Fichas de Asignaturas Comunes
|ACADEMIC YEAR: 2012/2013|
Course - Autumm
Course - Spring
The objective of this subject is to allow the student to develop the following generic competencies:
- Skilled to searching and selecting information, critical reasoning and writing and defending the reasonings within the defined area.
- Skilled for public speaking and in written and communicating information throughout documents and public speeches.
- Skilled for abstration, analysis and synthesis and problem solving.
- Skills for the use of Information Technologies and Communications.
And the following specific competencies (Ministerial Order CIN/352/2009, were the necessary requirements to be qualified to practice as a Telecommunications technical engineer are established):
- Capacity of solving mathematic problems that can appear in engineering. Aptitude for applying knowledges about: linear algebra, geometry, differential geometry, differential and integral calculus, differential equations, partial-differential equations, numeric methods, numeric algorithmics, statistics and optimization.
2. Learning outcomes
To develop the skills previously listed above, students must achieve the following learning outcomes:
- Perform basic operations on matrices. Computation of the inverse matrix.
- Manage the concepts of norm, distance and angle in Euclidian spaces and the orthogonalization of systems of vectors.
- "Solve linear ODEs with constant coefficients using the related theory and methods like ""undetermined coefficients"" or ""variation of constants""."
- Use tools to make calculations and to solve problems related to the subject.
- Model and solve physical problems by differencial equations systems.
- Propose and solve problems in the field of physics and engineering using linear ODEs. In particular the second orden ODE as a RLC circuit model.
- Use the concept of linear transformation between vector spaces.
- Get the diagonal form of a diagonalizable square matrix.
- Obtain the eigenvalues and eigenvectors of a square matrix.
- Use the vector space structure and its main properties.
- Represent and manage basis changes.
- Represent in a matrix form a linear transformation respect different basis.
- Compute determinants of square matrices using different techniques.
- Solve and discuss systems of linear equations using several methods.
- Obtain the LU factorization of a matrix.
The training activities that will be conducted in this subject are structured in the following thematic units:
SYSTEMS OF LINEAR EQUATIONS.
|1.1.||Systems of linear equations.|
|1.2.||Row Reduction and Echelon Forms.|
|1.4.||The matrix equation Ax = B|
|1.5.||Solution Sets of linear systems.|
|1.7.||Introduction to linear transformations|
MATRIX ALGEBRA AND DETERMINANTS.
|2.2.||Inverse of a matrix.|
|2.3.||Characterization of invertible matrices.|
|2.5.||Determinants and properties.|
VECTOR SPACE AND LINEAR APPLICATIONS.
|3.1.||Real vector spaces and subspaces.|
|3.2.||Linear dependence, rank, dimension and base.|
|3.3.||Linear Transformations: kernel, image, associated matrix,|
|3.4.||Applications composition and reverse application.|
|3.5.||Coordinate systems. Change of basis.|
|4.1.||Eigenvalues and eigenvectors.|
|4.2.||The Characteristic Equation. Eigenspace.|
ORTHOGONALITY AND LEAST SQUARES.
|5.1.||Inner product, length and norm.|
|5.4.||The Gram-Schmidt Process.|
|5.5.||Least-squares problem and applications.|
DIAGONALIZATION OF SYMMETRIC MATRICES.
LINEAR DIFFERENTIAL EQUATIONS OF HIGHER ORDER.
|7.1.||Order 2Resolution linear differential equations.|
|7.2.||Order n.Resolution linear differential equations.|
|7.3.||Systems of Linear Differential Equations.|