Algebra
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2010/2011 - 1S
Cycles of Study/Courses
Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
MIEIC |
156 |
Syllabus since 2009/2010 |
1 |
- |
5 |
70 |
135 |
Teaching language
Suitable for English-speaking students
Objectives
SPECIFIC AIMS:
This discipline has two main objectives: the promotion of logical reasoning and methods of analysis and the introduction and theoretical development of a set of concepts that will be fundamental to support the study of other disciplines along this course of studies.
LEARNING OUTCOMES:
Learning Outcomes:
At the end of the semester, students should be:
1. capable of analysing and solving systems of linear equations;
2. acquainted with basic matrix operations and its properties;
3. capable of defining a non-singular matrix and be acquainted with the properties of an inverse matrix and its calculation;
4. capable of defining the determinant of a matrix and be acquainted with its properties and calculation;
5. capable of defining vector space, vector subspace and Euclidian space;
6. capable of defining linear combination of vectors, linear independence/dependence vectors and subspace;
7. capable of defining and determining a base and the dimension of a vector space; be capable of obtaining the components of a vector in relation with its base;
8. capable of defining a linear transformation and calculate and characterize its kernel; be acquainted with algebraic operations and define and calculate inverse transformation;
9. capable of using a matrix to represent a linear transformation and operate linear transformations using matrix algebra;
10. capable of defining a change of base matrix and apply it to problems of change of base that involve elements of a vector space and linear transformations;
11. capable of defining similar matrices and be acquainted with their properties;
12. capable of calculating eigenvalues and eigenvectors of linear transformations and to be acquainted with their properties, and if possible identify a diagonal matrix representation for a linear transformation.
Program
Definition of vector space
Vector subspaces
Linear dependence and independence
Bases and dimension
Components
Inner product
Euclidian spaces
Norms and orthogonality
Linear spaces of matrices
Product of matrices
Transposed matrix
Inverse matrix
Square matrix
Orthogonal matrix
Similar matrices
Change of bases matrices
Determinants
Condensation method and Laplace theorem
Inversion of matrices using a determinant
Systems of linear equations
Gaussian method of elimination
Cramer’s rule
Linear transformation
Kernel
Algebraic operations with linear transformations
Injective linear transformations
Matrix representation of a linear transformation
Isomorphism between linear transformations and matrices
Eigenvalues and eigenvectors of linear transformations
Characteristic polynomial
Conditions for the existence of diagonal matrix representation and linear transformation
Mandatory literature
Anton, Howard;
Elementary linear algebra. ISBN: 0-471-44902-4
Apostol, Tom M.;
Calculus. ISBN: 84-291-5001-3
Barbosa, José Augusto Trigo;
Noções sobre matrizes e sistemas de equações lineares. ISBN: 972-752-069-3 972-752-065-0
J.A. Trigo Barbosa; ALGA - Apontamentos Teórico-Práticos
J.A. Trigo Barbosa, J.M.A. César de Sá, A.J. Mendes Ferreira; ALGA - Exercícios Práticos
Complementary Bibliography
Luís, Gregório;
Álgebra linear. ISBN: 972-9241-05-8
Ribeiro, Carlos Alberto Silva;
Álgebra linear. ISBN: 972-8298-82-X
Monteiro, António;
Álgebra linear e geometria analítica. ISBN: 972-8298-66-8
Teaching methods and learning activities
Theoretical classes: detailed exposition of the program of the discipline illustrated by application examples. Theoretical-practice classes: application of the theoretical concepts in the resolution of several exercises that can be found in the proposed literature.
Evaluation Type
Distributed evaluation without final exam
Assessment Components
Description |
Type |
Time (hours) |
Weight (%) |
End date |
Attendance (estimated) |
Participação presencial |
65,00 |
|
|
First Examination |
Exame |
2,00 |
|
|
Second Examination |
Exame |
2,00 |
|
|
3rd Examination |
Exame |
3,00 |
|
|
|
Total: |
- |
0,00 |
|
Amount of time allocated to each course unit
Description |
Type |
Time (hours) |
End date |
Weekly study hours |
Estudo autónomo |
39 |
|
Preparation for exams |
Estudo autónomo |
24 |
|
|
Total: |
63,00 |
|
Eligibility for exams
According to General Evaluation Rules of FEUP
Calculation formula of final grade
Students have to attend to three mini-tests.
Final mark will be based on the average mark of the three exams.
The dates of the mini-test and the final exam have not yet been set.
The exams are closed book exams.
Examinations or Special Assignments
Students have to attend to three mini-tests.
Final mark will be based on the average mark of the three exams.
The dates of the mini-test and the final exam have not yet been set.
The exams are closed book exams.
Special assessment (TE, DA, ...)
Although working students are exempt from classes, they must do the mini-tests
Classification improvement
During the final mini-test, students can improve the first and second mini-test.
Observations
Students are not allowed to use a graphics calculator on the exam.