Course title
微分積分学Ⅰ   [CalculusⅠ]
Course category   Requirement   Credit 2 
Department   Year 1  Semester 3rd 
Course type 3rd  Course code 01ma1002b
Instructor(s)
金城 謙作   [KINJO Kensaku]
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.
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. Review, and Exercise
8. Local maxima and minima, and limits of indeterminate forms
9. Indefinite integrals
10. 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. Review, and Exercise
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
「入門微分積分」三宅 敏恒 著, 培風館(ISBN 978-4-563-00221-3)
References
It will be introduced appropriately during the lecture.
Assessment/Grading
It will be announced in the first lecture.
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 6:51:17 PM