Course title
微分積分学Ⅱ   [CalculusⅡ]
Course category		Requirement		Credit	2
Department		Year	2～	Semester	1st
Course type	1st	Course code	01ma2004b
Instructor(s)
堀口 直之   [HORIGUCHI Naoyuki]
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 about differentiation and integration of multivariable functions, such as partial differentiations, criteria of local maxima and minima, double integrations, volumes of solids and areas of surfaces.

Expected Learning

・To be able to understand and calculate limit, partial differential, total differentiation and double integrals of a two-variable function. ・To be able to calculate extreme values of a two-variable function. ・To be able to calculate volumes of solids and areas of surfaces. Corresponding criteria in the Diploma Policy: See the Curriculum maps

Course schedule

1. Limit and continuity of a two-variable function 2. Partial and total derivatives 3. Partial derivatives of a composite function and tangent planes 4. Higher derivations and Taylor's Theorem of a two-variable function 5. Extreme values of a two-variable function 6. Implicit function theorem 7. An extreme value problem with conditions 8. Review, and midterm exam 9. Double integrals 10. Iterated integral 11. Change of variables 12. Improper integral of a two-variable function 13. Calculus of volumes and curved area 14. Gamma function and beta function 15. Review, and final exam

Prerequisites

Knowledge of the course of Calculus I will be used in the lecture. In addition to 30 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

References

Assessment/Grading

Midterm exam(50%), final exam(50%)

Message from instructor(s)

Course keywords

Multivariable functions, Partial differentiations, Local maxima and minima of functions of two variables, Multiple integrations, Volumes of solids and areas of surfaces, Beta function and gamma function

Office hours

It will be announced in the first lecture.

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

1/24/2021 6:48:42 PM