Course title
微分積分学Ⅱ   [CalculusⅡ]
Course category		Requirement		Credit	2
Department		Year	2～	Semester	1st
Course type	1st	Course code	01ma2004a
Instructor(s)
原 伸生   [HARA Nobuo]
Facility affiliation	Faculty of Engineering	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 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 differentiation and total differentiation 3. Partial differentiation of composite functions 4. Partial differentiation of higher order 5. Taylor's theorem for functions of two variables 6. Local maxima and minima of functions of two variables 7. Implicit functions: Local maxima and minima under bounded conditions 8. Exercises, or midterm examination 9. Double integration 10. Iterated integrations 11. Changes of variables 12. Triple integrations 13. Improper integrations 14. Volumes of solids and areas of surfaces 15. Exercise and term examination

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

to be introduced at the first lecture.

References

Assessment/Grading

Midterm exam 50%, Term exam 50%. In case of online lecture, see below. The grade evaluation in this online class is premised on all attendances, and comprehensively evaluates the attitude to learn, quizzes, report, and online tests. Standard study time set by the our university is required to get the grade. The rate of evaluation is as follows: test (schriftliche Prufung) 100%. Grade will be given according to the following criteria by comprehensive evaluation: S: 90 points or more, A: 80 or more and less than 90 points, B: 70 or more and less than 80 points, C: 60 or more and less than 70 points.

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

Office hours

in Fuchu, before/after the lecture

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

1/22/2021 1:24:15 PM