# 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).

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 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.

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