Differential and Integral Calculus 2

Course title

G0410210

	suwa masanori
	sunahata hiroki
	matsumoto masahiro

Course description

In differential and integral calculus 1, we learned about the differentiation and integration of a function with one independent variable, but when describing phenomena appearing in natural science and engineering by mathematical expressions, we need two or more independent variables.
In this lecture, we will learn about the differentiation and integration of a function with two or more independent variables. Also learn the graph of the function.

Note on Course: Mathematics is a stacked-up subject, so please make sure by reviewing the content of each lecture to solve the exercise problem inside and outside the lecture.

Purpose of class

Learn and understand the new definition of differentiation / integration of two variable function and the essential meaning of properties related to them, based on the differentiation / integration of one variable function, and various formulas and some effective Learn techniques and familiarize themselves with the fundamentals of differential integral calculation methods of typical two variable functions. In addition, by learning various formulas and some effective methods, calculation of differentiation and integration of function with two variables can be solved.

Goals and objectives

Be able to explain the meaning of limit, continuity, partial derivatives, specific functions of two variable function. Be able to handle the partial differential of the two-variable function, the total differentiation, and the (partial) differentiation of the composite function.
Be able to explain the meaning and nature of double integration. Be able to perform Change of integration order in heavy integration, heavy integration calculation including variable conversion can be performed.
Be able to deal with functions with two variables and solve related extreme problems.
Be able to understand the meaning of Taylor expansion for two variable functions and develop specific.
Be able to deal with improper double integral, triple integral. Be able to imagine the general shape of the graph of the two variable function, and various volume and curved area can be derived based on it.

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Graph of function with two variables, limit of function with two variables	Review Graph of function with two variables and limit of function with two variables	120minutes
1.		Problem exercises in the relevant part	240minutes
2.	Partial differential coefficients, meaning of partial derivatives, simple partial differential calculation	Review Partial differential coefficients, meaning of partial derivatives and simple partial differential calculation	120minutes
2.		Problem exercises in the relevant part	260minutes
3.	Calculation of (partial) differentiation of composite function, total differentials	Review Calculation of (partial) differentiation of composite function and review of total differentials	120minutes
3.		Problem exercises in the relevant part	260minutes
4.	Meaning of double integrals, properties of double integrals	Review Meaning of double integral and properties of double integrals	120minutes
4.	Meaning of double integrals, properties of double integrals	Problem exercises in the relevant part	260minutes
5.	Double integral calculation using repeated integrals, interchange the order of integration	Review Double integral calculation using repeated integrals and interchange the order of integration	120minutes
5.		Problem exercises in the relevant part	260minutes
6.	Calculation of double integrals using change of variables and using polar coordinates	Review Calculation of double integrals using change of variables and using polar coordinates	120minutes
6.		Problem exercises in the relevant part	260minutes
7.	Midterm and commenrtary	Preparation for midterm exam	380minutes
8.	High order partial derivative of two variable function, Taylor's theorem and Maclaurin's theorem with two variables	Review High order partial derivative of two variable function, and Review Taylor's theorem and Maclaurin's theorem with two variables	120minutes
8.		Problem exercises in the relevant part	260minutes
9.	Extreme problem of two variable function	Review Extreme problem of two variable function	120minutes
9.	Extreme problem of two variable function	Problem exercises in the relevant part	260minutes
10.	Extreme value problem with constrained condition	Review Extreme value problem with constrained condition	120minutes
10.	Extreme value problem with constrained condition	Problem exercises in the relevant part	260minutes
11.	Improper double integrals, definition of triple integral and repeated integrals	Review Improper double integrals and definition of triple integral and repeated integrals	120minutes
11.		Problem exercises in the relevant part	260minutes
12.	Triple integrations, cylindrical coordinates, spherical coordinates	Review Triple integrations, cylindrical coordinates, spherical coordinates	120minutes
12.		Problem exercises in the relevant part	260minutes
13.	Volume, surface area	Review volume and surface area	120minutes
13.	Volume, surface area	Problem exercises in the relevant part	260minutes
14.	Final exam and commentary	Preparation for final exam	380minutes
Total.	-	-	5300minutes

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	中間試験等	期末試験等	Total.
1.	10%	15%	25%
2.	10%	15%	25%
3.	6%	9%	15%
4.	4%	6%	10%
5.	10%	15%	25%
Total.	40%	60%	-

Evaluation method and criteria

Mid-term exams, exercises, reports, quizzes etc. are set to 40%, final exams are set to 60%, and a total score of 60 or more is accepted.

Textbooks and reference materials

"Introduction to Differential and Integral calculus" Miyake (Baihuukan publishing)

Prerequisites

Must have taken differential and integral calculus 1 once

Office hours and How to contact professors for questions

For full-time faculty, please refer to office hours of faculty profile. About part-time teachers are before and after class hours.
In mathematics department, basically each faculty does not rely on office hours, but as long as time permits, questions on subjects, etc. are accepted at any time so please do not hesitate to ask questions.
In the "Faculty of Engineering Learning Support Room" located on the 2nd floor of the University Hall, we give support for students with uneasy points and matters related to subjects on a one to one basis, so actively use it.

Relation to the environment

Non-environment-related course

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates a basic self-management skills
Course that cultivates a basic problem-solving skills

Active-learning course

About half of the classes are interactive

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicatable
N/A	該当しない

Last modified : Thu Mar 21 14:07:02 JST 2019