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ISCTE-IUL  >  Education  >  LETI , LEI , LEI-PL

Linear Algebra, Analytic Geometry and Vector Analysis (1 º Sem 2019/2020)

Code: L0143
Acronym: L0143
Level: 1st Cycle
Basic: No
Teaching Language(s): English, Portuguese
Friendly languages:
Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1 6.0 0.0 h/sem 54.0 h/sem 0.0 h/sem 0.0 h/sem 0.0 h/sem 0.0 h/sem 1.0 h/sem 55.0 h/sem 95.0 h/sem 0.0 h/sem 150.0 h/sem
Since year 2018/2019
Pre-requisites NA
Objectives Matrices became an elementary and essential tool in the formulation of many problems in science, engineering and mathematics. This course is aimed to give the basics of linear algebra, particularly matrix theory, and its applications in "real life" problems.
Program 1. Vectors and Systems of linear equations
1.1 The vector space R^n.
1.2 Linear combination and independence.
1.3 AX=B notation and systems of linear equations.
1.4 Gaussian elimination. Classification.

2. Matrices
2.1 The vector space M_{m x n}.
2.2 Product, transpose and inverse of matrices.
2.3 Systems of linear equations: matrix form Ax=b.

3. Determinants
3.1 Definition. Areas and volumes.
3.2Computing the inverse.

4. Vector spaces
4.1 Definition. Image and kernel.
4.2 Linear Independence. Bases and dimension. Coordinates.

5. Linear maps
5.1 Definition.
5.2 Matrix of a linear map.
5.3 Base change.

6. Eigenvalues and eigenvectors
6.1 Definition. Eigenspaces.
6.2 Diagonalization. Computing A^n.


7.Inner Product Spaces
7.1 Inner Product and Norm.
7.2 Orthogonal Bases.
7.3 Orthogonal Projections.
7.4 Quadratic forms.
Evaluation Method Periodic Evaluation: 1 midterm Test (45%) and a partial Exam in the 1st examination period (45%); 8 online tests (10%). Minimum grade of 8.0 for each one.
Final Evaluation: A final exam (100%) either in the 1st or the 2nd examination period.
Minimum grade for this course: 10.
Teaching Method LM1. Expositional: presentation of the theoretical concepts.
LM2. Participative: each theoretical concept will be illustrated with examples and exercises and, whenever possible, applications to engineering and "real life" problems.
LM3. Autonomous work: individual study should be complemented with the bibliography below and by solving exercises and problems given by the lecturer, according to the Class Planning.
Observations First grading scheme rules
1. A Student will be excluded from the First grading scheme (in which case he or she will be automatically in the Second grading scheme) if he or she:
a. Has not done 5 or more online tests;
b. Has a grading less or equal to 8.0 in the midterm test or in the final test;
c. Has been engaged in any fraud regarding the UC.
2. Missing online tests have a zero grade.
3. Online tests:
a. There are 10 online tests during the semester available at e-learning. Students have up to 30 minutes to complete each online test, which will be kept for one week.
b. The grading will be as follows: the 8 highest grades are the only ones that count for the arithmetic mean.
c. Any failure to access e-learning do not change the online tests schedule. We strongly recommend students to avoid last day to submit their answers.
4. Students repeating the UC are subject to the same rules and may choose First or Second grading scheme.

All the information regarding this UC, including handouts and homework assignments are
available from https://e-learning.iscte-iul.pt/.
Basic Bibliographic Nakos, G., Joyner, D., Linear Algebra With Applications, Brooks/Cole Publishing Company, 1998.

Strang, G., Introduction to Linear Algebra, Wellesley-Cambridge Press, 2009.

Elementos de apoio fornecidos pelos docentes.
Complementar Bibliographic Blyth, T.S. and Robertson, E.F. "Basic Linear Algebra", Springer, 2002.

Blyth, T.S. and Robertson, E.F. "Further Linear Algebra", Springer, 2002.

Curtis, C. W. Linear Algebra: An Introductory Approach, Springer, 1984.

Lipschutz, S., Álgebra Linear, Schaum's Outline Series, McGraw-Hill, 2004.

Magalhães, L., Álgebra Linear, como Introdução a Matemática Aplicada, Texto Editora, 1998.