Vector Calculus: Concept of free vector, collinear, coplanar vectors, coordinate systems. Inner, outer and mixed product of vectors. Geometric interpretation of vector products. Straight line in space: Vector equation, analytical and parametric equations of a straight line. Asymmetric straight lines. Plane: Vector, analytical and parametric equations of a plane. Distance of a point from a plane. Curves in the plane and in space. Algebraic Structures: Semigroup, group, ring, field. Vector spaces: definition, concept of subspace, linear combinations, sums of subspaces. Linearly independent and linearly dependent vectors. Concept of basis and dimension. Matrices: Definition, categories of matrices, matrix operations, properties. Determinants: Definition, properties. Calculation of inverse matrix. Linear systems: Solving linear systems, Gauss elimination method, Cramer system. Linear transformations: Matrix of linear transformation, change of basis, similar matrices, equivalent matrices. Rank of matrix, investigation of linear systems.
- Teacher: Σοφία Λαμπροπούλου
ECTS : 6
Language : el