We will conduct online teaching in Spring 2021.
In this course, you will learn the basic theory of matrices and their algebras with applications to linear equations and differential equations. Starting with how to represent linear equations via matrices, you will study the row and column operations of matrices with its application to solving linear equations with Gaussian elimination. Looking at solution sets of linear systems, you will reach the notions of linear independence of vectors, linear transformations, and vector spaces. Then you will learn the rank, determinant, eigenvalues, and eigenvectors of matrices to characterize the basic properties of matrices and linear equations. You will also see the correspondence between matrices and linear transformations of vector spaces.
In this course, you will learn the basic theory of matrices and their algebras with applications to linear equations and differential equations. Starting with how to represent linear equations via matrices, you will study the row and column operations of matrices with its application to solving linear equations with Gaussian elimination. Looking at solution sets of linear systems, you will reach the notions of linear independence of vectors, linear transformations, and vector spaces. Then you will learn the rank, determinant, eigenvalues, and eigenvectors of matrices to characterize the basic properties of matrices and linear equations. You will also see the correspondence between matrices and linear transformations of vector spaces.
You are expected to obtain skills, knowledge, and understandings of basics of matrices and linear transformations, which are
widely used in science and engineering.
| Goals and objectives | Course Outcomes | |
|---|---|---|
| 1. | The students can use basic operations of matrices to solve a linear equation with Gaussian elimination. |
A-1
|
| 2. | The students can raise concrete & non-trivial examples of the four fundamental vector subspaces and for each such example, you can find a basis and determine its dimension. |
A-1
|
| 3. | The students can use Gram-Schmidt to find an orthonormal basis for a given subspace of a vector space. |
A-1
|
| 4. | The students can use eigenvariables & eigenvectors of a given matrix A to diagonalize A and to compute the power of A as well as solve the linear differential equation given by A. |
A-1
|
| 5. | The students can determine the corresponding linear transformation given a change of basis of a vector space. |
A-1
|
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | The geometry of linear equations Elimination with matrices |
Review the content of the lecture (1.1-1.3, 2.1-2.3 in the textbook) | 200分 |
| Work on homework problems | 180分 | ||
| 2. | Matrix operations and inverses Elimination and factorization |
Review the content of the lecture (2.4-2.6 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 3. | Transposes and permutations Vector spaces and subspaces |
Review the content of the lecture (2.7, 3.1 in the textbook) | 120分 |
| Work on homework problems | 260分 | ||
| 4. | The nullspace The complete solution to Ax = b |
Review the content of the lecture (3.2-3.3 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 5. | Basis and dimension The four fundamental subspaces |
Review the content of the lecture (3.4-3.5 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 6. | Orthogonality Projections and subspaces |
Review the content of the lecture (4.1-4.2 in the textbook) | 120分 |
| Work on homework problems | 240分 | ||
| 7. | Mid-term presentation and discussions on the solutions afterwards | Preparation for the mid-term presentation | 380分 |
| 8. | Least squares approximations Orthonormal bases and Gram-Schmidt |
Review the content of the lecture (4.3-4.4 in the textbook) | 140分 |
| Work on homework problems | 240分 | ||
| 9. | Properties of determinants Formulas for determinants |
Review the content of the lecture (5.1-5.2 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 10. | Applications of determinants Eigenvalues and eigenvectors |
Review the content of the lecture (5.3, 6.1 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 11. | Diagonalization Differential equations |
Review the content of the lecture (6.2-6.3 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 12. | Symmetric matrices Positive definite matrices |
Review the content of the lecture (6.4-6.5 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 13. | Linear transformations Choice of basis |
Review the content of the lecture (8.1-8.3 in the textbook) | 160分 |
| Work on homework problems | 220分 | ||
| 14. | Final exam and discussions on the solutions afterwards | Preparation for the final exam | 380分 |
| Total. | - | - | 5300分 |
| Homework | Mid-term presentation | Final exam | Total. | |
|---|---|---|---|---|
| 1. | 20% | 4% | 5% | 29% |
| 2. | 15% | 4% | 5% | 24% |
| 3. | 10% | 4% | 3% | 17% |
| 4. | 10% | 3% | 10% | 23% |
| 5. | 0% | 0% | 7% | 7% |
| Total. | 55% | 15% | 30% | - |
Homework and mid-term presentation will contribute 70% of your grade.
Final exam will contribute 30% of your grade.
Those who get at least 60% of the full score will pass this course.
Final exam will contribute 30% of your grade.
Those who get at least 60% of the full score will pass this course.
Introduction to Linear Algebra (5th edition) by Gilbert Strang
ISBN: 978-0980232776
ISBN: 978-0980232776
Basic operations of vectors and the relationships between vectors and 2- & 3-dimensional Euclidean spaces. Basics of exponential
functions and differentiation. Basics of linear differential equations would be desirable.
- By appointment. Contact e-mail address: ikegami@shibaura-it.ac.jp
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Sun Mar 21 16:23:24 JST 2021