Calculus-2 2024/25

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Teachers and Assistants

Group 231 (M+P+) 232 233 234
Lecturer Andrey Mazhuga
Teacher Andrey Mazhuga Vladislav Balakirev (tg) Корней Томащук (tg) Павел Жуков (tg)
Consultations Sat, 17:00 -- 21:00, via Zoom
One must notify me beforehand
Assistant Дарья Бизина
([ tg])
Роман Бохян
(tg)
Елизавета Аникина
(tg)
Виктория Фокина
([ tg])

Course Description

This page contains basic information for the course Calculus-2 in 2024/2025 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).

Grading system

 [свернуть

During the course, the student will be formally graded on the following:

  • one in-class oral test (O);
  • one in-class written test (= midterm test) (W);
  • several quizzes (Q, where Q is the average grade of all the quizzes in the course);
  • several homework assignments (H, where H is the average grade of all the homework assignments in the course);
  • one written exam (E).

All grades (namely, O, W, Q, H, and E) are real numbers from 0 to 10.

The cumulative grade, C, is obtained without rounding by the following formula:

C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.

The final grade for the course, F, is obtained by the following formula:

F = Round(7/10*C + 3/10*E).

where the function Round(x) is defined as follows: if the decimal part of x is less than 0.2, the grade is rounded downwards; if the decimal part of x is greater than 0.7, the grade is rounded upwards; if the decimal part of x is from the interval [0.2;0.7] and the student's seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.

Lecture Notes

If you notice an error or do not understand something, please describe it in the Bugs Table.

Module 1

  • Lecture 6 (07.10.2024) Theorem on changing the order of two limits; theorem on continuity of a limit function; theorem on Riemann integrability of a limit function; theorem on integration of a uniformly convergent sequence; theorem on differentiability of a limit function; theorem on continuity of a series; theorem on term-by-term integration of a uniformly convergent series; theorem on term-by-term differentiation of a series; the Stone-Weierstrass theorem (without a proof).
  • Lecture 5 (30.09.2024) Functional sequences and series; poinwise convergence; uniform convergence; the Cauchy criterion for the uniform convegrence; the negation of the Cauchy criterion for the uniform convegrence; the nevessary condition for the uniform convergence; the Weierstrass M-test; the Dirichlet test for the uniform convergence; the Abel test for the uniform convergence.
  • Lecture 4 (23.09.2024) Product of series; the Mertens theorem; the Abel theorem on the Cauchy product; the Abel theorem on series products; the Wallis formula; the Stirling formula; the Robbins formula.
  • Lecture 3 (16.09.2024) The Abel transformation; the Dirichlet test; the Abel test; the Leibniz test; sine and cosine sums; absolutely and conditionally convergent series; alternating p-series; the Cauchy rearrangement theorem; the Riemann rearrangement theorem.
  • Lecture 2 (09.09.2024) Series with non-negative terms; the Cauchy Condensation test; the first comparison test; the second comparison test; p-series convergence; the integral test; the root test; the ration test; the Kummer test; the Bertrand test; the Gauss test.
  • Lecture 1 (02.09.2024) Series; convergence and divergence; Cauchy's criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.

Homework

The homework for group 231:

Module 1

The homework for group 232:

Module 1

The homework for group 233:

Module 1

The homework for group 234:

Module 1

Exams

Results

231 232 233 234

Navigation

DSBA 2022/2023
First year