Linear Space and Vector Calculus

Course title

3302790A

Middle-level Diploma Policy (mDP)

Program / Major	mDP	Goals
Mathematical Sciences Course	DP-4・2	キャリアを見据えた高度な専門知識現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。

Purpose of class

The object of this course is to understand the notion of linear spaces and linear maps and to be able to use differential forms in vector calculus.

Course description

This is a course on linear space and vector calculus. You will learn the notion of linear spaces, kernel and image of a linear map and vector calculus with differential forms.

Goals and objectives

To be able to understand the notion of linear spaces and linear maps.
To be able to calculate the diagonalization of simple symmetric matrices.
To be able to use differential forms in vector calculus.

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

	Assignment 1	Assignment 2	Assignment 3	Total.
1.	10%	20%	0%	30%
2.	10%	20%	0%	30%
3.	0%	0%	40%	40%
4.	0%			0%
5.	0%			0%
Total.	20%	40%	40%	-

Evaluation method and criteria

Assignment 1: 20%, Assignment 2: 40%, Assignment 3: 40%,

Language

English

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Linear space and subspace	Review of linear algebra	150minutes
2.	Linear maps	Review of linear space and subspace	200minutes
3.	Inner product space, assignment 1	Review of linear maps	200minutes
4.	Kernel and image of a linear map	Review of inner product space	200minutes
5.	Gram-Schmidt orthogonalization	Review of kernel and image of a linear map	200minutes
6.	Diagonalization of symmetric matrices	Review of Gram-Schmidt orthogonalization	200minutes
7.	Review and assignment 2	Review of all topics	200minutes
8.	Vector operators	Review of vector analysis	200minutes
9.	Differential forms	Review of vector operators	200minutes
10.	Exterior derivative	Review of differential forms	200minutes
11.	Surface integrals	Review of exterior derivative	200minutes
12.	Stokes’ theorem	Review of surface integrals	200minutes
13.	Gauss’ theorem	Review of Stokes’ theorem	200minutes
14.	Review and assignment 3	Review of all topics	200minutes
Total.	-	-	2750minutes

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
Feedback in the class

Textbooks and reference materials

Will be announced in the first class.

Prerequisites

Office hours and How to contact professors for questions

After class

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Non-social and professional independence development course

Active-learning course

More than one class is interactive

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicable
N/A	N/A

Education related SDGs:the Sustainable Development Goals

4.QUALITY EDUCATION

Last modified : Mon Mar 23 04:07:53 JST 2026