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 01MA0502b
Instructor(s)
大川 領   []
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 understand basic concepts of calculus, and
(2) 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.
Course schedule
1. Limits
2. Continuous functions and elementary functions
3. Differentiations of functions
4. Formulae of differentiations
5. The mean value theorem
6. Limits involving indeterminate forms
7. High derivatives
8. Taylor's theorem, and its applications 1
9. Taylor's theorem, and its applications 2
10. Definite integrals and indefinite integrals
11. Integrations of rational functions
12. Integrations of irrational functions
13. Improper integrals
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
Miyake Toshitsune, “Nyuumon-Bibun-Sekibun”, Baifu-kan (in Jananese)
References
Assessment/Grading
Term examination (100%)
Message from instructor(s)
Course keywords
Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral
Office hours
ohkawa.ryo@(*)aoni.waseda.jp
Remarks 1
Remarks 2
Related URL
Lecture Language
Japanese
Language Subject
Last update
10/12/2018 9:01:11 AM