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
12/24/2019 2:59:51 PM