# Differential Equations 2023

THE OBSERVANCE OF EXAM PAPERS WILL TAKE PLACE AT 12 TOMORROW Room T 513

## Содержание

## Syllabus

### or see 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

Lecturer | K.A. Bukin kbukin@hse.ru |
Assistants: | |

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 24.01.2023**. Solow's growth model. Linear DE of the 2nd order. Wronskian
link: https://us06web.zoom.us/rec/share/DaL3pw7DPoXWbtxGRZcr55Upe1d5Nk2Um3-6-v_sBFnlyYUVhGujXG4BvaF-8cCL.T1waUT-pmhwyOfuD
Пароль: .2QmK8dl

**Lecture 31.01.2022**. How to solve n-th order linear DE with constant coeffifcients.
recording: https://us06web.zoom.us/rec/share/kYotRyuFwYWurRbty5UOaZnNZSdn5_ov84LgzrGNYizT3K2y126MqCu1UuGYycRZ.ZuB_RTy-y_FIDLcC
Пароль: =5Jin56f

**Lecture 07.02.2023**. Solutions of the nonhomogeneous equations with quasipolynomials.
Youtube

**Lecture 14.02.2023**. Variation of parameters method.
Youtube

**Lecture 21.02.2023**. Systems of linear DE.
Youtube

**Lecture 28.02.2023** Solving systems using JNF.
Youtube

Supplementary materials for Laplace transform: https://disk.yandex.ru/i/cMT41ZhIGBPnyw

and https://disk.yandex.ru/i/MMmQ-dgiPRkQww
**Lecture 07.03.2023** Laplace transform.
Youtube

**Lecture 14.03.2023** Linear difference equations.
Youtube

how equations with the variable coefficient is solved : https://disk.yandex.ru/i/eAqPoTJ2nCSxoQ Youtube

**Lecture 04.04.2023** Systems of difference equations.
Youtube

**Lecture 21.03.2022** Matrix exponent.
Youtube

**Lecture 04.04.2022** Liouville formula.
Youtube

**Lecture 11.04.2022** Sturm theorem.
Youtube

LECTURE MATERIALS (SLIDES)

https://disk.yandex.ru/i/vr_ZH7BAyOIx3g https://disk.yandex.ru/i/cNe5baj_c2VaQw https://disk.yandex.ru/i/tcnP-Cefb1jthQ

**Lecture 30.05.2022** Autonomous systems and types of equilibria.
Youtube

**Lecture 06.06.2022** Liapounov's function.
Youtube

**Lecture 08.06.2022** Exam preparation.
Youtube

## Seminars

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

## Midterm test

#### Midterm lasts for 80 minutes

MIDTERM IS SET ON APRIL 5. STARTS AT 18.10 AND WILL LAST FOR 80 MIN. IT WILL TAKE PLACE AT R 401.
THOSE ON DISTANT LEARNING WILL TAKE IT LATER (TO BE SCHEDULED NEXT WEEK).
*Materials*: Demo version

Midterm is scheduled on April, 5th and will start at 18.10. you will be notified about examination halls later. Problems that will be included: from the first 3 home assignments plus the problem on the homogeneous systems of the third order.

A sample of the midterm test you may find here: https://disk.yandex.ru/i/36KLNSFQl8sIKA

## Final exam

FINAL EXAM will begin at 10.30 on Thursday, June 29th. Will be held at R 301 (Groups 1 and 2) and at R 304 (Groups 3 and 4)

*Exam demo version*: [1] (recommended to solve)

*Last year exam*: [2]

## UoL Materials

*Materials*: [Materials]

*Tasks for preparation*: [Tasks]

*Exam demo version*: [Demo version]

*Exam assessment rules*: [Assessment rules]

## Assignments

### Home assignments 2023

Home assignment 1, due on "February 10th"

Home assignment 2, due on "February 24th"

Home assignment 3, due on "March 10th"

Home assignment 4, due on "April 3rd" THE DATE OF SUBMITTANCE WAS POSTPONED

Home assignment 5, due on "April 22nd"

Home assignment 6, due on "June 14th" THE DATE OF SUBMITTANCE WAS POSTPONED
DUE on JUNE 19th

## 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 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

University of London Exam papers and Examiners reports for the last three years.