Course title
線形代数学Ⅰ   [Linear Algebra Ⅰ]
Course category technology speciality courses  Requirement   Credit 2 
Department   Year 14  Semester 1st 
Course type 1st  Course code 021908
Instructor(s)
原 伸生   [HARA Nobuo]
Facility affiliation Faculty of Engineering Office 12-214  Email address

Course description
Linear algebra provides indispensable tools to analyze various mathematical phenomena appearing in engineering. Computations in linear algebra are based on matrices and their elementary transformations, which enable us to treat more abstract notions such as linear maps and linear independence at hand. In this course we will learn about various computations with matrices (elementary transformation, determinants etc.), via which the concept of "linearity" behind them will be understood.
Expected Learning
The goal of this course is:
1) capable to perform basic operations on matrices
2) capable to calculate the reduced row echelon form of a matrix with elementary transformation
3) capable to calculate the determinant of a square matrix
4) capable to apply the above techniques to solving a system of linear equations, computations of inverse matrices and linear (in)dependence of column vectors
5) to understand the correspondence between the Euclidean vector space and the space of column vectors, as well as the basic notions for those vectors

Corresponding criteria in the Diploma Policy: See the Curriculum maps
Course schedule
1. Matrices and their operations
2. Square matrices: inverse matrices, regular matrices etc.
3. Block division of matrices
4. Elementary transformation and row echelon form
5. Applications: system of linear equations and inverse matrices
6. Determinants 1: permutations
7. Summary: Exercises and/or midterm examination
8. Determinants 2: a definition and basic properties
9. Determinants 3: cofactor expansion
10. Determinants 4: adjoints and Cramer's formula
11. The vector space of column vectors with real entries
12. Linear combination and linear independence of column vectors
13. 3-dimensional space vectors
14. Exercises summarizing the semester
15. Summary: Exercises and/or Term examination
Prerequisites
None.
Remark: In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending appropriate amount of time and using the lecture handouts as well as the references specified below.
Required Text(s) and Materials
Miyake, T.: "Nyuumon-Senkei-Daisuu", Baifu-kan (in japanese)
Remark: This lecture will be given in Japanese. Students who want to use a textbook written in English should consult the lecturer.
References
To be indicated in the lecture
Assessment/Grading
Midterm exam (50%), Term exam (50%)
Message from instructor(s)
Course keywords
matrix, vector, rank, system of linear equations, determinant, inverse matrix
Office hours
Arranged taking into account of students' requests
Remarks 1
Remarks 2
Related URL
Lecture Language
Japanese
Language Subject
Last update
1/22/2021 12:12:58 PM