Course title
V04106002
Linear Space and 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.
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.
Goals and objectives
1. To be able to understand the notion of linear spaces and linear maps.
2. To be able to calculate the diagonalization of simple symmetric matrices.
3. 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% -
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
Evaluation method and criteria
Assignment 1: 20%, Assignment 2: 40%, Assignment 3: 40%,
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
Knowledge of Vector Calculus (without differential forms) and fundamental linear algebra are needed.
Office hours and How to contact professors for questions
• Discussion on the Scomb
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