| Course title | |||||
| 微分積分学Ⅰおよび演習 [Calculus Ⅰ] | |||||
| Course category | technology speciality courses | Requirement | Credit | 3 | |
| Department | Year | 1～4 | Semester | 1st | |
| Course type | 1st | Course code | 021910 | ||
| Instructor(s) | |||||
| 中園 信孝 [NAKAZONO Nobutaka] | |||||
| 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 the differentiations and the integrations of various functions of one variable and their properties. We will practice advanced computations in this course rather than in high schools. |
| Expected Learning |
|
The goals of this course are (1) to master basic methods of the differentiations and the integrations of various functions, such as polynomials, rational and irrational functions, trigonometric functions, exponential functions and logarithmic functions, (2) to understand how to calculate extreme maximal and minimum values of functions, and (3) to be capable of performing practical computations on determining areas of figures and lengths of curves. 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. Review, and 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. Review, and 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 |
|
Mathematics in high schools (in particular, Mathematics I, II, III). 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 |
| Textbooks will be introduced in the first lecture, if necessary. |
| References |
| Assessment/Grading |
| Message from instructor(s) |
| Course keywords |
| Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral |
| Office hours |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 1/11/2022 2:43:18 PM |