| Course title | |||||
| 微分積分学Ⅰおよび演習 [Calculus Ⅰ] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 3 | |
| Department | Year | 1～4 | Semester | Spring | |
| Course type | Spring | Course code | 021403 | ||
| Instructor(s) | |||||
| 合田 洋 [GODA Hiroshi] | |||||
| Facility affiliation | Faculty of Engineering | Office | 12-211 | 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 with one variable, and their properties. We will practice advanced computations in this course rather than in high schools. |
| Expected Learning |
|
The goal of this course is (1) to master basic methods of the differentiations and the integrations of various functions, such as polynomials, rational and irrational functions, trigonometric functions, exponential and logarithmic function, (2) to understand how to calculate the values at maxima and minima of functions, and (3) to be capable of performing practical computations on determining areas of figures and lengths of curves. |
| Course schedule |
|
1. Continuity of real numbers and series 2. Limits of functions 3. Continuity of functions, and inverse functions 4. Differentiations of functions with one variable 5. The mean-value theorem and l'Hopital's rule 6. Parametric descriptions of curves, and differentiations in high order 7. Midterm examination 8. Taylor's theorem 9. Definite integrations, and indefinite integrations 10. Exercises on integrations I 11. Exercises on integrations II 12. Improper integrations 13. Applications of definite integrations I 14. Applications of definite integrations II 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 will be used in the lecture. |
| Required Text(s) and Materials |
| References |
| Miyake Toshitsune, "Nyuumon-Bibun-Sekibun", Baifu-kan (in Japanese) |
| Assessment/Grading |
| Results of the midterm examination and the common examination at the last of the term will be used for evaluation. |
| Message from instructor(s) |
| You should try to find your own suitable textbooks, and practice various problems in your private study hours. |
| Course keywords |
| Limit, Differentiation, Inverse function, Taylor's theorem, Indefinite integration, Definite integration, Area, Length |
| Office hours |
| Thusday 10:00-12:00 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| http://www.tuat.ac.jp/~hataken/top.html |
| Lecture Language |
| Language Subject |
| Last update |
| 3/4/2017 8:00:45 AM |