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mathematics:mathematics_ii [2018/05/09 09:36] – Tomáš Bodnár | mathematics:mathematics_ii [2021/04/12 07:56] – Tomáš Bodnár |
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====== Mathematics II ====== | ====== Mathematics II ====== |
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| __**Due to coronavirus quarantine measures, the courses of Mathematics II will be held temporarily at distance, using electronic communication only.**__ |
| === Virus teaching regime: === |
| * The primary communication channel is the email. We will contact you via your official email you have in KOS system. You may also use our email to contact us with anything related to our courses (asking questions, requesting extra study material, sending your completed homeworks). |
| * All the essential information and course materials will be published at this webpage. You will be notified of changes. |
| * A new, emergency communication channel for each course (subject) is set up at the university using [[https://teams.microsoft.com/l/team/19%3a714b09bc0d6a464e9af37957d533b42d%40thread.tacv2/conversations?groupId=8c0f32b9-198a-4c06-9f27-18be24870b1b&tenantId=f345c406-5268-43b0-b19f-5862fa6833f8 | Microsoft Teams]] platform. It can be used for //online chat-like communication with teachers during the usual course hours// according to standard schedule of the subject. |
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| /* |
| The [[https://teams.microsoft.com/l/team/19%3a714b09bc0d6a464e9af37957d533b42d%40thread.tacv2/conversations?groupId=8c0f32b9-198a-4c06-9f27-18be24870b1b&tenantId=f345c406-5268-43b0-b19f-5862fa6833f8 | Microsoft Team]] was created, for online consultations. |
| */ |
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| /* |
| Textbook material for implicit functions, Riemann, double, triple, line and surface integral, together with potential fields chapter was added to the webpage. |
| */ |
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| General study advices and rules for the emergency online study regime can be found in |
| {{ :mathematics:ma2en_study_advices.pdf | Study advices}} |
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| === Essential weekly information for regular study === |
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| * //Week:// February 22 - February 28, 2021 - //Topic:// Functions of multiple variables {{ :mathematics:ma2en_multiple_variables.pdf | Functions of multiple variables}} |
| * //Week:// March 1 - March 7, 2021 - //Topic:// Partial derivatives, differentials {{ :mathematics:ma2en_partial_derivatives.pdf | Partial derivatives, differentials}} |
| * //Week:// March 8 - March 14, 2021 - //Topic:// Implicit functions {{ :mathematics:ma2en_implicit_functions.pdf | Implicit functions}} |
| * //Week:// March 15 - March 21, 2021 - //Topic:// Extrema {{ :mathematics:ma2en_extrema.pdf | Extrema}} |
| * //Week:// March 22 - March 28, 2021 - //Topic:// Double integral {{ :mathematics:ma2en_double_integral.pdf | Double integral}} |
| * //Week:// April 12 - April 18, 2021 - //Topic:// Triple integral {{ :mathematics:ma2en_triple_integral.pdf | Triple integral}} |
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| === Assessment requirements: === |
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| **The delivery of all sample exams (completely and correctly solved) is necessary condition for obtaining the assessment from tutorials.** Sample exam tests: {{ :mathematics:ma2_exam_1n_en.pdf |Exam 1}}, {{ :mathematics:ma2_exam_2n_en.pdf |Exam 2}}, {{ :mathematics:ma2_exam_3n_en.pdf |Exam 3}}. |
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| **DEADLINE: March 31, 2021 - For the first part of the homework |
| (exercises 1,2 from the Exam 1, Exam 2 and Exam 3).** |
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| The homeworks solutions will be delivered in three parts (by chapters). The deadlines will be set during the semester by the tutorials teacher. __Students who will fail in any of the three parts of the homework will not obtain the assessment from tutorials (and can't participate in the exam).__ |
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| __Any homeworks that will either be incorrect, evidently just copied from someone else, or submitted after the deadline might be rejected. Please be careful, pay attention to your homework and deliver it in time, correctly solved and written.__ |
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| For additional explanation, clarification and extra material contact the Lecture/Tutorial teacher by email or the [[https://teams.microsoft.com/l/team/19%3a9faa9277f4524373806b921e2a43651e%40thread.tacv2/conversations?groupId=49fbdc73-45c5-44a4-9bac-4f27c645b22f&tenantId=f345c406-5268-43b0-b19f-5862fa6833f8 | Microsoft Teams]] platform for online consultation. You can post your questions and request anytime. The teachers will respond as quickly as possible. For //online live chat use the standard course hours// according to usual schedule. Ask for other extra consultations if needed. We will do our best to help you. |
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| ---- |
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This course is intended for foreign students studying at our faculty and domestic students who registered for this subject in their study plan. | This course is intended for foreign students studying at our faculty and domestic students who registered for this subject in their study plan. |
Conditions and requirements for this course are almost identical to the equivalent course being held in Czech language. | Conditions and requirements for this course are almost identical to the equivalent course being held in Czech language. |
Multiple integrals - double and triple integral, Fubini's theorem, applications | Multiple integrals - double and triple integral, Fubini's theorem, applications |
Line integral, surface integral, Gauss theorem, potential. | Line integral, surface integral, Gauss theorem, potential. |
* {{ :mathematics:ma2_2018_requirements_a.pdf | Requirements - Level A(Alpha)}} in academic year 2017/2018 | * {{ :mathematics:ma2_2021_requirements_a.pdf | Requirements - Level A(Alpha)}} in academic year 2020/2021 |
* {{ :mathematics:ma2_2018_requirements_b.pdf | Requirements - Level B(Beta)}} in academic year 2017/2018 | * {{ :mathematics:ma2_2021_requirements_b.pdf | Requirements - Level B(Beta)}} in academic year 2020/2021 |
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=== Lecturers === | === Lecturers === |
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[[Tomas.Bodnar@fs.cvut.cz|Mgr. Ing. Tomáš Bodnár, Ph.D.]], Office: KN:D-303\\ | [[Tomas.Bodnar@fs.cvut.cz|doc. Mgr. Ing. Tomáš Bodnár, Ph.D.]], Office: KN:D-303\\ |
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* lectures: Monday, 14:15 - 15:45 and Thursday 9:00 - 10:30. | * lectures: Monday, 10:45 - 12:15 and Friday 12:30 - 14:00. |
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[[Hynek.Reznicek@fs.cvut.cz|Mgr. Hynek Řezníček ]], Office: KN:D-205b | [[Hynek.Reznicek@fs.cvut.cz|Mgr. Hynek Řezníček ]], Office: KN:D-205b |
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* lectures: Tuesday 16:00-17:30 and Friday 9:00 - 10:30. | * lectures: Wednesday 16:00-17:30 and Friday 16:00 - 17:30. |
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In the case of any problem (especially with assessments from tutorials, or with exams) contact your teacher. | In the case of any problem (especially with assessments from tutorials, or with exams) contact your teacher. |
//Tutorials are obligatory.// Assessment from tutorials (written in the study record) confirms //student's presence and activity// at the tutorials and elaboration of homework and tests. Assessment is a necessary condition for the exam. (I.e. student can make the exam only with the assessment written in the study record.) The //assessments from tutorials obtained in previous years are not accepted//. Student has to obtain the assessment again. The assessments are written in the last semestral week, not later than one week after. Exceptions are possible only with the explicit agreement of the chair of the institute. | //Tutorials are obligatory.// Assessment from tutorials (written in the study record) confirms //student's presence and activity// at the tutorials and elaboration of homework and tests. Assessment is a necessary condition for the exam. (I.e. student can make the exam only with the assessment written in the study record.) The //assessments from tutorials obtained in previous years are not accepted//. Student has to obtain the assessment again. The assessments are written in the last semestral week, not later than one week after. Exceptions are possible only with the explicit agreement of the chair of the institute. |
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== Information for tutorials == | /* |
* Homework (instead of 2nd test) - examples from the //Collection of examples from Mathematics II// listed below | If you have failed in the 1st test, you should solve the following exercises (from the Examples section): |
| * {{::calculus1.pdf|Calculus - part 1}}: 42,46,49,60,66,71,78,82,87,90 |
| * {{::calculus2.pdf|Calculus - part 2}}: 92,96,102,103,108,131,132,136,151,159 |
| * {{::implicit_function.pdf|Implicit Functions}}: 163,166,167,168,180 |
| * {{::extrems.pdf|Extrema}}: 197,199,216,218,229 |
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{{::double_integral.pdf|Double integral}}: 241, 254, 256, 257, 262, 275, 282, 292, 303, 307 | If you have failed in the 2nd test, you should solve the following exercises (from the Examples section): |
| * {{::double_integral.pdf|Double integral}}: 242,245,246,247,248,249,250,252,254,257,262,270,279,292,310 |
{{::triple_integral.pdf|Triple integral}}: 345, 346, 351, 353, 354, 355, 358, 359, 370, 371 | * {{::triple_integral.pdf|Triple integral}}: 342,348,350,352,353,354,359,365,375,384 |
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* Last test from double and tripple integral {{ :mathematics:2018_pis_ma2_2.pdf | Test}} | |
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| //It is expected that your results will be correct (compare your results with the solution in Czech before submission).// |
| */ |
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=== Exams === | === Exams === |
These conditions will be followed strictly, without any exceptions. | These conditions will be followed strictly, without any exceptions. |
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| /* __//Dates of exams: Thursday 30.5., 6.6., 13.6., 20.6., 27.6., and 12. 9. 2019.//__ */ |
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| /* |
| * __**NEW: The last exam from Mathematics I in the academic year 2018/2019 will take a place on Monday, June 17, 2019.**__ |
| */ |
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__**Dates of exams: Thursday 31.5., 7.6., 14.6., 21.6., 28.6. and 13.9. 2018**__ | The detailed information will be made available at the end of semester in the //Notice of exams// from Mathematics II for the academic year 2019/20. |
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//The detailed information is available in the {{ :mathematics:ma2_2018_exams.pdf |**Notice of exams**}} from Mathematics II in the academic year 2017/18. | /* //The detailed information is available in the {{ :mathematics:ma2_2019_exams.pdf |Notice of exams}} from Mathematics II for the academic year 2018/19.// */ |
// | |
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Sample exam tests: {{ :mathematics:ma2_exam_1_en.pdf |Exam 1}}, {{ :mathematics:ma2_exam_2_en.pdf |Exam 2}}, {{ :mathematics:ma2_exam_3_en.pdf |Exam 3}} | |
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| Sample exam tests: {{ :mathematics:ma2_exam_1n_en.pdf |Exam 1}}, {{ :mathematics:ma2_exam_2n_en.pdf |Exam 2}}, {{ :mathematics:ma2_exam_3n_en.pdf |Exam 3}} |
=== Literature: === | === Literature: === |
* Neustupa, J., Kračmar S.: Mathematics II, CTU Publishing House, Prague, 1996, | * Neustupa, J., Kračmar S.: Mathematics II, CTU Publishing House, Prague, 1996, |
* Finney, R. L., Thomas, G.B.: Calculus, Addison-Wesley, New York, Ontario, Sydney, 1994 | * Finney, R. L., Thomas, G.B.: Calculus, Addison-Wesley, New York, Ontario, Sydney, 1994 |
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| * {{ :mathematics:pages_01-23.pdf |Functions of multiple variables pages_01-23}} |
| * {{ :mathematics:pages_24-33.pdf |Implicit functions pages_24-33}} |
| * {{ :mathematics:pages_34-47.pdf |Riemann integral pages_34-47}} |
| * {{ :mathematics:pages_48-57.pdf |Double integral pages_48-56}} |
| * {{ :mathematics:pages_56-69.pdf |Triple integral pages_56-69}} |
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| /* |
| * {{ :mathematics:pages_70-83.pdf |Line integral pages_70-83}} |
| * {{ :mathematics:pages_84-103.pdf |Surface integral pages_84-103}} |
| * {{ :mathematics:pages_104-118.pdf |Potential and solenoidal fields pages_104-118}} |
| */ |
=== Examples: === | === Examples: === |
The //Collection of examples from Mathematics II// written in Czech by authors E. Brožíková, M. Kittlerová and F. Mráz (2016) contains both examples and their solutions. Here you find several parts translated in English. The examples in English have the same numbering but they are without solutions (corresponding solution you can find in the Czech version, which is in the brackets). English translations will be added gradually. By the star (*) are denoted the examples, which go beyond the requirements of the exam this year. | The //Collection of examples from Mathematics II// written in Czech by authors E. Brožíková, M. Kittlerová and F. Mráz (2016) contains both examples and their solutions. Here you find several parts translated in English. The examples in English have the same numbering but they are without solutions (corresponding solution you can find in the Czech version, which is in the brackets). English translations will be added gradually. By the star (*) are denoted the examples, which go beyond the requirements of the exam this year. |
* {{::triple_integral.pdf|Triple integral}} [{{::trojny_integral.pdf|Trojný integrál}}] | * {{::triple_integral.pdf|Triple integral}} [{{::trojny_integral.pdf|Trojný integrál}}] |
* {{::line_integral_1.pdf|Line integral}} [{{::krivkovy_integral_komplet.pdf|Křivkový integrál}}] | * {{::line_integral_1.pdf|Line integral}} [{{::krivkovy_integral_komplet.pdf|Křivkový integrál}}] |
* {{::surface_integral.pdf|Surface integral}} [{{::plosny_integral_skalarni_funkce.pdf|Plošný integrál}}] | * {{::surface_integral.pdf|Surface integral}} [{{::19plosny-skalar.pdf|Skalární}}] [{{::plosny_integral_vektor_pole.pdf|Vektorový}}] |
* Divergence theorem [{{::veta_gauss_ostrogradsky.pdf|Gaussova-Ostrogradského věta}}] | * Divergence theorem [{{::veta_gauss_ostrogradsky.pdf|Gaussova-Ostrogradského věta}}] |
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**Web additional sources:** | **Web additional sources:** |
* Keisler, H. J.: [[http://www.math.wisc.edu/~keisler/calc.html|Elementary Calculus]]: An Infinitesimal Approach, 2nd edition, Prindle, Weber & Schmidt, 1986. | * **Keisler, H. J.: [[http://www.math.wisc.edu/~keisler/calc.html|Elementary Calculus]]: An Infinitesimal Approach, 2nd edition, Prindle, Weber & Schmidt, 1986.** |
* Calculus [[https://cnx.org/contents/i4nRcikn@2.88:BUxRn5Hd@16/Preface|Volume I.]], [[https://cnx.org/contents/HTmjSAcf@2.48:lgVeK9DB@12/Preface|Volume II.]], [[https://cnx.org/contents/oxzXkyFi@2.102:Zh8bDwa-@15/Preface|Volume III.]], provided by [[https://cnx.org/|https://cnx.org/]]. | * **Calculus [[https://cnx.org/contents/i4nRcikn@7.1:H2TLb2-S@4/Introduction|Volume I.]], [[https://cnx.org/contents/HTmjSAcf@6.1:rrzms6rP@6/Introduction|Volume II.]], [[https://cnx.org/contents/oxzXkyFi@6.1:72YaCFgv@5/Introduction|Volume III.]], provided by [[https://cnx.org/|https://cnx.org/]].** |
* [[http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx|Paul's Online Math Notes]] have gotten the notes/tutorials for Algebra, Calculus I, Calculus II, Calculus III and Differential Equations class online. | * [[http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx|Paul's Online Math Notes]] have gotten the notes/tutorials for Algebra, Calculus I, Calculus II, Calculus III and Differential Equations class online. |
* [[http://patrickjmt.com|Just Math Tutoring]] is a web site of Patrick from Vanderbilt University, who provide clear and thorough explanations, and to present them in an environment in which the student is comfortable. | * [[http://patrickjmt.com|Just Math Tutoring]] is a web site of Patrick from Vanderbilt University, who provide clear and thorough explanations, and to present them in an environment in which the student is comfortable. |
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=== Timetable: === | === Timetable: === |
{{ :mathematics:screenshot_20180227_161813.png?820 |}} | {{ :mathematics:schedule_ma2_2021.png?820 |}} |
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[[:predmet|<-back]] | [[:predmet|<-back]] |