| 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 | 021930 | ||
| Instructor(s) | |||||
| 直井 克之 [NAOI Katsuyuki] | |||||
| Facility affiliation | Faculty of Engineering | Office | 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. Functions of several variables 2. Ttotal differentiations and differenciations of composite functions 3. Higher order partial differentiations, and Taylor's theorem 4. Local maxima and minima of functions of two variables 5. Implicit functions 6. Constrained extremal problem 6. Exercises midterm examination 7. Double integrations 8. Improper integrations 8. Changes of variables 9. Applications of double integrations 12. Line integrations and Green's theorem 13. Series and power series 1 14. Series and power series 2 15. Exercises term 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 |
| 入門微分積分（三宅敏恒）培風館 |
| References |
| Assessment/Grading |
| midterm examination（40%）, term examination（40%）, common examination（20%） |
| 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 |
| after the class |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/11/2019 11:28:01 AM |