Course Objectives
(1) Understand the definition and basic properties of linear transformation by matrix and learn its computational techniques.
(2) Understand the definition of matrix eigenvalues and eigenvectors, and learn computational techniques for diagonal matrices.
Rubric
| Ideal Level | Standard Level | Unacceptable Level |
| Achievement 1 | Learn and can use basic computing techniques for matrices. | Understand the basic computing techniques for matrices. | Do not understand the basic computing techniques for matrices. |
| Achievement 2 | Learn and can use some advanced computational techniques for matrices and vectors. | Understand some advanced computational techniques for matrices and vectors. | Do not understand the more advanced computing techniques for column vectors. |
Assigned Department Objectives
Teaching Method
Outline:
Students will learn the application of matrices as a basis for linear algebra.
Style:
The lecture will be given according to the textbook on the assumption that students have prepared for the lecture. In addition, exercises will be conducted.
Students are expected to concentrate on understanding the lecture, and to ask questions about what they did not understand in the lecture or what they did not understand in the preparation for the lecture.
Be sure to review and try to solve problems in the textbook and problem books on the same day.
Notice:
Make every effort to understand the lectures. Be sure to ask questions and try to clear up any doubts you may have. Students are also expected to review the textbook and practice problems in the textbook and problem books on the same day.
Students who miss 1/3 or more of classes will not be eligible for evaluation.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Class Description
|
Confirm how to proceed with the class.
|
| 2nd |
Linear transformation
|
Can understand and use the computational representation of matrices.
|
| 3rd |
Linear transformation
|
Can understand the definition of linear transformation.
|
| 4th |
Linear transformation |
Can find the image by linear transformation.
|
| 5th |
Linear transformation
|
Can find matrices representing composite, inverse, and rotational transformations.
|
| 6th |
Linear transformation
|
Can understand orthogonal matrices and orthogonal transformations.
|
| 7th |
Eigenvalues and their applications |
Can find eigenvalues and eigenvectors.
|
| 8th |
Summary
|
Review of the total.
|
| 2nd Quarter |
| 9th |
Eigenvalues and their applications
|
Can use diagonalization to find A^n.
|
| 10th |
Eigenvalues and their applications
|
Can diagonalize the symmetric matrices using orthogonal matrices.
|
| 11th |
Eigenvalues and their applications
|
Can perform Gram-Schmidt calculations.
|
| 12th |
Eigenvalues and their applications
|
Can determine if it is a vector space.
|
| 13th |
Eigenvalues and their applications
|
Can find the basis of the kernel and image of a linear map.
|
| 14th |
Summary |
Review of the total.
|
| 15th |
Eigenvalues and their applications |
Can obtain the representation matrix of the linear transformation when the basis is changed.
|
| 16th |
Exam
|
Confirmation of the studies.
|
Evaluation Method and Weight (%)
| Examination | Little test・Task | Total |
| Subtotal | 60 | 40 | 100 |
| Basic Proficiency | 60 | 40 | 100 |
| Specialized Proficiency | 0 | 0 | 0 |
| Cross Area Proficiency | 0 | 0 | 0 |