Course title
微分積分学Ⅱおよび演習   [Calculus Ⅱ]
Course category technology speciality courses  Requirement   Credit 3 
Department Department of Mechanical Systems Engineering, Mechanical Systems Engineering(~2018)  Year 14  Semester 3rd 
Course type 3rd  Course code 021929
Instructor(s)
前田 博信   [MAEDA Hironobu]
Facility affiliation Faculty of Engineering Office 12-212  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 and triple integrations, volumes of solids, line integrations and series. Various computations will be practiced with drawing diagrams
Expected Learning
The goals of this course are
(1) to master basic methods of the differentiation and integration of two, or multivariable functions, and
(2) to be capable of performing practical computations.
Corresponding criteria in the Diploma Policy: See the Curriculum maps
Course schedule
1. Limits and continuity of functions of two variables
2. Partial differentiations and total differentiations
3. Higher order partial differentiations, and partial differentiations of composite functions
4. Taylor’s theorem for functions of two variables
5. Local maxima and minima of functions of two variables
6. Exercises, or midterm examination
7. Double integrations
8. Changes of variables
9. Triple integrations, and changes of variables by using the system of polar coordinates
10. Improper integrations
11. Volumes of solids and areas of surfaces
12. Line integrations and Green's theorem
13. Series and power series 1
14. Series and power series 2
15. Exercise and final 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
Knowledge of the course of Calculus I and Exercise 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
will be introduced at the first lecture.
References
R. Dedekind, Was sind und was sollen die Zahlen.(Japanese Trans. Iwanami)
Assessment/Grading
Evaluation will be done according to the Klausuren(Midterm examination 50%. Final examination 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, Series
Office hours
Tuesday, between 930 and 1130, Room 210 in Bld.12
Remarks 1
Remarks 2
Related URL
Lecture Language
Japanese
Language Subject
Last update
3/16/2019 8:58:57 AM