| Course title | |||||
| 線形代数学Ⅰ [Linear Algebra Ⅰ] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 1～4 | Semester | Spring | |
| Course type | Spring | Course code | 021802 | ||
| Instructor(s) | |||||
| 原 伸生 [HARA Nobuo] | |||||
| Facility affiliation | Faculty of Engineering | Office | 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 |
| 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. Exercises, 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 space $R^n$ 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. Term examination |
| Prerequisites |
| None |
| Required Text(s) and Materials |
| Miyake, T.: "Nyuumon-Senkei-Daisuu", Baifu-kan (in japanese) |
| 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 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/1/2018 1:20:04 PM |