| 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 | 021505 | ||
| 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 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 functions, (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, continuous functions, inverse functions 3. Differentiation and tangential line, formulae of differentiation 4. Differentiation of inverse trigonometric functions, Rolle's theorem and the mean-value theorem 5. Differentiation in high order, Leibniz's theorem, Taylor's theorem 6. l'Hopital's rule 7. Values at maxima and minima, parametric descriptions of curves 8. Midterm examination 9. Indefinite integrals 10. Integrations of rational functions, possibly containing trigonometric functions 11. Definite integrals 12. Fundamental theorem of calculus 13. Improper integrals 14. Areas of figures and lengths of curves 15. Term examination |
| Prerequisites |
| Mathematics in high schools will be used in the lecture. |
| Required Text(s) and Materials |
|
Author: Toshitsune Miyake Title: Introduction of calculus Publisher; Baihu-kan |
| References |
| Assessment/Grading |
| Results of the midterm examination, the term examination and exercises will be used for evaluation. |
| Message from instructor(s) |
| Course keywords |
| Differentiation of inverse functions, values of maxima and minima, l'Hopital's rule, Taylor's theorem, Improper integrals, Area, Length of curves |
| Office hours |
| Hours after the lecture |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/1/2018 4:15:59 PM |