1. Can compute vectors and apply them to shapes.
2. Understand the definition of matrices, and can perform matrix computations and solve simultaneous linear equations.
3. Understand the definition and properties of determinants, and can calculate the values of basic ones.
Outline:
Classes and exercises will be given on the basics of linear algebra, which is used in a wide range of fields. The goal is to become able to relate computation to geometry by using equations for shapes in a plane or in space
Style:
There will be lecture-style classes, tests at appropriate times, and report assignments. (Omoda is the liaison and will not teach the classes.)
Notice:
Try to understand the material thoroughly during the classes. Make an effort to always ask about things that are unclear, and solve them then and there. Also, always review the material on the same day, and do the problem exercises properly.
Students who miss 1/3 or more of classes will not be eligible for a passing grade.
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Planar vectors |
Can compute vectors.
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| 2nd |
Planar vectors |
Can compute the inner product of vectors.
|
| 3rd |
Planar vectors |
Can apply vectors to shapes.
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| 4th |
Planar vectors |
Can check the linear independence of planar vectors.
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| 5th |
Spatial vectors |
Can handle spatial coordinates.
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| 6th |
Spatial vectors |
Can compute the inner product of spatial vectors.
|
| 7th |
Overall |
Can solve problems related to the content thus far.
|
| 8th |
Midterm exam |
|
| 2nd Quarter |
| 9th |
Spatial vectors |
Can handle the equations of spatial shapes.
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| 10th |
Spatial vectors |
Can check the linear independence of spatial vectors.
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| 11th |
Matrices |
Understand the definition of a matrix.
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| 12th |
Matrices |
Can compute the sum and difference of matrices, and multiply them by numbers.
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| 13th |
Matrices |
Can compute the product of matrices.
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| 14th |
Matrices |
Can compute inverse matrices.
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| 15th |
Overall |
Can solve problems related to the content thus far.
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| 16th |
Final exam |
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| 2nd Semester |
| 3rd Quarter |
| 1st |
Simultaneous linear equations and matrices |
Understand the elimination method.
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| 2nd |
Simultaneous linear equations and matrices |
Can solve simultaneous equations using the elimination method.
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| 3rd |
Simultaneous linear equations and matrices |
Can solve simultaneous equations using inverse matrices.
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| 4th |
Simultaneous linear equations and matrices |
Can compute the rank of a matrix.
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| 5th |
Definition and properties of determinants |
Understand the definition of determinants.
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| 6th |
Definition and properties of determinants |
Can compute determinants.
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| 7th |
Overall |
Can solve problems related to the content thus far.
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| 8th |
Midterm exam |
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| 4th Quarter |
| 9th |
Definition and properties of determinants |
Can compute determinants using their properties.
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| 10th |
Definition and properties of determinants |
Can compute the determinants of products of matrices.
|
| 11th |
Applications of determinants |
Can expand determinants.
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| 12th |
Applications of determinants |
Can compute inverse matrices using determinants.
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| 13th |
Applications of determinants |
Can investigate the properties of simultaneous equations using determinants.
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| 14th |
Applications of determinants |
Understand the geometric meaning of determinants.
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| 15th |
Overall |
Can solve problems related to the content thus far.
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| 16th |
Final exam |
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