1. Understand the definition and properties of determinants, and be able to calculate them.
2. Be able to solve simultaneous equations by using determinants.
3. Understand the relationship between linear transformations and matrices.
4. Understand the concept of eigenvalues and eigenvectors, and be able to calculate them and perform matrix diagonalization.
5. Understand the concept of vector functions, and be able to calculate them.
Outline:
Building on their knowledge of vector spaces, students will learn the basics of matrices and vector functions.
Style:
The class will consist mainly of lectures and exercises, with assignments and quizzes as needed.
Notice:
Lecture B（Lecture(30h) and Self-study(15h) for 1Credit)
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Inverse matrices, Cramer's rule I |
To be able to solve practice problems.
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| 2nd |
Area of a parallelogram, Volume of a parallelepiped |
To be able to solve practice problems.
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| 3rd |
Sign of a permutation, Determinants of a square matrix |
To be able to solve practice problems.
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| 4th |
Basics of determinants |
To be able to solve practice problems.
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| 5th |
Determinants of inverse matrices, Elementary matrix transformations |
To be able to solve practice problems.
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| 6th |
Elementary matrices, Regular matrices |
To be able to solve practice problems.
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| 7th |
Cofactor expansion I |
To be able to solve practice problems.
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| 8th |
Exam. |
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| 2nd Quarter |
| 9th |
Cofactor expansion II, Cramer's rule II |
To be able to solve practice problems.
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| 10th |
Linear transformation on a plane I |
To be able to solve practice problems.
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| 11th |
Linear transformation on a plane II |
To be able to solve practice problems.
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| 12th |
Linear transformation on a space,
Linearity, Composition of linear transformations |
To be able to solve practice problems.
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| 13th |
Inverse transformations, Diagrams and linear transformations |
To be able to solve practice problems.
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| 14th |
Eigen values, Eigen vectors I |
To be able to solve practice problems.
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| 15th |
Exercise |
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| 16th |
Exam. |
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| 2nd Semester |
| 3rd Quarter |
| 1st |
Eigen values, Eigen vectors II |
To be able to solve practice problems.
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| 2nd |
Diagonalization of a square matrix I |
To be able to solve practice problems.
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| 3rd |
Diagonalization of a square matrix II |
To be able to solve practice problems.
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| 4th |
Inner product, Orthogonal matrices and Orthogonal transformations |
To be able to solve practice problems.
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| 5th |
Eigen values and Eigen vectors of a symmetric matrix |
To be able to solve practice problems.
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| 6th |
Diagonalization of a symmetric matrix by using Orthogonal matrices |
To be able to solve practice problems.
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| 7th |
n-th power of a square matrix, Canonical form of quadratic curves |
To be able to solve practice problems.
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| 8th |
Exam. |
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| 4th Quarter |
| 9th |
Outer product of vectors |
To be able to solve practice problems.
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| 10th |
Differential of vector functions |
To be able to solve practice problems.
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| 11th |
Curves in a vector space |
To be able to solve practice problems.
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| 12th |
Surfaces in a vector space |
To be able to solve practice problems.
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| 13th |
Scalar field, Vector field, level surface |
To be able to solve practice problems.
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| 14th |
Divergence, Rotation |
To be able to solve practice problems.
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| 15th |
Exercise |
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| 16th |
Exam. |
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