Preliminaries
Example of System of 2 Equations of 2 Variables
The Systems of 2 Linear Equations in 2 Variables
The Vectors in the Euclidean Plane
The Dot Product and the Norm of Vectors
Angles in Radian and Trigonometric Functions
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Oriented Angle of a Unit Vector with the x Axis (4:49)
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Trigonometry in the Unit Circle (10:22)
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The Trigonometric Functions in the Real Set (3:59)
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Angle of any Non Zero Vector with the x Axis (8:03)
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Angles between any Two Non-Zero Vectors (6:14)
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Angles in Radians and Trigonometric Functions (pdf)
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Section 6 Test
The Polar Coordinates and the Rotations
The Complex Numbers as Vectors
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Discover the Complex Numbers (14:14)
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The Complex Numbers in Python (5:20)
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Add, Subtract and Multiply Complex Numbers (7:21)
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The Module and Argument of a Complex Numbers (5:07)
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The Complex Exponential in Python (4:34)
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Rotations as Multiplications by Complex Numbers (3:31)
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The complex Numbers as Vectors (pdf)
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Section 8 Test
The Linear Mappings and their Matrices
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The Linear Mappings, Definition and Examples (4:26)
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The Matrix of a Linear Mapping (5:03)
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Addition, Subtraction and Scalar Multiplication of Linear Mappings (13:28)
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Composition of Linear Mappings (13:03)
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Kernel, Image and Rank of a linear mapping (10:49)
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The Linear Mappings and their Matrices (pdf)
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Section 9 Test
Basis and Change of Basis
Symmetric, Skew Symmetric and Unit Matrices
Eigenvalues and Eigenvectors
Diagonalisation in the Field of Complex Numbers
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The Field of Complex Numbers (21:54)
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Conjugate Complex Numbers (14:13)
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Resolution of quadratic equations in C (13:34)
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Matrices and Column Vectors with Complex Elements (18:06)
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2x2 Linear Systems in C (4:41)
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Diagonalisation in C of Real Matrices (15:10)
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Diagonalisation in the Field of Complex Numbers (pdf)
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Section 13 test
Final Assessment
Conclusion
