# Differential Equations 2021

## 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 11.01.2021**. First order equations (part 1).
[1]

**Lecture 18.01.2021**. First order equations (part 2).
[2]

**Lecture 25.01.2021**. Fundamental theorem and introduction to linear DE.
[3]

**Lecture 01.02.2021**. Linear DE with constant coefficients solutions (part 1).
Passcode: JVN%1f6c, [4]

**Lecture 08.02.2021**. Linear DE with constant coefficients solutions (part 2).
Passcode: z#+7ZzuB, [5]

**Lecture 15.02.2021**. Solution of systems of DE (general case).
Passcode: @H6bhfv6 , [6]

Laplace transform tables: [7], [8]

**Lecture 22.02.2021**. Solution of nonhomogeneous systems.
[9], [10]

**Lecture 01.03.2021**. Laplace transform.
Passcode: Y8nd*mhe, [11]

**Lecture 06.03.2021**. Linear Systems.
[12], [13]

**Lecture 15.03.2021**. Liouville formula.
Passcode: 9.J*k3AG , [14], [15]

**Lecture 22.03.2021**. Equations with variable coefficients.
[16], [17]

**Lecture 05.04.2021**. Autonomous systems.
Passcode: En+3SzJ= , [18]

**Lecture 12.04.2021**. Lyapunov's function.
Passcode: pQSp6b&% , [19]

**Lecture 19.04.2021**. First integrals.
Passcode: H%9+MpP7 , [20]

**Lecture 26.04.2021**. Math methods solution 2020.
Passcode: 9+wJxu3$ , [21]

**Lecture 14.05.2021**. Elementary difference equations.
Passcode: h0Pn!x+$

**Lecture 31.05.2021**. General theory of difference systems and equations.
Passcode: v2Z3qdZ=

**Lecture 07.06.2021**. Solving problems from past exam variants.
Passcode: 4l@D@1^+

## Seminars

## Midterm test

*Date*: 10.04.2021

#### Midterm begins at 14:40 and lasts for 80 minutes

- Group 191 will take it at R405

- Group 192, 193 will take it at R404

*Materials*: Demo version

## Final exam

*Exam demo version*: [22] (recommended to solve)

#### Final exam is set on Monday June 21 at 16.20

- group 191 will sit exam in R 404

- group 192 in R 406

- group 193 in R 405

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

## UoL Materials

*Materials*: [Materials]

*Tasks for preparation*: [Tasks]

*Exam demo version*: [Demo version]

*Exam assessment rules*: [Assessment rules]

## Assignments

### Home assignments

Home assignment 1, due on **January 27th**

Home assignment 2, due on **February 10th**

Home assignment 3, due on **February 24th**

Home assignment 4, due on **March 10th**

Home assignment 5, due on **April 3rd**

Home assignment 6, due on **April 29th**

#### Homework results

## 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.