Linear Algebra and Analytical Geometry

Recommended Prerequisites

Basic knowledge of plane geometry, analytical geometry and elementary three-dimensional geometry. Elementary notions of set theory as well as the main properties of the real and complex number systems.

Teaching Methods

Detailed exposition lectures (using audiovisual means) of the concepts, principles and fundamental theories.  Resolution of some practical exercises filling the needed guidelines of the subject. In the tutorials it is intended that the student, under the guidance of teachers, solve practical application exercises.

Learning Outcomes

Concise study of   fundamental topics of linear algebra with some applications to analytic geometry (in R² and R³). The level of mathematical abstraction used is surpassed due to the presentation of various examples and reference to several applications.
The main purpose of this course is to provide the minimum linear algebra tools that allow the use of this new language in other areas of science.

Work Placement(s)

No

Syllabus

1. Matrices and Determinants   

2. Systems of Linear Equations

3. Vector Spaces and Linear Transformations

4. Vector spaces with inner product

5. Matrix Diagonalization

6. Analytical Geometry

Head Lecturer(s)

Joana Maria da Silva Teles Correia

Assessment Methods

Continuous
Presentation of three papers and realization of three frequencies: 100.0%

Final
Exam: 100.0%

Bibliography

[T.Oliveira-Martins] M Teresa F Oliveira-Martins, Álgebra Linear e  Geometria Analítica, Apontamentos das Aulas Teóricas,  DMFCTUC,  2011

[Santana-Queiró,2010] Ana Paula Santana, João Filipe Queiró, Introdução à Álgebra Linear, Gradiva, 2010

[Goodaire,2003] Edgar G. Goodaire, Linear Algebra, A Pure and Applied First Course, Pearson Education Inc, Prentice Hall, 2003

[S.Leon,2002] Steven J. Leon,  Linear Algebra with Applications, (Sixth Edition), Prentice Hall, New Jersey, 2002

[Strang,1988] Gilbert Strang, Linear Algebra and its Applications, Harcourt Brace Jovanovich Publishers, San Diego, 1988