

== 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:''' 
- Mathematics for economists, Simon C. P., Blume L., 1994 
'''Optional:''' 
- A.F. Fillipov. Collection of problems on differential equations. Moscow, “Nauka”, 1973 and later editions. 
- V.K. Romanko, Course on Differential Equations and Calculus of Variations. Moscow and Saint-Petersburg, “Fizmatlit”, 2001 and later editions. 
== 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].

Основы матричных вычислений 2022/2023

2023-01-18T17:59:43Z

Yavmaksimov: sdfs

== О курсе ==

Курс для студентов 2 курса в 3-4 модулях.

'''Первая лекция состоится 13.01, первые семинары - начиная с 16.01.'''

'''Лектор:''' Рахуба Максим Владимирович

'''Семинаристы:'''
{| class="wikitable"
|-
! Группа !! Преподаватель !! Учебный ассистент || Чат в телеграм
|-
| 1 || Рахуба Максим Владимирович || Максим Васильев || [https://t.me/+Hj_1QPjwC38xNTJi tg]
|-
| 2 || Рахуба Максим Владимирович || Александра Сендерович || [https://t.me/+Ch8p3rht0YJhMTAy tg]
|-
| 3 || Тяпкин Даниил Николаевич || Николай Юдин || [https://t.me/+Nxz3yqh1w44zNzUy tg]
|-
| 4 || Самсонов Сергей Владимирович || Кирилл Королев || [https://t.me/+rmLqljCEV8c0ZDcy tg]
|-
| 5 || Медведь Никита Юрьевич || Ян Максимов || [https://t.me/+BuVLj9Nb4P8xZjJi tg]
|-
| 6 || Зароднюк Алёна Владимировна || Тимофей Грицаев || [https://t.me/+CzT7VrOuTGswYmQy tg]
|}

=== Полезные ссылки ===

[https://t.me/+IaUcrCPEVd9jNWVi Телеграм-канал курса]

[https://t.me/+P8SYuAIKP2kwM2Fi Телеграм-чат курса]

[https://disk.yandex.ru/d/LX1ljriMmEhGQQ Папка с материалами]

== План курса ==

=== Лекции ===

# '''Основы матричного анализа''' (11.01.2023). Векторные и матричные нормы. Скалярное произведение и ортогональность. Разложение Шура. [https://disk.yandex.ru/i/WaqG5nJqh9QvjQ Слайды] [https://disk.yandex.ru/i/oaQwnZ_2lfcYLA Запись] [https://disk.yandex.ru/i/1mOyrdZg4-mZ7A Конспект (TeX)]

=== Проверочные работы на семинарах ===

На семинарах будут проходить короткие тесты (проверочные работы) по теме лекции и семинара с предыдущей недели.

=== Домашние задания ===

На курсе предусмотрены теоретические домашние задания и практические домашние задания на языке Python. Выдаются каждые 2-3 недели.

Каждый студент 2 раза за семестр может просрочить дедлайн ДЗ на 1 сутки. Чтобы использовать эту возможность, достаточно просто загрузить работу после дедлайна.

=== Коллоквиум ===

=== Экзамен ===

=== Итоговая оценка за курс ===

Итог = Округление(min(10, 0.2 * ТДЗ + 0.15 * ПДЗ + 0.1 * БДЗ + 0.1 * ПР + 0.25 * К + 0.3 * Э))

Обратите внимание, что в 4-м модуле ТДЗ, ПДЗ, ПР являются средними оценками ''за оба модуля''.

* ТДЗ – средняя оценка за теоретические домашние задания.
* ПДЗ – средняя оценка за практические домашние задания в Python.
* БДЗ – средняя оценка за бонусные задачи.
* ПР – средняя оценка за проверочные работы на семинарах.
* К – оценка за коллоквиум.
* Э – оценка за письменный экзамен, проводимый в конце 4-го модуля.

Округление арифметическое.

'''Автоматов не предусмотрено'''.

== Литература ==

1) Golub, G. H., & Van Loan, C. F. (2013). Matrix Computations 4th Edition. The Johns Hopkins University Press. Baltimore.

2) Тыртышников, Е. Е. (2007). Методы численного анализа. Академия, Москва.

3) Trefethen, L. N., & Bau III, D. (1997). Numerical linear algebra. (Vol. 50). Siam. Philadelphia.

4) Demmel, James W. Applied numerical linear algebra. Society for Industrial and Applied Mathematics, 1997.