Linear Algebra and Analytical Geometry

Recommended Prerequisites

Knowledge and mastering of topics that were taught in Mathematics in High school.

Teaching Methods

This curricular unit comprises:
(i) 45 hours of theoretical lecture classes.
(ii) 30 hours of theoretical and practical classes in which students are required to present to their classmates the solved exercises that were prepared at home.
(iii) the emergence of weekly tutorial classes (to clarify students’ doubts).

Learning Outcomes

Given the fact that this is the first formal contact students have with mathematical abstraction, the topics to be developed in this curricular unit require that different mathematical examples, that students are able to master, are presented and their generalizations in order to introduce the generic concepts of matrix, vector space and linear transformation. These are the mathematical tools that students will develop with the main objective of using them in other mathematical areas and apply them in Engineering (determinants, method of Gaussian elimination and the method of least squares in the resolution of linear systems, matrix diagonalization).
Generic competences in:
analysis and summary
organization and planning
oral and written communication
solve problems
critical thinking
communicate with people who are not specialists in the field
understand the language of other specialists
autonomous learning
apply the theoretical knowledge in practice
self-criticism and self-assessment.

Work Placement(s)

No

Syllabus

1. Matrices – Operations with matrices.
2. Systems of Linear Equations - Method of Gaussian elimination.
3. Matrices inversion – Gauss-Jordan Algorithm.
4. Determinants.
5. Vector Spaces.
6. Linear transformations.
7. Vector Spaces with Intern Product. – The method of least square.
8. Matrix diagonalization.
9. Geometric applications in R2 and R3.

Head Lecturer(s)

Margarida Maria Lopes da Silva Camarinha

Assessment Methods

Contnuous
Mini Tests: 10.0%
Frequency: 90.0%

Assessment
Exam: 100.0%

Bibliography

Referências Principais

Ana Paula SANTANA, João QUEIRÓ (2010) Introdução à Álgebra linear.Trajectos Ciência, 10. Gradiva.

Seymour LIPSCHUTZ (1972) Álgebra linear, McGraw-Hill.

Referências Complementares

GOODAIRE, Edgar (2003). Liner Algebra: A Pure and Applied First Course. Prentice Hall, Pearson Education Inc.

LEON, Steven J. (2002).  Linear Algebra with Applications. New Jersey: Prentice Hall.

MAGALHÃES, Luís T. (1989). Álgebra Linear como Introdução a Matemática Aplicada. Texto Editora.

STRANG, Gilbert (1988). Linear Algebra and its Applications, San Diego: Harcout Brace Jovanovich.