5. Linear Algebra

Polynomial, matrices , binomial ,linear spaces, linear transformations, λ-matrix. Euclid space . Determinant of a square matrix and its properties. Rank of a matrix, inverse matrix, linear systems of equations. Eigenvalues and eigenvectors of a matrix, matrix similitude and diagonal form of a real symmetric matrix. Orthogonal matrix and their basic properties, vector spaces linear dependence and linear independence. Bases and dimension. Linear maps . Matrices related to a linear map, rank and nullity theorem, analytic geometry. Geometric vectors and their algebra. Chauchy-Schwartz Theorem. Straight lines and planes in the space. Parallelism and orthogonality properties. Matrices and determinants. Methods for solving linear systems. Eigenvalues and eigenvectors. Matrix diagonalization. canonical forms.

6.Analytic geometry

Basis concepts of vector and coordinate, locus and equation, plane and space, space line, cylindercal surface, conical surface, revolve surface and quadratic surface. Planar and spatial vectors. Vector space and scalar product. Straight lines and planes. Parallelism and orthogonality. Linear applications. Changes of planar and spatial coordinates. Polar coordinates. Conic sections and quadric surfaces, qualitative study of the graph of a function.

7. General Physics

Short description ,the electric field and magnetic field, electromagnetics, vibrate and undulate, quantum physics.

## Tuesday, March 25, 2008

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