Obě strany předchozí revizePředchozí verzeNásledující verze | Předchozí verze |
mathematics:mathematics_ii [2019/04/24 19:23] – Tomáš Bodnár | mathematics:mathematics_ii [2024/05/10 08:17] (aktuální) – Tomáš Bodnár |
---|
====== Mathematics II ====== | ====== Mathematics II ====== |
| |
| |
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_2019_requirements_a.pdf | Requirements - Level A(Alpha)}} in academic year 2018/2019 | * {{ :mathematics:ma2_2024_requirements.pdf | Requirements}} in academic year 2023/2024 |
* {{ :mathematics:ma2_2019_requirements_b.pdf | Requirements - Level B(Beta)}} in academic year 2018/2019 | |
| |
| |
=== Lecturers === | === Lecturers === |
| |
[[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\\ |
| |
* lectures: Wednesday, 14:15 - 15:45 and Friday 9:00 - 10:30. | * lectures: Monday, 14:15-15:45 and Thursday 10:45 - 12:15. |
| |
[[Hynek.Reznicek@fs.cvut.cz|Mgr. Hynek Řezníček ]], Office: KN:D-205b | [[Hynek.Reznicek@fs.cvut.cz|Mgr. Hynek Řezníček ]], Office: KN:D-205b |
| |
* lectures: Wednesday 16:00-17:30 and Friday 12:30 - 14:00. | * lectures: Monday 16:00-17:30 and Thursday 12:30 - 14:00. |
| |
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. |
| |
| [[https://users.fs.cvut.cz/hynek.reznicek/2024_Ma2.html|Tasks solved in tutorials]] |
| |
| /* |
If you have failed in the 1st test, you should solve the following exercises (from the Examples section): | 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 | * {{::calculus1.pdf|Calculus - part 1}}: 42,46,49,60,66,71,78,82,87,90 |
* {{::triple_integral.pdf|Triple integral}}: 342,348,350,352,353,354,359,365,375,384 | * {{::triple_integral.pdf|Triple integral}}: 342,348,350,352,353,354,359,365,375,384 |
| |
//It is expected that your results will be correct (compare your results with the solution in Czech before submission).// | //It is expected that your results will be correct (compare your results with the solution in Czech before submission).// |
| */ |
| |
=== Exams === | === Exams === |
The exams from Mathematics II (level A and B) will be organized in the same way as in Mathematics I. | The exams from Mathematics II will be organized in the same way as in Mathematics I. |
There are several necessary conditions to be fulfilled by students in order to be admitted to the exam: | There are several necessary conditions to be fulfilled by students in order to be admitted to the exam: |
* Student must have a //valid assessment// from tutorials registered in the electronic system KOS. (students without valid assessment can't subscribe for the exam) | * Student must have a //valid assessment// from tutorials registered in the electronic system KOS. (students without valid assessment can't subscribe for the exam) |
* Student has to //subscribe (register) in the [[https://kos.is.cvut.cz/kos/logout.do|KOS]]// system for the chosen date and level of the exam. (students who will be not subscribed for the exam in the [[https://kos.is.cvut.cz/kos/logout.do|KOS]] system can't participate in the exam) | * Student has to //subscribe (register) in the [[https://www.kos.cvut.cz/|KOS]]// system for the chosen date of the exam. (students who will be not subscribed for the exam in the [[https://www.kos.cvut.cz/|KOS]] system can't participate in the exam) |
* Student should come to the exam //in time//, i.e. he/she should be present in the examination room at least 10 minutes before the official start of the exam. (students who will come late, will be not allowed to participate in the exam) | * Student should come to the exam //in time//, i.e. he/she should be present in the examination room at least 10 minutes before the official start of the exam. (students who will come late, will be not allowed to participate in the exam) |
* Student has to bring his/her //Student Identification Card//. (students will be not allowed to participate in the exam without presenting this card) | * Student has to bring his/her //Student Identification Card//. (students will be not allowed to participate in the exam without presenting this card) |
| |
| |
| __//Dates of exams: Thursday 30.5., 6.6., 20.6., 27.6. and 5.9. 2024.//__ |
| |
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}} | |
| /* |
| * __**NEW: The last exam from Mathematics I in the academic year 2018/2019 will take a place on Monday, June 17, 2019.**__ |
| */ |
| |
| /* |
| The detailed information will be made available at the end of semester in the //Notice of exams// from Mathematics II for the academic year 2023/24. |
| */ |
| |
| |
| //The detailed information is available in the {{ :mathematics:ma2_2024_exams.pdf |Notice of exams}} from Mathematics II for the academic year 2023/24.// |
| |
| |
| |
| 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 |
| |
| /* |
| |
| |
| * {{ :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}} |
| |
| */ |
=== 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}}] |
| |
**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. |
| |
=== Timetable: === | === Timetable: === |
{{ :mathematics:Screenshot_20190225_122327.png?820 |}} | {{ :mathematics:screenshot_20240219_132654.png?820 |}} |
| |
[[:predmet|<-back]] | [[:predmet|<-back]] |