| 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 | 021803 | ||
| Instructor(s) | |||||
| 村田 実貴生 [MURATA Mikio] | |||||
| Facility affiliation | Faculty of Engineering | Office | Room 213, Building 12, Koganei | 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. |
| Course schedule |
|
1. Real numbers 2. Continuous functions 3. Elementary functions 4. Limit 5. Differentiations of functions 6. The mean-value theorem 7. Exercise 1 8. Midterm examination 9. Higher order derivatives 10. Taylor's theorem 11. Indefinite integrals and definite integrals 12. Calculation of integrals 13. Improper integrals 14. Piecewise quadrature method and application of definite integrals 15. Exercise 2 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 etc.) will be used in the lecture. |
| Required Text(s) and Materials |
| Miyake, Toshitsune (1992) Nyumon Bibunsekibun, Baifukan |
| References |
| Assessment/Grading |
| Midterm examination (40％)，Final examination (40％)，Exercises (20％) |
| Message from instructor(s) |
| Course keywords |
| Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral |
| Office hours |
| 15:00-16:00 on Friday, Room 213, Building 12, Koganei Campus |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/19/2018 11:00:21 AM |