https://wikicshse.ru/index.php?action=history&feed=atom&title=Calculus-2_2024%2F25 Calculus-2 2024/25 - История изменений 2026-06-06T13:25:34Z История изменений этой страницы в вики MediaWiki 1.45.3 https://wikicshse.ru/index.php?title=Calculus-2_2024/25&diff=96&oldid=prev imported>Mazhuga.A.M.: /* Lecture Notes */ 2024-12-09T06:09:25Z <p><span class="autocomment">Lecture Notes</span></p> <p><b>Новая страница</b></p><div>== Teachers and Assistants ==<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! Group !! 231 (M+P+) !! 232 !! 233 !! 234 <br /> |-<br /> || Lecturer ||colspan=&quot;4&quot;| [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga]<br /> |- <br /> || Teacher || [https://www.hse.ru/org/persons/224875083 Andrey Mazhuga] || [https://www.hse.ru/org/persons/207901592 Vladislav Balakirev] ([https://t.me/vvbalakirev 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])<br /> |- <br /> || Consultations || Sat, 17:00 -- 21:00, via Zoom &lt;br&gt;&lt;span style=&quot;color:#DC143C&quot;&gt;One must notify me beforehand&lt;/span&gt; || || || <br /> |-<br /> || Assistant || Дарья Бизина &lt;br&gt; ([ tg])<br /> || Роман Бохян &lt;br&gt; ([https://t.me/@warning172 tg])<br /> || Елизавета Аникина &lt;br&gt; ([https://t.me/lizokkolobok25 tg])<br /> || Виктория Фокина &lt;br&gt; ([ tg])<br /> |- &lt;!--<br /> || Course &lt;br&gt; Assistant ||colspan=&quot;4&quot;| Белоновский Пётр &lt;br&gt; pibelonovskiy@edu.hse.ru <br /> |- --&gt;<br /> |}<br /> <br /> == Course Description ==<br /> This page contains basic information for the course Calculus-2 in 2024/2025 academic year at Bachelor’s Programme &#039;HSE and University of London Double Degree Programme in Data Science and Business Analytics&#039; (DSBA).<br /> <br /> == Grading system == <br /> <br /> &lt;div class=&quot;mw-collapsible&quot;&gt;<br /> <br /> During the course, the student will be formally graded on the following:<br /> *one in-class oral test (&#039;&#039;&#039;O&#039;&#039;&#039;);<br /> *one in-class written test (= midterm test) (&#039;&#039;&#039;W&#039;&#039;&#039;);<br /> *several quizzes (&#039;&#039;&#039;Q&#039;&#039;&#039;, where &#039;&#039;&#039;Q&#039;&#039;&#039; is the average grade of all the quizzes in the course);<br /> *several homework assignments (&#039;&#039;&#039;H&#039;&#039;&#039;, where &#039;&#039;&#039;H&#039;&#039;&#039; is the average grade of all the homework assignments in the course);<br /> *one written exam (&#039;&#039;&#039;E&#039;&#039;&#039;).<br /> <br /> All grades (namely, &#039;&#039;&#039;O&#039;&#039;&#039;, &#039;&#039;&#039;W&#039;&#039;&#039;, &#039;&#039;&#039;Q&#039;&#039;&#039;, &#039;&#039;&#039;H&#039;&#039;&#039;, and &#039;&#039;&#039;E&#039;&#039;&#039;) are real numbers from 0 to 10.<br /> <br /> &#039;&#039;&#039;&lt;span style=&quot;color:#228B22&quot;&gt;The cumulative grade&lt;/span&gt;&#039;&#039;&#039;, &#039;&#039;&#039;C&#039;&#039;&#039;, is obtained &#039;&#039;&#039;without rounding&#039;&#039;&#039; by the following formula:<br /> <br /> &#039;&#039;&#039;C = 4/17*H + 4/17*Q + 4/17*W + 5/17*O.&#039;&#039;&#039;<br /> <br /> &#039;&#039;&#039;&lt;span style=&quot;color:#DC143C&quot;&gt;The final grade for the course&lt;/span&gt;&#039;&#039;&#039;, &#039;&#039;&#039;F&#039;&#039;&#039;, is obtained by the following formula:<br /> <br /> &#039;&#039;&#039;F = Round(7/10*C + 3/10*E).&#039;&#039;&#039;<br /> <br /> 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&#039;s seminar attendance during the first semester is not below 66%, the grade is rounded upwards; otherwise the grade is rounded downwards.<br /> <br /> &lt;/div&gt;<br /> <br /> == Lecture Notes ==<br /> &#039;&#039;&#039; &lt;span style=&quot;color:#DC143C&quot;&gt;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 &#039;&#039;&#039;Bugs Table.&#039;&#039;&#039;]&lt;/span&gt; &lt;span style=&quot;color:#DC143C&quot;&gt;&lt;/span&gt;&#039;&#039;&#039;<br /> <br /> &#039;&#039;&#039; Module 2 &#039;&#039;&#039;<br /> * [ &#039;&#039;&#039;Lecture 14&#039;&#039;&#039;] (09.12.2024) Fourier series: Part II.<br /> <br /> * [ &#039;&#039;&#039;Lecture 13&#039;&#039;&#039;] (02.12.2024) Fourier series: Part I.<br /> <br /> * [ &#039;&#039;&#039;Lecture 12&#039;&#039;&#039;] (25.11.2024) Improper integrals depending on a parameter; Gamma and Beta functions.<br /> <br /> * [ &#039;&#039;&#039;Lecture 11&#039;&#039;&#039;] (18.11.2024) Multiple Riemann integrals: Part III; Improper multiple integrals.<br /> <br /> * [ &#039;&#039;&#039;Lecture 10&#039;&#039;&#039;] (11.11.2024) Multiple Riemann integrals: Part II.<br /> <br /> * [https://www.dropbox.com/scl/fi/gnun2r1ys31ltw11cyluv/Calculus_2_Lecture_9.pdf?rlkey=m5dge8pgcn11bmvfzegy0ni1x&amp;st=l81a97dz&amp;dl=0 &#039;&#039;&#039;Lecture 9&#039;&#039;&#039;] (02.11.2024) Multiple Riemann integrals: Part I].<br /> <br /> &#039;&#039;&#039; Module 1 &#039;&#039;&#039;<br /> * [https://www.dropbox.com/scl/fi/zulvgcj3qsl822ju2ibf9/Calculus_2_Lecture_8.pdf?rlkey=sagkjdg5fczs3ihq9g1x048ur&amp;dl=0 &#039;&#039;&#039;Lecture 8&#039;&#039;&#039;] (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.<br /> <br /> * [https://www.dropbox.com/scl/fi/8qx6y7263t97lpdrykidd/Calculus_2_Lecture_7.pdf?rlkey=e4vofnajrpecdd5uc21fhfhs9&amp;dl=0 &#039;&#039;&#039;Lecture 7&#039;&#039;&#039;] (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).<br /> <br /> * [https://www.dropbox.com/scl/fi/h529pu8qfus8doc8flw0b/Calculus_2_Lecture_6.pdf?rlkey=b08lx7c7dvjpvzxeh680ynk03&amp;st=wi1fdyto&amp;dl=0 &#039;&#039;&#039;Lecture 6&#039;&#039;&#039;] (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).<br /> <br /> * [https://www.dropbox.com/scl/fi/3pkd7tu6yqzo6iu14973u/Calculus_2_Lecture_5.pdf?rlkey=fgmy2lcrpqui8pr2ybjok09ku&amp;dl=0 &#039;&#039;&#039;Lecture 5&#039;&#039;&#039;] (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.<br /> <br /> * [https://www.dropbox.com/scl/fi/a6quigky0ww3xr4r8c1of/Calculus_2_Lecture_4.pdf?rlkey=lcs9y3qydkcnk9u9qv0up0d6e&amp;dl=0 &#039;&#039;&#039;Lecture 4&#039;&#039;&#039;] (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.<br /> <br /> * [https://www.dropbox.com/scl/fi/x9srwlnecmcdbklaidlk7/Calculus_2_Lecture_3.pdf?rlkey=7kr1iyzw8ftm8lryralc5y5mn&amp;dl=0 &#039;&#039;&#039;Lecture 3&#039;&#039;&#039;] (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.<br /> <br /> * [https://www.dropbox.com/scl/fi/pn5upm5x6khbs7s3a565e/Calculus_2_Lecture_2.pdf?rlkey=am9cqmo0m1mk40gxo00kycumz&amp;dl=0 &#039;&#039;&#039;Lecture 2&#039;&#039;&#039;] (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.<br /> <br /> * [https://www.dropbox.com/scl/fi/4sp8sbruiowo9t1fjpeah/Calculus_2_Lecture_1.pdf?rlkey=9o9pg6ksix7xohp2wn8fhpyts&amp;dl=0 &#039;&#039;&#039;Lecture 1&#039;&#039;&#039;] (02.09.2024) Series; convergence and divergence; Cauchy&#039;s criterion and its negation; necessary condidion for convergence; the tale (= remainder) of a series; linear combination of series; grouping theorem.<br /> <br /> == Homework ==<br /> <br /> === The homework for group 231: ===<br /> <br /> &#039;&#039;&#039;Module 2&#039;&#039;&#039;<br /> * [https://www.dropbox.com/scl/fi/biyoe8trfxv7qa4831pot/Calculus_2_HW_13_C-231.pdf?rlkey=jba14sknburr1kcalktnvim7w&amp;st=j2isy78k&amp;dl=0 &#039;&#039;&#039;HW 13&#039;&#039;&#039;] (release: 02.11.24; deadline: 11.12.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/dqdaegxhgdonysb7u1nb3/Calculus_2_HW_12_C-231.pdf?rlkey=le06e5zgvhh5lfjm1ze9r4k5y&amp;st=mkbzd1t6&amp;dl=0 &#039;&#039;&#039;HW 12&#039;&#039;&#039;] (release: 28.11.24; deadline: 08.12.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/kjbipj8jhqprqs5lj5xww/Calculus_2_HW_11_C-231.pdf?rlkey=dxmdq0km7den03onrm8uez388&amp;st=3169knjr&amp;dl=0 &#039;&#039;&#039;HW 11&#039;&#039;&#039;] (release: 18.11.24; deadline: 25.11.24)<br /> <br /> * [https://www.dropbox.com/scl/fi/p4rnmbgr0qqd51c67r4zi/Calculus_2_HW_10_C-231.pdf?rlkey=ev1ttamf12gosbefpje97kqr5&amp;st=fu5fn2yx&amp;dl=0 &#039;&#039;&#039;HW 10&#039;&#039;&#039;] (release: 11.11.24; deadline: 18.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/8by5mima2pusyimge8lnm/Calculus_II_Sem_10.pdf?rlkey=9dv3sj1u8ggp12pb9u8w7nede&amp;st=497p51i8&amp;dl=0 Seminar_10 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=h9zdqm3d&amp;dl=0 &#039;&#039;&#039;HW 9&#039;&#039;&#039;] (release: 03.11.24; deadline: 11.11.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/aqnnddfvbszhdbowyfq6g/Calculus_2_Seminar_9.pdf?rlkey=0yq2mplut6g6d6coh7xzgx8kj&amp;st=xiiei8ji&amp;dl=0 Seminar_9 notes])&lt;/small&gt;<br /> <br /> &#039;&#039;&#039;Module 1&#039;&#039;&#039;<br /> * [No &#039;&#039;&#039;HW 8&#039;&#039;&#039;] &lt;small&gt;([https://www.dropbox.com/scl/fi/c3ip2bmyx2iqrgrxkof02/Calculus_2_Seminar_8.pdf?rlkey=gcpx41p1sx40ose3goyg9xekl&amp;st=mhohccyo&amp;dl=0 Seminar_8 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/bbfsxta8unjy1plrtdo8n/Calculus_2_HW_7_C-231.pdf?rlkey=m43gczr3zi8n168cywz1eir3a&amp;st=dd766qau&amp;dl=0 &#039;&#039;&#039;HW 7&#039;&#039;&#039;] (release: 14.10.24; deadline: 21.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/60sg2dz842xdmwxidug5x/Calculus_2_Seminar_7.pdf?rlkey=mwefwy349bvr864e5rrkdzng1&amp;st=bqpg2eao&amp;dl=0 Seminar_7 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/p1amv17v4v5gped31bt2u/Calculus_2_HW_6_C-231.pdf?rlkey=sggoyiopcvb9s2knowrxn8whp&amp;st=u471ja68&amp;dl=0 &#039;&#039;&#039;HW 6&#039;&#039;&#039;] (release: 07.10.24; deadline: 14.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/jy8to35redpw26j620jc2/Calculus_2_Seminar_6.pdf?rlkey=qt991pcfmfsdedbhs6y1kezps&amp;st=96ma0xx2&amp;dl=0 Seminar_6 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/5sxvgaereyxyyc51vm00p/Calculus_2_HW_5_C-231.pdf?rlkey=hpr46kq2z2pp8xsroeu4vu0s1&amp;st=wvdm90vc&amp;dl=0 &#039;&#039;&#039;HW 5&#039;&#039;&#039;] (release: 30.09.24; deadline: 07.10.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/i3qy7k8ueg7vjahrav3qb/Calculus_2_Seminar_5.pdf?rlkey=6u0gwc1x3y8bet62hmw0f0t9n&amp;dl=0 Seminar_5 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/lxh72z9oyhflgncutbi82/Calculus_2_HW_4_C-231.pdf?rlkey=8k9gye3tpbn5rxzbu6r9s1q6x&amp;st=740c3poi&amp;dl=0 &#039;&#039;&#039;HW 4&#039;&#039;&#039;] (release: 23.09.24; deadline: 30.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/pp35izxfrcub3wqcn05o5/Calculus_2_Seminar_4.pdf?rlkey=6765w81ya4cgwbh3gq9nc4xl5&amp;dl=0 Seminar_4 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/ghgt3fz6z6shez784pfmh/Calculus_2_HW_3_C-231.pdf?rlkey=jxw7g8wazfnfqath79w0meoxh&amp;st=qh8jyynd&amp;dl=0 &#039;&#039;&#039;HW 3&#039;&#039;&#039;] (release: 16.09.24; deadline: 23.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/7e4g0s87d2145vw1dbg13/Calculus_2_Sem_3.pdf?rlkey=2yz5t1op25zocnbrpehgjrmgw&amp;st=tw6sc57o&amp;dl=0 Seminar_3 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/h9n1w21hb3zxjosvpom4t/Calculus_2_HW_2_C-231.pdf?rlkey=b1rfknn2vpf58oq3sjeo2tt05&amp;st=y0j4upd8&amp;dl=0 &#039;&#039;&#039;HW 2&#039;&#039;&#039;] (release: 09.09.24; deadline: 16.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/woo21dyrhvhu45w4ycz95/Calculus_2_Sem_2.pdf?rlkey=8kcvzib7ujh0tcgnqg4d7vstr&amp;dl=0 Seminar_2 notes])&lt;/small&gt;<br /> <br /> * [https://www.dropbox.com/scl/fi/g114bn8m5wuuxfi18a9mk/Calculus_2_HW_1_C-231.pdf?rlkey=kmn3i7vl2noa0vhwc291pmz6n&amp;st=4hb7op4i&amp;dl=0 &#039;&#039;&#039;HW 1&#039;&#039;&#039;] (release: 02.09.24; deadline: 09.09.24) &lt;small&gt;([https://www.dropbox.com/scl/fi/71xhdg4o2d1i4focjlpxg/Calculus_2_Sem_1.pdf?rlkey=yua3julsz1g085k449kjeikxz&amp;st=lfhiiexd&amp;dl=0 Seminar_1 notes])&lt;/small&gt;<br /> <br /> === The homework for group 232: ===<br /> <br /> &#039;&#039;&#039;Module 1&#039;&#039;&#039;<br /> <br /> === The homework for group 233: ===<br /> <br /> &#039;&#039;&#039;Module 1&#039;&#039;&#039;<br /> <br /> === The homework for group 234: ===<br /> <br /> &#039;&#039;&#039;Module 1&#039;&#039;&#039;<br /> <br /> == Exams ==<br /> <br /> == Results ==<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:center&quot;<br /> |-<br /> ! [https://docs.google.com/spreadsheets/d/1L53aAhw5r5BjqP0y6qmDfydK7pRwInCf5VXOb0acBcY/edit?gid=1043223803#gid=1043223803 231] !! [https://docs.google.com/spreadsheets/d/1OKlmuffASFOMHMUWgYeRsEkaN0y1TzCIKN3EHZLCTi4/edit?gid=1043223803#gid=1043223803 232] !! [https://docs.google.com/spreadsheets/d/1tRpgJsDfRDNjz2LHDhdi0KyiY64-7z2he1if2BkqawU/edit?gid=1043223803#gid=1043223803 233] !! [https://docs.google.com/spreadsheets/d/1hJTDQYdK4nsS6kmds8kYzJlxH0jrvOAZtQjQdn8-wBQ/edit?gid=1043223803#gid=1043223803 234] <br /> |}<br /> <br /> == Navigation ==<br /> &lt;div style=&quot;border:1px; border-style:solid; border-color:#a2a9b1; padding:3px&quot;&gt;<br /> &lt;table style=&quot;border-spacing:0; background:transparent; color:inherit; width:100%&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;th scope=&quot;colgroup&quot; style=&quot;background-color:#cfe3ff&quot; colspan=&quot;2&quot;&gt;&lt;div id=&quot;DSBA22&quot; style=&quot;font-size:114%; margin:0 5em&quot;&gt;DSBA 2022/2023&lt;/div&gt;&lt;/th&gt;<br /> &lt;/tr&gt;<br /> &lt;tr &gt;<br /> &lt;th scope=&quot;row&quot; style=&quot;border-top-width:2px; border-top-color:#fdfdfd; border-top-style:solid; width:10%; background-color:#dcebff&quot;&gt;First year&lt;/th&gt;<br /> &lt;td style=&quot;text-align:left; border-left-width:2px; border-left-style:solid; border-color:#fdfdfd; width:90%; padding:0px&quot;&gt;<br /> &lt;div style=&quot;padding:0em 0.25em&quot;&gt;<br /> &lt;ul&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[LAaG_DSBA_2022/2023|Linear Algebra and Geometry]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Discrete_Mathematics_DSBA_2022/2023|Discrete Mathematics]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Calculus_DSBA_2022/2023|Calculus]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[Introduction_to_Programming_DSBA_2022/2023|Introduction to Programming]] &amp;bull; &lt;/li&gt;&lt;li style=&quot;display:inline-block; padding:2px&quot;&gt;[[DSBA_Algebra_2022_2023|Algebra]] &lt;/li&gt;&lt;/ul&gt;<br /> &lt;/div&gt;&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;</div> imported>Mazhuga.A.M.