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mathematics:mathematics_ii [2018/05/09 09:36] – Tomáš Bodnár | mathematics:mathematics_ii [2022/04/26 10:50] – Tomáš Bodnár |
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====== Mathematics II ====== | ====== Mathematics II ====== |
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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_2022_requirements_a.pdf | Requirements - Level A(Alpha)}} in academic year 2021/2022 |
* {{ :mathematics:ma2_2018_requirements_b.pdf | Requirements - Level B(Beta)}} in academic year 2017/2018 | * {{ :mathematics:ma2_2022_requirements_b.pdf | Requirements - Level B(Beta)}} in academic year 2021/2022 |
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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, 14:15-15:45 and Thursday 10:45 - 12:15. |
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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 9:00-10:30 and Friday 10:45 - 12:15. |
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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 == | [[https://marian.fsik.cvut.cz/~reznicek/2022_Ma2.html|Tasks solved in tutorials]] |
* Homework (instead of 2nd test) - examples from the //Collection of examples from Mathematics II// listed below | |
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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 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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{{::triple_integral.pdf|Triple integral}}: 345, 346, 351, 353, 354, 355, 358, 359, 370, 371 | 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 |
* Last test from double and tripple integral {{ :mathematics:2018_pis_ma2_2.pdf | Test}} | * {{::triple_integral.pdf|Triple integral}}: 342,348,350,352,353,354,359,365,375,384 |
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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 26.5., 2.6., 9.6., 16.6., 23.6., and 8.9. 2022.//__ |
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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 2021/22. |
| */ |
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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_2022_exams.pdf |Notice of exams}} from Mathematics II for the academic year 2021/22.// |
// | |
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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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| /* |
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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}} |
| * {{ :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}} |
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| */ |
=== 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_2022.png?820 |}} |
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[[:predmet|<-back]] | [[:predmet|<-back]] |