Course title
微分積分学Ⅰ   [CalculusⅠ]
Course category	general education courses	Requirement		Credit	2
Department		Year	1～	Semester	Fall
Course type	Fall	Course code	01MA0502a
Instructor(s)
公文 雅之   [KUMON Masayuki]
Facility affiliation	Graduate School of Agriculture	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 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. 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. Exercises, or midterm examination 8. Local maxima and minima, and limits of indeterminate forms 9. Midterm examination 10. Indefinite integrals Integrations of rational functions, possibly containing trigonometric functions 11. Definite integrals, and their properties 12. Improper integrals 13. Areas of figures and lengths of curves 14. Exercises of various problems on integrals 15. Term examination

Prerequisites

Mathematics in high schools (in particular, Mathematics I, II, III etc.) will be used in the lecture.

Required Text(s) and Materials

Mogi Isamu, Yokote Ichiro, ‘’Kiso-Bibun-Sekibun’’, Shoka-bo (in Japanese) Miyake Toshitsune, “Nyuumon-Bibun-Sekibun”, Baifu-kan (in Jananese)

References

Assessment/Grading

Homework reports (20%), midterm examination (35%), term examination (45%)

Message from instructor(s)

Course keywords

Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral

Office hours

Any questions are received by the open E-mail address：masayuki_kumon@smile.odn.ne.jp

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

9/14/2017 4:21:54 PM