Differential Equations 2021 — различия между версиями

Версия 11:55, 18 апреля 2022

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

Lectures

Lecture 10.01.2022. First order equations. Passcode: $76B5rUc

Lecture 17.01.2022. Fundamental theorem of DE. Passcode: ^Ts*1y69

Lecture 24.01.2022. Solow's growth model. Linear DE of the 2nd order. Passcode: ECxmcT1# , Youtube

Lecture 31.01.2022. How to solve n-th order linear DE with constant coeffifcients. Passcode: 9r*2cYy#, Youtube

Lecture 07.02.2022. Solutions of the nonhomogeneous equations with quasipolynomials. Passcode: 5Pyyqf#J, Youtube

Lecture 14.02.2022. Variation of parameters method. Passcode: 48+rFgL^, Youtube

Lecture 21.02.2022. Systems of linear DE. Passcode: !p.Aunz9, Youtube

Lecture 28.02.2022 Solving systems using JNF. Passcode: Ftd?4B%g, Youtube

Lecture 14.03.2022 Laplace transform. Passcode: 5!%Z1sfW, Youtube

Lecture 21.03.2022 Matrix exponent. Passcode: #?q2#XjS, Youtube

Lecture 04.04.2022 Liouville formula. Passcode: &p=h38l9, Youtube

Lecture 11.04.2022 Sturm theorem. Passcode: 3pkAKW.7, Youtube

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

Seminars

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: Demo version

Final exam

Exam demo version: [1] (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: [Materials]

Tasks for preparation: [Tasks]

Exam demo version: [Demo version]

Exam assessment rules: [Assessment rules]

Assignments

Home assignments

Home assignment 1, due on "February 3rd"

Home assignment 2, due on "February 17th"

Home assignment 3, due on "March 3rd"

Home assignment 4, due on "March 24th"

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 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.