Linear Algebra and Analytical Geometry

Recommended Prerequisites

High School

Teaching Methods

The classes are of theoretical and theoretical-practical type. The teaching methods in the theoretical components will be predominantly expository. In the practical components problems will be solved under the guidance of the teacher.

The strong interaction between concepts and their practical application must be discussed, giving as much as possible a central role in the visualization and analysis of particular situations before making a progressive abstraction of the concepts being introduced.

Some tutorial support will be available to help the students solving the proposed tasks.

Learning Outcomes

To provide the students with the basic knowledge of Linear Algebra and Analytical Geometry. Namely, to solve linear systems of equations, to perform algebraic operations with matrices, understand and relate fundamental concepts and results on vectorial spaces, to determine orthogonal projections and understand their importance in the context of mathematical optimization, to understand and compute eigenvalues and find the spectral decomposition of a matrix. It is also intended that students acquire a knowledge of the concepts in order to assess the scope and limitations of the materials studied and their applications.

The course aims at developing the following skills: analysis and synthesis, organization and planning, oral and written communication, problem-solving skills and computational ability. On the personal level it also allows to develop self-learning skills and independent thinking.

Work Placement(s)

No

Syllabus

Matrices.

Solving of linear systems of equations – the Gaussian elimination method.

Inversion of matrices.

Determinants.

$\bkR^n$ and its subspaces: linear Independence, base and dimension, linear transformations, inner product, least squares method.

Diagonalization of matrices. Application to linear differential equations.

Head Lecturer(s)

João Luís Cardoso Soares

Assessment Methods

Assessment
- Problem solving [0-50%] - Tests [0-50%] - Midterm exams [0-100%] - Exam [0-100%]: 100.0%

Bibliography

• Ana Paula Santana e João Filipe Queiró, Introdução à Álgebra Linear, Gradiva, 2010.
• Gilbert Strang, Linear Algebra and Its Applications,  Harcourth Brace Jovanovich, 3rd ed, 1988.