Álgebra Linear e Geometria Analítica

Contents covered in Mathematics in primary and secondary education.

The following teaching methodologies are used in this curricular unit

1) Verbal methods (say), making use of the following educational resources: Exposition, Explanation, Dialogue and questioning;

2) Intuitive Methodologies (show), making use of the following educational resources: Demo, Audiovisual, written texts;

3) Active Methodologies (doing), making use of pedagogical resources: problem solving; technology.

Students should be able to:

1. 1. operate with matrices and calculate determinants;
1.2. discuss and solve systems of linear equations using matrix representation and selecting appropriate methods;
1.3. relate concepts associated with matrices and determinants deducing properties;
1.4. apply concepts and properties associated with matrices and determinants in problem solving;
2.1. identify and describe geometric objects in the plane and in the space;
2.2. relate concepts and characteristics of geometric objects in order to characterize other objects, to characterize the relative position of two objects and to calculate distances in the plane and in space;
3.1. identify a vector space, recognizing this structure in the most common examples;
3.2. deduce and apply the properties of a vector space;
3.3. characterize the concepts associated with vector spaces and relate them to other content;
4.1. characterize a linear application;
4.2. Use different ways of representing a linear application;
4.3. Identify and relate the properties of a linear application.

I – Matrices and Systems of Linear Equations

II – Determinants and Systems of Linear Equations

III – Vectors in IRⁿ

IV – Vector Spaces

V – Linear transformations

• - Individual Written Exams - 100.0%

• - Individual Written Exams - 100.0%

NAO

Anton, H., Rorres, C., & Kaul, A. (2020). Elementary linear algebra, Applications version (12th Edition). Ed.,Wiley.

Banchoff, T. & Werner, J. (1992). Linear algebra through geometry (2ª Ed.). Springer-Verlag.

Cabral, I., Perdigão, C., & Saiago, C. (2012). Álgebra linear (3ª Ed.). Escolar Editora.

Dias Agudo, F. R. (1996). Introdução à álgebra linear e geometria analítica. Escolar Editora.

Giraldes, E., Fernandes, V. H. & Smith, M. P. M. (1997). Curso de álgebra linear e geometria analítica. McGraw-Hill.

Magalhães, L.T. (1998). Álgebra linear como introdução à matemática aplicada. Texto Editora.

Steven, J. L. & de Pillis, L. (2020). Linear algebra with applications (10th Ed.). Pearson.

Strang, G. (2023). Introduction to Linear Algebra (6th ed). Wellesley-Cambridge Press. ISBN : 978-17331466-7-8.

Khan Academy. https://www.khanacademy.org/math.