(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.
(3) Understand the meaning of differential equations and learn the primary solution of first order differential equations.
(4) Understand the basic properties of second order linear differential equations and learn their primary solutions.
Outline:
Students will learn the application of matrices, first order differential equations, and the second order differential equations as the basis for linear algebra and differential equations.
Style:
Classes will be conducted through lectures and exercises, scheduled assignments and quizzes, etc.
Notice:
The following items are essential for taking this course. New Linear Algebra I (textbook above) Ch. 2: Matrices, Ch. 3: Matrices and New Differential Integration II (textbook above) Ch. 4: Variable Separation Form of Differential Equations
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 |
Linear transformation
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Understand the definition of a linear transformation.
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2nd |
Linear transformation
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Understand and can apply the nature of linear transformations.
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3rd |
Linear transformation
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Understand and can calculate synthesis transformations.
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4th |
Linear transformation |
Understand and can calculate reverse conversion.
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5th |
Linear transformation
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Understand and can calculate the linear transformation representing the rotation.
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6th |
Linear transformation
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Understand and can calculate the nature of orthogonal transformations.
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7th |
Summary |
Review / development
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8th |
Exercise |
Exercise
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2nd Quarter |
9th |
Eigenvalues and their applications
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Understand the definitions of eigenvalues and eigenvectors.
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10th |
Eigenvalues and their applications
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Can calculate eigenvalues and eigenvectors.
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11th |
Eigenvalues and their applications
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Understand diagonal matrices.
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12th |
Eigenvalues and their applications
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Can calculate for diagonal matrices.
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13th |
Eigenvalues and their applications
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Understand and can calculate the probability of diagonals.
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14th |
Eigenvalues and their applications
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Understand and can calculate the diagonals of a symmetric matrix by an orthogonal matrix.
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15th |
Exercise |
Exercise
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16th |
Exam
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2nd Semester |
3rd Quarter |
1st |
First order differential equations |
Understand the meaning of differential equations.
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2nd |
First order differential equations |
Understand and can calculate the general solution for the separation of variables in differential equations.
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3rd |
First order differential equations |
Understand the general solution of same-order differential equations and can compute them
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4th |
First order differential equations |
Understand the general solution for first order differential equations.
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5th |
First order differential equations |
Can calculate the general solution for unequal first order linear differential equations.
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6th |
First order differential equations |
Can calculate the application of first order linear differential equations.
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7th |
Summary |
Review / development
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8th |
Exercise
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Exercise
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4th Quarter |
9th |
Second order differential equations |
Understand the solution of the second order differential equations.
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10th |
Second order differential equations |
Understand linear differential equations.
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11th |
Second order differential equations |
Understand and can calculate the general solution of the constant coefficient parabolic second order linear differential equations.
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12th |
Second order differential equations |
Understand and can calculate constant coefficient non-quatinic second order linear differential equations.
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13th |
Second order differential equations |
Can calculate for various linear differential equations.
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14th |
Second order differential equations |
Can calculate for non-linear second order differential equations.
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15th |
Exercise |
Can solve various problems with second order differential equations.
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16th |
Exam
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