Просмотр исходного текста страницы Calculus-2 2023/24

== Teachers and Assistants ==
{| class="wikitable" style="text-align:center"
|-
! Group !! 221 (M+P+) !! 222 !! 223 !! 224 
|-
|| Lecturer ||colspan="4"| [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/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/225584739 Корней Томащук] ([https://t.me/KkO_oRrNnEeYy tg]) || [https://www.hse.ru/org/persons/25910956 Павел Жуков] ([https://t.me/Pavel_Zhukof tg])
|- 
|| Consultations || Sat, 17:00 -- 21:00, via Zoom <br><span style="color:#DC143C">One must notify me beforehand</span> ||  ||  ||  
|-
|| Assistant || Алмасбек Стамбеков <br> ([https://t.me/KingOfTheFlies tg])
|| Елизавета Аникина <br> ([https://t.me/lizokkolobok25 tg])
|| Елизавета Аникина <br> ([https://t.me/lizokkolobok25 tg])
|| Тимур Нигматзянов <br> ([https://t.me/chakchak77 tg])
|- <!--
||  Course <br> Assistant ||colspan="4"| Белоновский Пётр <br> pibelonovskiy@edu.hse.ru 
|- -->
|}

== Course Description ==
This page contains basic information for the course Calculus-2 in 2023/2024 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 2 '''
* [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&dl=0 '''Lecture 8'''] (01.11.2023) Analytic functions; differentiability classes; smooth functions; the Taylor series; the Taylor formula; criteria for analyticity; the Borel lemma; some pathological examples of smooth functions.

''' Module 1 '''
* [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&dl=0 '''Lecture 7'''] (18.10.2023) 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).

* [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&st=wi1fdyto&dl=0 '''Lecture 6'''] (11.10.2023) 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).

* [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&dl=0 '''Lecture 5'''] (04.10.2023) 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'''] (27.09.2023) 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'''] (20.09.2023) 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'''] (13.09.2023) 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'''] (06.09.2023) 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 ==

=== Group 221: ===

''' Module 2 '''
* [https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&dl=0 '''Seminar 8'''] (03.11.23)

''' Module 1 '''
* [https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&dl=0 '''Seminar 7'''] (20.10.23)

* [https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&dl=0 '''Seminar 6'''] (20.10.23)

* [https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&dl=0 '''Seminar 5'''] (13.10.23)

* [https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&dl=0 '''Seminar 4'''] (06.10.23)

* [https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&dl=0 '''Seminar 3'''] (29.09.23)

* [https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&dl=0 '''Seminar 2'''] (22.09.23)

* [https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&dl=0 '''Seminar 1'''] (15.09.23)

=== Groups 222, 223: ===


''' Module 2 '''
* [https://www.dropbox.com/scl/fi/qsslo2fzycu0ass8i130h/S10.pdf?rlkey=j41kdtjuzvijtiuzdxxryzsdj&dl=0 '''Seminar 10'''] (24.11.23)
* [https://www.dropbox.com/scl/fi/27zpep5yvv0wglz6kx91j/S9.pdf?rlkey=dmhahfcpxm79oflamrdyqrt9n&dl=0 '''Seminar 9'''] (17.11.23)
* [https://www.dropbox.com/scl/fi/yq64sprdhopcin0au2mhi/S8.pdf?rlkey=8911qlf22pbufprszj5a8yxeo&dl=0 '''Seminar 8'''] (10.11.23)
* [https://www.dropbox.com/scl/fi/xqfgrkkldf2t2lmbjbu5f/S7.pdf?rlkey=2k6y1gy1umu4c67stzbi7zro8&dl=0 '''Seminar 7'''] (03.11.23)

''' Module 1 '''
* [https://www.dropbox.com/scl/fi/pyc3xgvnkyfiy9sd1qwb0/Seminar6.pdf?rlkey=zk2lb8n8dlyt6fvkjyk558bif&dl=0 '''Seminar 6'''] (20.10.23)
* [https://www.dropbox.com/scl/fi/s8cqbxjaqevh8bslu0vdr/Seminar5.pdf?rlkey=07nqqhkw6amxrph9wphcyuovr&dl=0 '''Seminar 5'''] (13.10.23)
* [https://www.dropbox.com/scl/fi/14e0i9q1vf4ijp9m3tp06/Seminar4.pdf?rlkey=5kz6jmniait1rwlu2ucgc0wm0&dl=0 '''Seminar 4'''] (06.10.23)
* [https://www.dropbox.com/scl/fi/raufzbhsr8resta9bed20/Seminar3.pdf?rlkey=w8p1up8wjgdgfn0chcfw3k5dh&dl=0 '''Seminar 3'''] (29.09.23)
* [https://www.dropbox.com/scl/fi/vmdsav2sjrr16nvbadj9t/Seminar2.pdf?rlkey=95t3vc4gcahiv5qmh0th4e6if&dl=0 '''Seminar 2'''] (22.09.23)
* [https://www.dropbox.com/scl/fi/rqtjkxjdtcxmf3fdwu3c3/S1.pdf?rlkey=908iruycxo11yfcnpq3h1gc4o&dl=0 '''Seminar 1'''] (15.09.23)

== Homework ==

=== The homework for group 221: ===

'''Module 2'''
* [https://www.dropbox.com/scl/fi/rh8qawp72bfe14mrtf4j9/Calculus_2_HW_13_C-221.pdf?rlkey=q14ac4y4dnhp4gq6qv9iocd01&dl=0 '''HW 13'''] (release: 10.12.23; deadline: 17.12.23 [23:59 MSK])
* no HW 12 (since Oral Test)
* [https://www.dropbox.com/scl/fi/a345qkddp77beuoejq76q/Calculus_2_HW_11_C-221.pdf?rlkey=5k1k1wljcaeyma9gooqmwe9dr&dl=0 '''HW 11'''] (release: 27.11.23; deadline: 03.12.23 [23:59 MSK])
* [https://www.dropbox.com/scl/fi/fzk5uf3bvxncuyez9bk7v/Calculus_2_HW_10_C-221.pdf?rlkey=qpps5pi1oe5dd5r65dmvohruy&dl=0 '''HW 10'''] (release: 19.11.23; deadline: 26.11.23 [23:59 MSK]) <small>([https://www.dropbox.com/scl/fi/zljtqq5im6aj4a3wxvlzy/Calculus_II_Sem_10.pdf?rlkey=scon4zzu8qr3aqevr5uguy8jk&dl=0 seminar notes])</small>
* [https://www.dropbox.com/scl/fi/gra5ty4lsnel2cykp942a/Calculus_2_HW_9_C-221.pdf?rlkey=7spwmljgxzitzbly7mg061xe6&dl=0 '''HW 9'''] (release: 12.11.23; deadline: 19.11.23 [23:59 MSK])

* no HW 8(since Midterm)

'''Module 1'''
* [https://www.dropbox.com/scl/fi/7pt1zmegu86064ayxz5nn/Calculus_2_HW_7_C-221.pdf?rlkey=z9pgjh063er9wcdnofrumk5l9&dl=0 '''HW 7'''] (release: 24.10.23; deadline: 05.11.23 [23:59 MSK])

* no HW 6(since we had two seminars in one day)

* [https://www.dropbox.com/scl/fi/mfkxkh91o2nstf805cti9/Calculus_2_HW_5_C-221.pdf?rlkey=o9rea5cezwzxcvkmveccp81ep&dl=0 '''HW 5'''] (release: 14.10.23; deadline: 22.10.23 [23:59 MSK])

* [https://www.dropbox.com/scl/fi/0fqtq4488q5c26z8srvhz/Calculus_2_HW_4_C-221.pdf?rlkey=5avkmjkjtq10e58gb84sk0dna&dl=0 '''HW 4'''] (release: 07.10.23; deadline: 15.10.23 [23:59 MSK])

* [https://www.dropbox.com/scl/fi/olzzd9e9hse3e28npir7b/Calculus_2_HW_3_C-221.pdf?rlkey=e5exn314ict736t1uhq9huijy&dl=0 '''HW 3'''] (release: 29.09.23; deadline: 08.10.23 [23:59 MSK])

* [https://www.dropbox.com/scl/fi/fiz6h485txv3g25k8p8yb/Calculus_2_HW_2_C-221.pdf?rlkey=ghhnrjxvgfb9ean3v0fofqt67&dl=0 '''HW 2'''] (release: 22.09.23; deadline: 01.10.23 [23:59 MSK])

* [https://www.dropbox.com/scl/fi/der5ht5nh0jy8ojxjp1r6/Calculus_2_HW_1_C-221.pdf?rlkey=7pbs1axcr4dcgqevoibet7jdh&dl=0 '''HW 1'''] (release: 15.09.23; deadline: 24.09.23 [23:59 MSK])

=== The homework for groups 222, 223: ===

'''Module 2'''
* [https://www.dropbox.com/scl/fi/g5qbnyxtedrzo7dkdqig6/HW10.pdf?rlkey=fmi0ervxq5s7qm41aq28lnsza&dl=0 '''HW 10'''] (release: 26.11.23; deadline: 03.12.23)
* [https://www.dropbox.com/scl/fi/5pkblynst5jqsafrxn4nf/HW9.pdf?rlkey=004gkna7xljxlz8v5cpeek2ts&dl=0 '''HW 9'''] (release: 19.11.23; deadline: 26.11.23)
* [https://www.dropbox.com/scl/fi/wrvg8zfzd7m4o1lhtdibk/HW8.pdf?rlkey=ppq44b1zic87pz7dzcw39yv98&dl=0 '''HW 8'''] (release: 14.11.23; deadline: 19.11.23)
* [https://www.dropbox.com/scl/fi/k8emisk2erbruqfog6x3j/HW7.pdf?rlkey=6wycrl124qx4d044r9uesnn5t&dl=0 '''HW 7'''] (release: 05.11.23; deadline: 12.11.23)

'''Module 1'''
* [https://www.dropbox.com/scl/fi/j2cfapu1l7to6rpewh77l/HW6.pdf?rlkey=lsuu3he7y4x1z5xuuaovz2ys6&dl=0 '''HW 6'''] (release: 22.10.23; deadline: 05.11.23)
* [https://www.dropbox.com/scl/fi/t0gl9t4ztp8293pyp0x5u/HW5.pdf?rlkey=qzrpair27cn6ccdxlw00v1qao&dl=0 '''HW 5'''] (release: 15.10.23; deadline: 22.10.23)
* [https://www.dropbox.com/scl/fi/qysyjwqqbakare6yerrx8/HW4.pdf?rlkey=s4zdldevgiw91564fsimwgn40&dl=0 '''HW 4'''] (release: 08.10.23; deadline: 15.10.23)
* [https://www.dropbox.com/scl/fi/svtsmiiqylm0co8zp2d3b/HW3.pdf?rlkey=shf5ntlpj1kl62rd8otsi32ul&dl=0 '''HW 3'''] (release: 01.10.23; deadline: 08.10.23)
* [https://www.dropbox.com/scl/fi/puf6ht0u0pmlyem7z664y/HW2.pdf?rlkey=dy0524ycah0ix4dkjdxl4t8op&dl=0 '''HW 2'''] (release: 23.09.23; deadline: 01.10.23)
* [https://www.dropbox.com/scl/fi/92juzofvh8fev8hrkwy1f/HW1.pdf?rlkey=v3zdpjof4phphio9fme9tytax&dl=0 '''HW 1'''] (release: 16.09.23; deadline: 24.09.23)

=== The homework for group 224: ===
'''Module 1'''
* [??? '''HW 1'''] (release: ???; deadline: ???) <small>([??? seminar notes])</small>

== Exams ==

== Results ==

{| class="wikitable" style="text-align:center"
|-
! [ 221] !! [https://docs.google.com/spreadsheets/d/1e8MJhZrRCoF2CkCCzki_JBJpuWZkwGKVHFArVBhudT0/edit#gid=1043223803 222] !! [https://docs.google.com/spreadsheets/d/1PB5lmL62csREaK9haM6KRL1IN5NGfWFR5VaKNg1HYmw/edit#gid=1043223803 223] !! [https://docs.google.com/spreadsheets/d/1ORDKPkKd84pGF7NRhLpqsWH4ib_B-i7oWeXBvVP-iy0/edit#gid=1043223803 224] 
|}

== Navigation ==
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<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>
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  <th scope="row" style="border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff">First year</th>
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   <ul><li style="display:inline-block; padding:2px">[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &bull; </li><li style="display:inline-block; padding:2px">[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &bull; </li><li style="display:inline-block; padding:2px">[[Calculus_DSBA_2022/2023|Calculus]] &bull; </li><li style="display:inline-block; padding:2px">[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &bull; </li><li style="display:inline-block; padding:2px">[[DSBA_Algebra_2022_2023|Algebra]] </li></ul>
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