| Course title | |||||
| 微分積分学Ⅰ [CalculusⅠ] | |||||
| Course category | Requirement | Credit | 2 | ||
| Department | Year | 1～ | Semester | 3rd | |
| Course type | 3rd | Course code | 01ma1002a | ||
| Instructor(s) | |||||
| 奥村 喜晶 [] | |||||
| Facility affiliation | Graduate School of Agriculture | Office | afjgxte/L1151 | 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. Takayuki Okuda (a part-time lecturer) will be in charge of this course. |
| 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. (URL: https://www.tuat.ac.jp/campuslife_career/campuslife/policy/ ) |
| Course schedule |
|
1. Continuity of real numbers, and limits of sequences 2. Limits and continuity of functions 3. Differentiability of functions, and differential calculus 4. High derivatives, and local maxima and minima 5. Rolle’s theorem and the mean-value theorem 6. l’Hospital’s rule 7. Taylor’s theorem, and its applications 8. Review 9. Definite integrals 10. Fundamental theorem of calculus 11. Integral calculus 12. Integrations of rational functions, possibly containing trigonometric functions and irrational expressions 13. Improper integrals 14. Plane curve 15. Review * This schedule may be changed to be suit interest and understanding of students |
| Prerequisites |
|
Mathematics in high schools (in particular, Mathematics Ⅰ, Ⅱ, Ⅲ etc.) will be used in the lecture. In addition to 30 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 |
| 数研講座シリーズ 大学教養 微分積分 加藤文元 数研出版 |
| Assessment/Grading |
|
It will be announced in Google Classroom. |
| Message from instructor(s) |
| Course keywords |
| Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral |
| Office hours |
| It will be announced in the first lecture. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 9/4/2020 4:58:06 PM |