| Course title | |||||
| 微分積分学Ⅱおよび演習 [Calculus Ⅱ] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 3 | |
| Department | Year | 1～4 | Semester | Fall | |
| Course type | Fall | Course code | 021211 | ||
| Instructor(s) | |||||
| 金城 謙作 [KINJO Kensaku] | |||||
| Facility affiliation | Graduate School of Engineering | Office | Email address | ||
| Course description |
| Calculus provides indispensable tools to analyze various mathematical changes appearing in natural and social phenomina. In the course, we will learn about differentiation and integration of multivariable functions, such as partial differentiations, criteria of local maxima and minima, double integrations, volumes of solids, line integrations and series. Various computations will be practiced with drawing diagrams. |
| Expected Learning |
|
The goals of this course are (1) to master basic methods of the differentiation and integration of two variable functions, and (2) to be capable of performing practical computations. |
| Course schedule |
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1. Limits and continuity of functions of two variables 2. Partial differentiations 3. Total differentiations and partial differentiations of composite functions 4. Differentiations in higher order, and Taylor’s theorem(1) 5. Taylor's theorem(2) 6. Local maxima and minima of functions of two variables 7. Double integrations(1) 8. Double integrations(2) 9. Improper integrations 10. Triple integrations, and changes of variables by using the system of polar coordinates 11. Volumes of solids and areas of surfaces 12. Line integrations and Green's theorem 13. Series and power series 1 14. Series and power series 2 15. Final examination A common examination will be conducted extra at the last of the term in the adjustment period for all the classes of this course. |
| Prerequisites |
| Knowledge of the course of Calculus I and Exercise will be used in the lecture. |
| Required Text(s) and Materials |
| TAKAHASHI Yasuji, KATO Mikio, KOSHI Syouzou, “Bibun Sekibun Gairon”, Science-sya, ISBN 978-4781913292, (in Japanese) |
| References |
| MIYAKE Toshitsune, “Nyuumon Bibun Sekibun”, Baifu-kan, ISBN 978-4-563-00221-3, (in Japanese) |
| Assessment/Grading |
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Results of the common and the final examinations will be used for evaluation. (The ratio of the common and the final examinations is the larger of 5:5 and 6:4) |
| Message from instructor(s) |
| You can ask me anything whenever you want. Enjoy mathematics and celebrate the joy of youth. |
| Course keywords |
| Multivariable functions, Partial differentiations, Local maxima and minima of functions of two variables, Multiple integrations, Volumes of solids and areas of surfaces, Series |
| Office hours |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Language Subject |
| Last update |
| 9/28/2018 3:04:44 PM |