| Course title | |||||
| 微分積分学Ⅱおよび演習 [Calculus Ⅱ] | |||||
| Course category | technology speciality courses | Requirement | Credit | 3 | |
| Department | Department of Mechanical Systems Engineering, Mechanical Systems Engineering(~2018) | Year | 1～4 | Semester | 3rd |
| Course type | 3rd | Course code | 021929 | ||
| Instructor(s) | |||||
| 前田 博信 [MAEDA Hironobu] | |||||
| Facility affiliation | Faculty of Engineering | Office | 12-212 | Email address | |
| Course description |
| Calculus provides indispensable tools to analyze various mathematical changes appearing in natural and social phenomena. In this course, we will learn about differentiation and integration of multivariable functions, such as partial differentiations, criteria of local maxima and minima, double and triple 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, or multivariable functions, and (2) to be capable of performing practical computations. Corresponding criteria in the Diploma Policy: See the Curriculum maps |
| Course schedule |
|
1. Limits and continuity of functions of two variables 2. Partial differentiations and total differentiations 3. Higher order partial differentiations, and partial differentiations of composite functions 4. Taylor’s theorem for functions of two variables 5. Local maxima and minima of functions of two variables 6. Exercises, or midterm examination 7. Double integrations 8. Changes of variables 9. Triple integrations, and changes of variables by using the system of polar coordinates 10. Improper integrations 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. Exercise and 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. In addition to 60 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below |
| Required Text(s) and Materials |
| will be introduced at the first lecture. |
| References |
| R. Dedekind, Was sind und was sollen die Zahlen.（Japanese Trans. Iwanami） |
| Assessment/Grading |
| Evaluation will be done according to the Klausuren(Midterm examination 50%. Final examination 50%) |
| Message from instructor(s) |
| 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 |
| Tuesday, between 930 and 1130, Room 210 in Bld.12 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/16/2019 8:58:57 AM |