Course title
微分積分学Ⅰおよび演習   [Calculus Ⅰ]
Course category technology speciality courses  Requirement   Credit 3 
Department Department of Applied Chemistry, Applied Chemistry(~2018), Organic and Polymer Materials Chemistry(~2018)  Year 14  Semester 1st 
Course type 1st  Course code 021911
Instructor(s)
畠中 英里   [HATAKENAKA Eri]
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 function,
(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.

Corresponding criteria in the Diploma Policy: See the Curriculum maps
Course schedule
1. Continuity of real numbers and series
2. Limits of functions
3. Continuity of functions, and inverse functions
4. Differentiations of functions with one variable
5. The mean-value theorem and l'Hopital's rule
6. Parametric descriptions of curves, and differentiations in high order
7. Review, midterm examination
8. Taylor's theorem
9. Definite integrations, and indefinite integrations
10. Exercises on integrations I
11. Exercises on integrations II
12. Improper integrations
13. Applications of definite integrations I
14. Applications of definite integrations II
15. Review, term examination

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 will be used in the lecture.
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
References
Miyake Toshitsune, "Nyuumon-Bibun-Sekibun", Baifu-kan (in Japanese)
Assessment/Grading
Results of the midterm examination, the term examination, and the common examination at the last of the term will be used for evaluation. Some effort in the hour of exercise will be evaluated additively.
Message from instructor(s)
You should try to find your own suitable textbooks, and practice various problems in your private study hours.
Course keywords
Limit, Differentiation, Inverse function, Taylor's theorem, Indefinite integration, Definite integration, Area, Length
Office hours
Thusday 10:00-12:00
Remarks 1
Remarks 2
Related URL
http://www.tuat.ac.jp/~hataken/top.html
Lecture Language
Japanese
Language Subject
Last update
3/7/2019 10:39:29 AM