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Type A
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Code |
Competences Specific | | | FB1 |
Have the ability to solve mathematical problems that may arise in engineering. Have the ability to apply knowledge on: linear algebra; geometry, differential geometry, differential and integrated calculation, differential equations and partial derivatives, numerical methods, numerical algorithmics, statistics and optimisation. |
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Type B
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Code |
Competences Transversal | | | B2 |
Have knowledge in basic and technological subjects, which gives them the ability to learn new methods and theories, and the versatility to adapt to new situations. |
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Type C
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Code |
Competences Nuclear |
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Type A
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Code |
Learning outcomes |
| | FB1 |
Distinguished vectors linearly independent of vectors linearly dependent.
Determine bases of specific vector sub-spaces.
Calculate the core and image of a linear application.
Determine a linear application knowing the images of the vectors of a base.
Determine the range of a matrix using the properties of linear dependence and the concept of dimension of a vector sub-space.
Calculate the determinant of a square matrix.
Apply the calculation of determinants to the resolution a linear equation system.
Distinguish systems of determinate compatible, indeterminate compatible and incompatible linear equations.
Use the concept of range of a matrix in the classification of systems of linear equations.
Determine the diagonal nature of specific square matrices.
Determine the relative position of straight lines and planes.
Solve metric problems between straight lines and planes.
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Type B
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Code |
Learning outcomes |
| | B2 |
Know the structures of vectorial space and vectorial subspace.
Know the concept of linear application and its relationship with matrices.
Know the notion of characteristic polynomials of a matrix.
Understand the concept of the diagonal matrix and its relationship with linear applications.
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Type C
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Code |
Learning outcomes |
| Topic |
Sub-topic |
| Vector spaces |
Destinació
Anglès
?
Definition. First properties of vector spaces. Vector subspaces. Sum of vector subspaces. Direct sum. Linear dependence of vectors. Linear combinations. Subspace engendered by a set of vectors. Steinitz's theorem. Basis of a vector space. Base existence theorem. Grassman's formula. Range of a set of vectors.
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| Aplicacions Lineals i Matrius |
Definició. Teorema d'existència i unicitat d'aplicacions lineals. Propietats de les aplicacions lineals. Espai dual. Definició de matriu. Igualtat de matrius. Tipus de matrius. Suma de matrius. Producte d'un escalar per una matriu. Producte de matrius. Matriu transposta. Matriu inversa d'una matriu quadrada. Matriu associada a una aplicació lineal en unes bases determinades. Suma d'aplicacions lineals. Producte d'un escalar per una aplicació lineal. Composició d'aplicacions lineals. Anell dels endomorfismes d'un espai vectorial. Anell de les matrius quadrades. Matriu de canvi de base. Rang d'una matriu. Mètode de Gauss per buscar el rang d'una matriz. |
| Determinants |
Preliminars. Introducció. Regla de Sarrus per calcular un determinant d'ordre 3. Propietats dels determinants. Menor complementari d'un element. Adjunt complementari d'un element. Càlcul d'un determinant a partir dels adjunts d'una fila o d'una columna. Mètode per calcular la matriu inversa utilitzant determinants. Determinant d'un conjunt de n vectors respecte d'una base. Determinant d'un endomorfisme. Característica d'una matriu. |
| Sistemes d'equacions lineals |
Introducció. Teorema de Rouché. Mètode de Cràmer per la resolució de sistemes. Mètode de Gauss per la resolució de sistemes. Aplicació pràctica per buscar la matriu inversa |
| Diagonalització |
Introducció. Vectors propis i valors propis d'un endomorfisme. Polinomi característic. Caracterització dels endomorfismes diagonalitzables |
| Geometria Afí i Euclidiana |
Espai Afí .Sistemes de referència.Canvi del sistema de referència .Rectes i plans.Producte vectorial.Producte escalar.Problemes mètrics entre rectes i plans |
| Methodologies :: Tests |
| |
Competences |
(*) Class hours
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Hours outside the classroom
|
(**) Total hours |
| Introductory activities |
|
1 |
1 |
2 |
| Lecture |
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28 |
56 |
84 |
| Practical cases/ case studies in the classroom |
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14 |
14 |
28 |
| Problem solving, exercises in the classroom |
|
26 |
0 |
26 |
| Personal attention |
|
1 |
0 |
1 |
| |
| Extended-answer tests |
|
3 |
0 |
3 |
| Practical tests |
|
2 |
4 |
6 |
| |
(*) On e-learning, hours of virtual attendance of the teacher.
(**) The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies
| |
Description |
| Introductory activities |
Presentació de l'assignatura |
| Lecture |
Desenvolupament dels continguts |
| Practical cases/ case studies in the classroom |
Plantejament de problemes |
| Problem solving, exercises in the classroom |
Resolució d'exercicis que s'han plantejat amb anterioritat |
| Personal attention |
|
|
Description |
|
Atenció personal a l'aula , ajudant a la resolució dels exercicis.
Atenció personal al despatx per resoldre dubtes |
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Methodologies |
Competences
|
Description |
Weight |
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| Practical tests |
|
1 Global Test where it will be necessary to solve problems and answer theoretical questions. It will be
necessary to obtain a minimum of 3/10 points in this exam in order to get the
assessment of this course. |
40% |
| Extended-answer tests |
|
2 tests where it will necessary to solve exercises. The fits test can have a weight in the final evaluation between the 20% and 30%, to be decided by the professor, and the second will have also a weight between 20% or 30% in order to reach the total of 60% of the course.
These tests do not need to be a standard exam. The professors of the course may use any web application in order to get an accurate personalized evaluation. |
60% |
| Others |
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Other comments and second exam session |
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Second Evaluation : 1 global exam inclunding problems and theoretical questions (100%) |
| Basic |
M.A.Acebo , M.T.García , J.M.Jornet, Apunts d'Àlgebra, Tarragona, Tarragona
M.A.Acebo , M.T.García , J.M.Jornet, Problemes resolts d'Àlgebra, Tarragona, Tarragona
Stanley Grossman , Joel Ibarra, Álgebra Lineal, McGraw-Hill, 2016
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| Complementary |
Jesús Rojo , Isabel Martín, Ejercicios y Problemas de Álgebra Lineal, , Colección Schaum
Jorge Arvesu i altres, Problemas resueltos de Álgebra Lineal, , Ed.Paraninfo
Miguel A.Acebo i Josep M.Jornet, Exàmens resolts a la plana web :http://deim.urv.cat/~josepmaria.jornet/ETIE/welcome, ,
Juan Carlos del Valle, Álgebra Lineal, 1ª, Mc Graw-Hill
Roberto Benavent , Cuestiones sobre Álgebra Lineal, , Ed. Paraninfo
Mencía Bravo , José, Notas de Álgebra, , Copistería
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| Other comments |
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Requereix una dedicació constant, per part de l’alumne, tenint molta cura d’entendre els conceptes i de dedicar un temps a la resolució de problemes. |
(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation. |
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