| Section |
Topics within the section
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| Vector algebra |
- Vector spaces
- Basic operations on vectors (summation, multiplication by scalar, dot product)
- Linear dependency and in-dependency of the vectors
- Basis in vector spaces
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| Introduction to matrices and determinants |
- Relationship between Linear Algebra and Analytical Geometry
- Matrices 2x2, 3x3
- Determinants 2x2, 3x3
- Operations om matrices and determinants
- The rank of a matrix
- Inverse matrix
- Systems of linear equations
- Changing basis and coordinates
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| Lines in the plane and in the space |
- General equation of a line in the plane
- General parametric equation of a line in the space
- Line as intersection between planes
- Vector equation of a line
- Distance from a point to a line
- Distance between lines
- Inter-positioning of lines
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| Planes in the space |
- General equation of a plane
- Normalized linear equation of a plane
- Vector equation of a plane
- Parametric equation a plane
- Distance from a point to a plane
- Projection of a vector on the plane
- Inter-positioning of lines and planes
- Cross Product of two vectors
- Triple Scalar Product
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| Quadratic curves |
- Circle
- Ellipse
- Hyperbola
- Parabola
- Canonical equations
- Shifting of coordinate system
- Rotating of coordinate system
- Parametrization
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| Quadric surfaces |
- General equation of the quadric surfaces
- Canonical equation of a sphere and ellipsoid
- Canonical equation of a hyperboloid and paraboloid
- Surfaces of revolution
- Canonical equation of a cone and cylinder
- Vector equations of some quadric surfaces
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