Medicine and Surgery HT

Linear algebra: 1)n-tuples of real numbers: addition, scalar multiplication, dot product, linear independence. 2)Matrices over real numbers: definitions, addition, scalar multiplication, matrix multiplication, basic properties. 3)Determinant and inverse of a square matrix. Rank of a matrix and its connection with linear independence. 4)Systems of linear equations: definitions, homogeneous systems, Gaussian elimination, Cramer's rule, Rouché-Capelli theorem. 5)Subspaces of R^n in cartesian form and their dimension. 6)Eigenvalues and eigenvectors of a square matrix. Algebraic and geometric multiplicity. Diagonalization. Analytic geometry: 1)Analytic geometry in dimension 2:coordinate system and Euclidean vectors, parallelism, dot product, angle between two vectors, equations of a line, intersection and mutual position of two lines, distance between two points and between a point and a line. 3)Analytic geometry in dimension 3: coordinate system and Euclidean vectors, cross product, equations of a plane, intersection and mutual position of two planes, equations of a line, reciprocal position of two lines and a line and a plane, sheaves and bundles of lines, distance between two points, a point and a plane, the area of a parallelogram.

Lecture notes.