- 担当教員
- BREZINA JAN
- 使用教室
- 水1-2(H104)
- 単位数
- 講義：2 演習：0 実験：0
- 講義コード
- 1121
- シラバス更新日
- 2015年5月20日
- 講義資料更新日
- 2015年6月8日
- 学期
- 前期 / 推奨学期：1
講義概要
In Linear Algebra I we introduce numerical vectors and matrices which are indispensable tools of modern computation and thinking. We learn and practice calculation. The idea of linear algebra is to take known geometrical objects, describe them algebraically and create rules for calculation. Computers could not work without linear algebra and so you can't either.
講義の目的
To develop and strengthen the understanding of what was is linear algebra and how to successfully use it in other technical subjects.
講義計画
1. Vectors, numerical vectors, matrices.
2. Identity matrix, symmetric matrices, diagonal matrices, triangular matrices.
3 Operations with matrices.
4. Invertible matrices and inverse matrix.
5. System of linear equations and Gaussian elimination.
6. Elementary operations and elementary matrices.
7. General solution of system of linear equations.
8. Method for calculating an inverse matrix.
9. Rank of matrices.
10. Definition of determinant(up to 3×3 matrices), geometrical meaning of determinant.
11. Definition of determinant(from 4×4 matrices) (permutations), multilinearity (adding rows, multiplying by constant), alternating sign (interchange of rows).
12. Methods for calculating determinant, special determinant (triangular matrix, Vandermonde determinant) .
13. Laplace expansion of determinant
14. Determinant of transposed matrix and product of matrices.
15. Cramer's formula, formula for inverse matrices.
教科書・参考書等
We will follow "Linear Algebra: A Modern Introduction" by David Poole, 3rd or newer edition. This book will be also used in Linear Algebra II in winter. You are not required to buy it, but it would definitely help you.
You can compare with any English or Japanese textbook on introduction to linear algebra you find online or in the library. The main topics are always the same.
関連科目・履修の条件等
You should register together with the course "Exercise in Linear Algebra I (Course No. 1331)".
成績評価
Based on the results of tests, mid-term exam and final exam. Also your work during semester counts. Details to be explained on first lecture (see content of the first class).
担当教員の一言
The course will contain the same amount of mathematical knowledge as Japanese courses, but with the advantage of learning mathematical English.
連絡先（メール、電話番号）
Email : brezina＠math.titech.ac.jp
Office : Room 219, Main Bldg., Ookayama Campus
TA information:
Name: Hiroki Murakami
Email: murakami.h.ah＠m.titech.ac.jp
Office: H316
オフィスアワー
Setup a meeting time after class or by an email first.
