Calculus-2 2024/25 — различия между версиями

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(Seminar Notes)
(Lecture Notes)
 
(не показано 27 промежуточных версии этого же участника)
Строка 49: Строка 49:
 
== Lecture Notes ==
 
== Lecture Notes ==
 
''' <span style="color:#DC143C">If you notice an error or do not understand something, please describe it in the  [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']</span> <span style="color:#DC143C"></span>'''
 
''' <span style="color:#DC143C">If you notice an error or do not understand something, please describe it in the  [https://docs.google.com/spreadsheets/d/1MObdMXWccc98bIEJf17jLzd4FcADOXdShz2uVOz1wsY/edit?hl=ru#gid=0 '''Bugs Table.''']</span> <span style="color:#DC143C"></span>'''
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''' Module 2 '''
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* [ '''Lecture 14'''] (09.12.2024) Fourier series: Part II.
 +
 +
* [ '''Lecture 13'''] (02.12.2024) 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.
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 +
* [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&st=l81a97dz&dl=0 '''Lecture 9'''] (02.11.2024) Multiple Riemann integrals: Part I].
  
 
''' Module 1 '''
 
''' Module 1 '''
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* [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&dl=0 '''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.
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* [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&dl=0 '''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).
 +
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* [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&st=wi1fdyto&dl=0 '''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).
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* [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&dl=0 '''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.
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* [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&dl=0 '''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.
 
* [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&dl=0 '''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.
  
Строка 59: Строка 80:
 
* [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&dl=0 '''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.
 
* [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&dl=0 '''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.
  
== Seminar Notes ==
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== Homework ==
  
=== Group 231: ===
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=== The homework for group 231: ===
  
''' Module 1 '''
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'''Module 2'''
* [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&dl=0 '''Seminar 4'''] (23.09.24)
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* [https://www.dropbox.com/scl/fi/biyoe8trfxv7qa4831pot/Calculus_2_HW_13_C-231.pdf?rlkey=jba14sknburr1kcalktnvim7w&st=j2isy78k&dl=0 '''HW 13'''] (release: 02.11.24; deadline: 11.12.24)
  
* [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&dl=0 '''Seminar 3'''] (16.09.24)
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* [https://www.dropbox.com/scl/fi/dqdaegxhgdonysb7u1nb3/Calculus_2_HW_12_C-231.pdf?rlkey=le06e5zgvhh5lfjm1ze9r4k5y&st=mkbzd1t6&dl=0 '''HW 12'''] (release: 28.11.24; deadline: 08.12.24)
  
* [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&dl=0 '''Seminar 2'''] (09.09.24)
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* [https://www.dropbox.com/scl/fi/kjbipj8jhqprqs5lj5xww/Calculus_2_HW_11_C-231.pdf?rlkey=dxmdq0km7den03onrm8uez388&st=3169knjr&dl=0 '''HW 11'''] (release: 18.11.24; deadline: 25.11.24)
  
* [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&dl=0 '''Seminar 1'''] (02.09.24)
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* [https://www.dropbox.com/scl/fi/p4rnmbgr0qqd51c67r4zi/Calculus_2_HW_10_C-231.pdf?rlkey=ev1ttamf12gosbefpje97kqr5&st=fu5fn2yx&dl=0 '''HW 10'''] (release: 11.11.24; deadline: 18.11.24) <small>([https://www.dropbox.com/scl/fi/8by5mima2pusyimge8lnm/Calculus_II_Sem_10.pdf?rlkey=9dv3sj1u8ggp12pb9u8w7nede&st=497p51i8&dl=0 Seminar_10 notes])</small>
  
== Homework ==
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* [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&st=h9zdqm3d&dl=0 '''HW 9'''] (release: 03.11.24; deadline: 11.11.24) <small>([https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&st=xiiei8ji&dl=0 Seminar_9 notes])</small>
 
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=== The homework for group 231: ===
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'''Module 1'''
 
'''Module 1'''
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* [No '''HW 8'''] <small>([https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&st=mhohccyo&dl=0 Seminar_8 notes])</small>
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* [https://www.dropbox.com/scl/fi/bbfsxta8unjy1plrtdo8n/Calculus_2_HW_7_C-231.pdf?rlkey=m43gczr3zi8n168cywz1eir3a&st=dd766qau&dl=0 '''HW 7'''] (release: 14.10.24; deadline: 21.10.24) <small>([https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&st=bqpg2eao&dl=0 Seminar_7 notes])</small>
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* [https://www.dropbox.com/scl/fi/p1amv17v4v5gped31bt2u/Calculus_2_HW_6_C-231.pdf?rlkey=sggoyiopcvb9s2knowrxn8whp&st=u471ja68&dl=0 '''HW 6'''] (release: 07.10.24; deadline: 14.10.24) <small>([https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&st=96ma0xx2&dl=0 Seminar_6 notes])</small>
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* [https://www.dropbox.com/scl/fi/5sxvgaereyxyyc51vm00p/Calculus_2_HW_5_C-231.pdf?rlkey=hpr46kq2z2pp8xsroeu4vu0s1&st=wvdm90vc&dl=0 '''HW 5'''] (release: 30.09.24; deadline: 07.10.24) <small>([https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&dl=0 Seminar_5 notes])</small>
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* [https://www.dropbox.com/scl/fi/lxh72z9oyhflgncutbi82/Calculus_2_HW_4_C-231.pdf?rlkey=8k9gye3tpbn5rxzbu6r9s1q6x&st=740c3poi&dl=0 '''HW 4'''] (release: 23.09.24; deadline: 30.09.24) <small>([https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&dl=0 Seminar_4 notes])</small>
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* [https://www.dropbox.com/scl/fi/ghgt3fz6z6shez784pfmh/Calculus_2_HW_3_C-231.pdf?rlkey=jxw7g8wazfnfqath79w0meoxh&st=qh8jyynd&dl=0 '''HW 3'''] (release: 16.09.24; deadline: 23.09.24) <small>([https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&st=tw6sc57o&dl=0 Seminar_3 notes])</small>
 
* [https://www.dropbox.com/scl/fi/ghgt3fz6z6shez784pfmh/Calculus_2_HW_3_C-231.pdf?rlkey=jxw7g8wazfnfqath79w0meoxh&st=qh8jyynd&dl=0 '''HW 3'''] (release: 16.09.24; deadline: 23.09.24) <small>([https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&st=tw6sc57o&dl=0 Seminar_3 notes])</small>
  

Текущая версия на 09:09, 9 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 14] (09.12.2024) Fourier series: Part II.
  • [ Lecture 13] (02.12.2024) 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 13 (release: 02.11.24; deadline: 11.12.24)
  • 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

DSBA 2022/2023
First year