到達目標
Students can describe and solve the solvability of simultaneous linear equations.
Students can state linear independence of vectors.
Students can understand the concept of subspace and can find dimensions and bases.
Students can obtain matrix eigenvalues and eigenvectors. Eigenvalues and eigenvectors can be applied to problems such as quadratic normalization.
ルーブリック
| Ideal Level of Achievement (Very Good) | Standard Level of Achievement (Good) | Unacceptable Level of Achievement (Fail) |
| Evaluation 1 | Students can discuss the solvability of simultaneous equations and solve them. | Students can solve simultaneous equations. | Students can't solve simultaneous equations. |
| Evaluation 2 | Students can understand the concept of subspace and can find dimension bases. | Students can understand the concept of subspace. | Students can't understand the concept of subspace. |
| Evaluation 3 | Students can obtain matrix eigenvalues and eigenvectors, and can apply them to problems concerned with matirx. | Students can obtain matrix eigenvalues and eigenvectors. | Students can't obtain matrix eigenvalues and eigenvectors. |
学科の到達目標項目との関係
教育方法等
概要:
We first teach the theory of simultaneous linear equations and use it to describe the linear independence of vectors.
Next, we define a subspace of the number vector space and lecture on its dimensions and bases.Furthermore, we consider linear mapping and prove the dimension theorem.
Finally, we give lectures on matrix eigenvalues, eigenvectors and their applications.
授業の進め方・方法:
Lectures and exercises by the teacher alone
注意点:
Those who do not have a score of 60 can take the certification test upon request.
授業計画
|
|
週 |
授業内容 |
週ごとの到達目標 |
| 後期 |
| 3rdQ |
| 1週 |
Guidance
Simultaneous linear equations |
Students can use method of elimination to slove simultaneous equations.
|
| 2週 |
Linear independence
linear dependence |
Students can understand the simultaneous equations and the linear independence relationship, and can verify the linear independence.
|
| 3週 |
linear space and subspace |
Students understand the concept of subspace and can determine if it is a subspace.
|
| 4週 |
Dimension and bases |
Students can determine the dimensions and bases of a given subspace.
|
| 5週 |
Linear mapping |
Students can determine the dimensions and bases of a given subspace.
|
| 6週 |
Image and kernel |
Students can understand definitions of the image and kernel of linear mapping, and can determine the dimension and base of the image and kfernel.
|
| 7週 |
Simension theorem |
Students can understand definitions of the image and kernel of linear mapping, and can determine the dimension and base of the image and kfernel.
|
| 8週 |
Intermediate examination |
We do the test to confirm the students' level of understanding.
|
| 4thQ |
| 9週 |
Eigenvalue and eigenvector |
Students can obtain eigenvalues and eigenvectors for 2-dim square matrix and 3-dim square matrix.
|
| 10週 |
Diagonalization |
Students can determine whether a given square matrix can be diagonalized.
|
| 11週 |
Orthogonal matrix |
Students can understand the definition of the orthogonal matrix and the nature that it satisfies.
|
| 12週 |
Diagonalization by orthogonal matrix of symmetric matrix |
Students can diagonalize symmetric matrices using orthogonal matrices.
|
| 13週 |
Schmidt's orthogonalization method |
Students can create orthonormal bases from linearly independent vectors.
|
| 14週 |
Application of diagonalization |
Students can normalize quadratic forms using eigenvalues.
|
| 15週 |
Final exam |
We do the test to confirm the students' level of understanding.
|
| 16週 |
Explanation of final exam |
I will explain the items that are considered to be poorly understood by students in the final exam.
|
モデルコアカリキュラムの学習内容と到達目標
| 分類 | 分野 | 学習内容 | 学習内容の到達目標 | 到達レベル | 授業週 |
| 基礎的能力 | 数学 | 数学 | 数学 | 線形変換の定義を理解し、線形変換を表す行列を求めることができる。 | 3 | |
| 合成変換や逆変換を表す行列を求めることができる。 | 3 | |
| 平面内の回転に対応する線形変換を表す行列を求めることができる。 | 3 | |
評価割合
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | 合計 |
| 総合評価割合 | 140 | 0 | 0 | 0 | 0 | 60 | 200 |
| Basic Ability | 70 | 0 | 0 | 0 | 0 | 30 | 100 |
| Technical Ability | 50 | 0 | 0 | 0 | 0 | 20 | 70 |
| Interdisciplinary Ability | 20 | 0 | 0 | 0 | 0 | 10 | 30 |