Calculus-2 2024/25 — различия между версиями

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(Lecture Notes)
(Lecture Notes)
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''' Module 2 '''
 
''' Module 2 '''
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* [ '''Lecture 12'''] (01.12.2024) Fourier series: Part I.
 +
 
* [ '''Lecture 12'''] (25.11.2024) Improper integrals depending on a parameter; Gamma and Beta functions].
 
* [ '''Lecture 12'''] (25.11.2024) Improper integrals depending on a parameter; Gamma and Beta functions].
  

Версия 22:37, 1 декабря 2024

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 2

  • [ Lecture 12] (01.12.2024) Fourier series: Part I.
  • [ Lecture 12] (25.11.2024) Improper integrals depending on a parameter; Gamma and Beta functions].
  • [ Lecture 11] (18.11.2024) Multiple Riemann integrals: Part III; Improper multiple integrals].
  • [ Lecture 10] (11.11.2024) Multiple Riemann integrals: Part II].
  • Lecture 9 (02.11.2024) Multiple Riemann integrals: Part I].

Module 1

  • Lecture 8 (21.10.2024) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.
  • Lecture 7 (14.10.2024) Power series; the radius and the interval of convergence of a power series; the Cauchy-Hadamard Formula; theorem on the uniform convergence of power series; theorem on derivative of power series; theorem on analyticity of power series; theorem on antiderivative of power series; theorem on equality of power series; the Abel theorem on the Cauchy product (proof).
  • 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 2

  • HW 12 (release: 28.11.24; deadline: 08.12.24)
  • HW 11 (release: 18.11.24; deadline: 25.11.24)

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

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