Purpose of learning: The purpose of learning is to understand the basic concepts and theories of linear algebra, to be able to apply them, and to be able to smoothly understand the mathematics to be learned.
Course Objectives:
1. To understand the operation of vectors between plane and space, and find the equations for straight lines, planes, and spheres in space.
2. To understand the definition of inverse matrix, find the inverse matrix of quadratic square matrices, and interpret multiplication as the inverse transformation of regular linear transformations.
3. To understand the definition and properties of determinants and be able to find the values of basic determinants.
4. To understand the meaning of matrix eigen values and eigen vectors, and be able to diagonalize matrices.
Outline:
General or Specialized : General
Field of learning : Natural science common / basic
Required, Elective: Elective must complete subjects
Foundational academic disciplines : Mathematical science / Mathematics / Foundations of mathematics
Relationship with JABEE programs : This subject is equivalent to "(2) Acquire basic science and technical knowledge".
Relationship with engineer education program: The main goal of learning / education in this subject is "(A)".
Course outline : Linear algebra is widely used not only in the natural sciences but also in engineering and economics. In this class, we first learn the basic properties of planes and space vectors. Next, we define matrices and determinants and apply them to the solution of simultaneous linear equations.
Style:
Course method: Proceed with the class while confirming the students' understanding.
Grade evaluation method: 4 regular examinations, weighted equally (70%) and reports and quizzes (30%). Retest depending on grades. The retest will be evaluated in the same way as regular tests, with a maximum of 80 points. Textbooks, notebooks, etc. are not allowed in the exam.
Notice:
Precautions on the enrollment : Students must take this class (no more than one-third of the required number of class hours missed) in order to complete the 2nd year course.
Course advice: This course is required to be taken (the number of absentee hours is less than 1/3 of the prescribed number of class hours) in order to complete the course of the academic year.
Foundational subjects : Fundamental Mathematics (1st year), Fundamental Mathematics Practice (1st)
Related subjects: Mathematics, physics, and other subjects after the third year
Attendance advice : If you are late after, you may be treated as absent after a warning.
Part-time lecturers are in charge of this subject. The liaison faculty member is Matsuda.
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Early Guidance, Planar Vector Calculations and Components |
Understanding plane vector operations
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| 2nd |
Inner product of vectors, parallel and vertical |
Understanding vector dot product, parallel and vertical
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| 3rd |
Application to figures, exercises |
Understanding of application to figures
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| 4th |
Spatial coordinates |
Understanding spatial coordinates
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| 5th |
Vector component of space |
Understanding the components of the vector in space
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| 6th |
inner product |
Understanding the inner product
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| 7th |
Sphere equation |
Understanding sphere equations
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| 8th |
First term midterm exam |
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| 2nd Quarter |
| 9th |
Mid-term exam return and commentary, straight and plane equations |
Understanding straight and plane equations
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| 10th |
Linear independence and linear dependence of vectors |
Understanding Linear Independence and Linear Subordination of Vectors
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| 11th |
Matrix definition and product of matrix sum, difference, number |
Understanding matrix definitions and the products of matrix sums, differences, and numbers
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| 12th |
Exercises |
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| 13th |
Matrix multiplication, transposed matrix |
Understanding matrix multiplication and transposed matrix
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| 14th |
Inverse matrix, inverse transformation |
Understanding of inverse matrix and inverse transformation
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| 15th |
Last term exam |
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| 16th |
Return and commentary of the final exam |
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| 2nd Semester |
| 3rd Quarter |
| 1st |
Late guidance |
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| 2nd |
Elimination, inverse matrix and simultaneous linear equations |
Understanding Elimination, Inverse Matrix, and System of Equations
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| 3rd |
Definition of determinant and nature of determinant |
Understanding the definition of determinants and the nature of determinants
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| 4th |
Matrix product determinant and matrix product and composite transformation |
Understanding determinant of matrix product, matrix product and synthetic transformation
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| 5th |
Expansion of determinant and determinant and inverse matrix |
Understanding of expansion of determinant and determinant and inverse matrix
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| 6th |
Determinant of matrix product, matrix product and composite transformation |
Understanding of determinant of matrix product, matrix product and composite transformation
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| 7th |
Graphical meaning of determinant |
Understanding of graphical meaning of determinant
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| 8th |
Late midterm exam |
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| 4th Quarter |
| 9th |
Return and commentary of the mid-term exam |
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| 10th |
Definition of linear transformation, basic properties of linear transformation |
Understanding of definition of linear transformation, basic properties of linear transformation
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| 11th |
Synthetic transformation and inverse transformation, transformation representing rotation |
Understanding of synthetic transformation and inverse transformation, transformation representing rotation
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| 12th |
Orthogonal matrix and orthogonal transformation |
Understanding of orthogonal matrix and orthogonal transformation
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| 13th |
Eigenvalues and eigenvectors |
Understanding of eigenvalues and eigenvectors
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| 14th |
Calculation of eigenvalues and eigenvectors, diagonalization of matrix
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Understanding of calculation of eigenvalues and eigenvectors, diagonalization of matrix
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| 15th |
Late final exam |
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| 16th |
Return and commentary of the final exam |
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