| 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 | 021914 | ||
| Instructor(s) | |||||
| 直井 克之 [NAOI Katsuyuki] | |||||
| Facility affiliation | Faculty of Engineering | Office | afjgxte/L1151 | Email address | |
| Course description |
|
We study differential and integral calculus of one variable function and its application. Differential and integral calculus is the foundation of the natural science and it contains very ample contents. We study further high level differential and integral calculus in the base of the contents studied in the high school. |
| 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. Continuity of real numbers and limits of functions 2. Continuity and differentiability 3. Formulae of differentiations, inverse functions and their differentiations 4. Differentiations of inverse trigonometric functions, high derivatives, and Leibniz’s theorem 5. Rolle's theorem and the mean-value theorem 6. Taylor's theorem, and its applications 7. Local maxima and minima, and limits of indeterminate forms 8. Indefinite integrals 9. Integrations of rational functions, possibly containing trigonometric functions 10. Definite integrals, and their properties 11. Improper integrals 12. Areas of figures and lengths of curves 13. Exercises of various problems on integrals |
| 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 |
| Miyake Toshitsune, “Nyuumon-Bibun-Sekibun”, Baifu-kan (in Jananese) |
| References |
| Assessment/Grading |
|
Normal score 50%, exercise 50%. If face-to-face class is restarted, we will hold an term examination. In this case, the evaluation will be as follows: Normal score 25%, exercise 25%, term examination 50% |
| Message from instructor(s) |
| Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral |
| Course keywords |
| Office hours |
| after the class |
| Remarks 1 |
|
past grade distribution 2018: S 11.6% A 20.3% B 37.7% C 23.2% D 7.2% 2017: S 26.6% A 28.1% B 25.0% C 17.2% D 3.1% |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 4/30/2020 1:47:11 PM |