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Calculus 2 DSBA 2025/2026

2025-09-26T00:20:58Z

Andrey zhizhin: Внесены семинары и ДЗ 3 и 4 для группы 243

== Teachers and Assistants ==
{| class="wikitable" style="text-align:center"
|-
! Group !! 241 (M+P+) !! 242 !! 243 !! 244 !! 245 !! 246
|-
|| Lecturer ||colspan="6"| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]
|-
|| Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] <br> ([https://t.me/vvbalakirev tg]) || Жижин Андрей <br> ([https://t.me/meh_heh tg]) || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/en/org/persons/23597271/ Ian Marshall] || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]
|-
|| Consultations || Sat, 17:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> || Fri, 13:00 -- 14:20, N504 || || || ||
|-
|| Assistant || Зинкин Захар <br> ([https://t.me/Avgustine_iw tg])
|| Зинкин Захар <br> ([https://t.me/Avgustine_iw tg])
|| Суворова Александра <br> ([https://t.me/lunciare tg])
|| Бизина Дарья <br> ([https://t.me/dashulkinnnn tg])
|| Биктибаев Аскар <br> ([https://t.me/askbkt tg])
|| Мамакина Екатерина <br> ([https://t.me/katemamakina tg])
|- 
|}

== Course Description ==
This page contains basic information for the course Calculus-2 in 2025/2026 academic year at Bachelor’s Programme 'HSE and University of London Double Degree Programme in Data Science and Business Analytics' (DSBA).

== Grading system ==

<div class="mw-collapsible">

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.

'''<span style="color:#228B22">The cumulative grade</span>''', '''C''', is obtained '''without rounding''' by the following formula:

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

'''<span style="color:#DC143C">The final grade for the course</span>''', '''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.

</div>

== 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>'''

''' Module 1 '''
* [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&dl=0 '''Lecture 5'''] (26.09.2025) 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.

* [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&dl=0 '''Lecture 4'''] (19.09.2025) 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/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&dl=0 '''Lecture 3'''] (12.09.2025) 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.

* [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&dl=0 '''Lecture 2'''] (05.09.2025) 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.

* [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&dl=0 '''Lecture 1'''] (01.09.2025) 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 ==
{| class="wikitable"
{| class="wikitable" style="text-align:center"
|-
!| 241 || 242 || 243 || 244 || 245 || 246
|-
!| [https://www.dropbox.com/scl/fi/0dou6nqcuct2gslzkcaib/Calculus_2_HW_1_C-241.pdf?rlkey=nr3r79fqikonzlkbjftu6yr0p&st=qbwvqjro&dl=0 HW_1] (12.09.25)<br> [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&st=lfhiiexd&dl=0 Sem_1] || [https://www.dropbox.com/scl/fi/7g8h1qdvk5v98ay9dn31f/HW-1.pdf?rlkey=tv55f3mao7lkib526e9rju22j&st=mg9lbf8w&dl=0 HW_1] (08.09.25)<br> [https://www.dropbox.com/scl/fi/oo3s7ebfexh88vqcp7qzg/Seminar-1-problems.pdf?rlkey=be4qqlj4cglx6srn19y2gqwzl&st=41v7yceh&dl=0 Sem_1] <br> [https://www.dropbox.com/scl/fi/1a75u91uqcncznuo5eyq5/Seminar-1-solutions.pdf?rlkey=q1nx2pgscb1qzm9eyc0m9or1f&st=4t8e717f&dl=0 Solutions_1]|| [https://drive.google.com/file/d/1eqHEVSDBup6yu4kdrZNi53t4QKSGByi8/view?usp=drive_link HW_1] (09.09.25)<br> [https://drive.google.com/file/d/1Hdr4hb4m84XhnZEdK3RnQSAaBuk1YwDg/view?usp=drive_link Sem_1]|| [ HW_1] (??.??.25)<br> [ Sem_1]|| [ HW_1] (??.??.25)<br> [ Sem_1]|| [https://www.dropbox.com/scl/fi/6acrls00sosfli1cs25wb/Calculus_2_HW_1_C-246.pdf?rlkey=vvbfnongzz3ho9fa4tdrdmlg0&st=8usez3w4&dl=0 HW_1] (12.09.25)<br> [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&st=lfhiiexd&dl=0 Sem_1]
|-
!| [https://www.dropbox.com/scl/fi/2pz9tmu6cfg9hp1xjurpj/Calculus_2_HW_2_g241.pdf?rlkey=5zm6l036qfhnzrl872xxvp9f9&st=oaovhs69&dl=0 HW_2] (19.09.25)<br> [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&dl=0 Sem_2] || [https://www.dropbox.com/scl/fi/c5wd7b3ftj5j09ch3dxm0/HW-2.pdf?rlkey=t3y9fq6rtdlji1gkfm4k9c7j2&st=st4zzc8z&dl=0 HW_2] (15.09.25)<br> [https://www.dropbox.com/scl/fi/pqmjtjwk7h9s8dl6s4b2m/Seminar-2-problems.pdf?rlkey=uacileykfb95e92orwwsza6cx&st=gyrthixn&dl=0 Sem_2] <br> [https://www.dropbox.com/scl/fi/3vcbc1tu3qhgwohaesah2/Seminar-2-solutions.pdf?rlkey=cqizv04qu5aygmwyi6mj2unu6&st=etzgo47s&dl=0 Solutions_2] || [https://drive.google.com/file/d/1Bbo2bWeIabTOnw-_38pBLEMTbZXXNO6g/view?usp=drive_link HW_2] (16.09.25)<br> [https://drive.google.com/file/d/1wkZx8NUoAFakDVrrMHm6lIj_y5t6v2Mi/view?usp=drive_link Sem_2] || [ HW_2] (??.??.25)<br> [ Sem_2] || [ HW_2] (??.??.25)<br> [ Sem_2] || [https://www.dropbox.com/scl/fi/qnjzl0nh7tqdq4ppq0z5l/Calculus_2_HW_2_g246.pdf?rlkey=vke6udp75k7hajk2ej3vb8mxl&st=31jdcdgi&dl=0 HW_2] (19.09.25)<br> [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&dl=0 Sem_2]
|-
!| [https://www.dropbox.com/scl/fi/ssjhx72pziuqj5cj5qe5f/Calculus_2_HW_3_g241.pdf?rlkey=gnoq79ay1ibivc70p54h4p998&st=5l6sh20e&dl=0 HW_3] (26.09.25)<br> [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&st=j7mfl7q8&dl=0 Sem_3] || [https://www.dropbox.com/scl/fi/rusf9hne41u3jx7ui6om2/HW-3.pdf?rlkey=uo66plpawz99vcrowt1hasefd&st=8q53sw20&dl=0 HW_3] <br> [https://www.dropbox.com/scl/fi/97bflhzqm9md5ahrle9xg/Seminar-3-problems.pdf?rlkey=0kx1urnfb2g6r6tcuquspd5qk&st=hseqkny3&dl=0 Sem_3] <br> [https://www.dropbox.com/scl/fi/feogjwl8d18voq85lhcsf/Seminar-3-solutions.pdf?rlkey=uvtf6qzku9k8bq6h68asybneo&st=57k8aqw2&dl=0 Solutions_3] || [https://drive.google.com/file/d/1Dg1ysP4N1zEaFfnoXDwLPArDOOLBZtn9/view?usp=drive_link HW_3] (16.09.25)<br> [https://drive.google.com/file/d/1RNGA7DUJQKEKKI51TD6xesZpwzdaymbm/view?usp=drive_link Sem_3] || [ HW_3] (??.??.25)<br> [ Sem_3] || [ HW_3] (??.??.25)<br> [ Sem_3] || [https://www.dropbox.com/scl/fi/6azwt9z2tgnx9onvwoy79/Calculus_2_HW_3_g246.pdf?rlkey=qi10x3vdfbqdmixgrw93cj9w6&st=xcx7z9s1&dl=0 HW_3] (26.09.25)<br> [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&st=j7mfl7q8&dl=0 Sem_3]
|-
!| [https://www.dropbox.com/scl/fi/oj49ruzn4ilvuubx7tl3s/Calculus_2_HW_4_g241.pdf?rlkey=6h4ng632xz14igucr1lidgdbp&st=2lzpqhv0&dl=0 HW_4] (03.10.25)<br> [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&dl=0 Sem_4] || [https://www.dropbox.com/scl/fi/rb0xzxt5n3kg29t7wayxg/HW-4.pdf?rlkey=0qtt4r395sfr4si47yabdrt81&dl=0 HW_4] <br> [https://www.dropbox.com/scl/fi/r7gi4zugjaxk5lwbfjjsw/Seminar-4-problems.pdf?rlkey=sdi2mxt5iql4ftfc43mlna698&dl=0 Sem_4] <br> [https://www.dropbox.com/scl/fi/jvocho91zup7dlwwd4xpn/Seminar-4-solutions.pdf?rlkey=d7ct6xv5x7p2uae3ucnfxwwrc&dl=0 Solutions_4] || [https://drive.google.com/file/d/1UAUilqoMRjA-3lgRbN7aR3faWIP7lJ5Q/view?usp=drive_link HW_4] (25.09.25)<br> [https://drive.google.com/file/d/17cmSbvQgwqsQuKvT5RfWhcL4gAfZyKaN/view?usp=drive_link Sem_4] || [ HW_4] (??.??.25)<br> [ Sem_4] || [ HW_4] (??.??.25)<br> [ Sem_4] || [https://www.dropbox.com/scl/fi/1oe8xjn3zz4aeeaga01yk/Calculus_2_HW_4_g246.pdf?rlkey=eq20cjsubiyym9oyo84csgydd&st=12fav0if&dl=0 HW_4] (03.10.25)<br> [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&dl=0 Sem_4]
|}

== Exams ==

== Results ==

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1qexwBdQyO_BFXZAK3hikzPS02QW6bdkvcxyLBjmNXwE/edit?gid=1043223803#gid=1043223803 241] !! [https://docs.google.com/spreadsheets/d/1s6uKvnzy3Jp38NNVstc4VgocUrJAN4nW2uJ25KFy2A4/edit?gid=1043223803#gid=1043223803 242] !! [https://docs.google.com/spreadsheets/d/14KfOd52RgHD0JKvIjCgDniCID1eWixAKqQDmZRUeVns/edit?gid=1043223803#gid=1043223803 243] !! [https://docs.google.com/spreadsheets/d/1yk2CxUacnahllXfHpsqucu5Sy38-sjapyFFIFXOUf0s/edit?gid=1043223803#gid=1043223803 244] !! [https://docs.google.com/spreadsheets/d/195HTm7JGISCMU3a35lU8a8R-2_mK5oADpcDEn6UDR0w/edit?gid=1043223803#gid=1043223803 245] !! [https://docs.google.com/spreadsheets/d/1pI4lGlfeUvFEpYeAPh1M0WItBILkOYg9dJ9PCQGj5Mc/edit?gid=1043223803#gid=1043223803 246]
|}

== Navigation ==
<div style="border:1px; border-style:solid; border-color:#a2a9b1; padding:3px">
<table style="border-spacing:0; background:transparent; color:inherit; width:100%">
<tr>
<th scope="colgroup" style="background-color:#cfe3ff" colspan="2"><div id="DSBA22" style="font-size:114%; margin:0 5em">DSBA 2022/2023</div></th>
</tr>
<tr >
<th scope="row" style="border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff">First year</th>
<td style="text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px">
<div style="padding:0em 0.25em">
<ul><li style="display:inline-block; padding:2px">[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] • </li><li style="display:inline-block; padding:2px">[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] • </li><li style="display:inline-block; padding:2px">[[Calculus_DSBA_2022/2023|Calculus]] • </li><li style="display:inline-block; padding:2px">[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] • </li><li style="display:inline-block; padding:2px">[[DSBA_Algebra_2022_2023|Algebra]] </li></ul>
</div></td>
</tr>
</table>
</div>

Calculus 2 DSBA 2025/2026

2025-09-09T14:07:19Z

Andrey zhizhin: добавил сем 2 и дз 2 для 3 группы

Calculus 2 DSBA 2025/2026

2025-09-02T13:42:51Z

Andrey zhizhin: Добавлен семинар 1 для 243

Calculus 2 DSBA 2025/2026

2025-09-02T13:41:51Z

Andrey zhizhin: Добавлено ДЗ-1 для 243