Linear Algebra and Analytical Geometry

Year
1
Academic year
2018-2019
Code
01001917
Subject Area
Basic Sciences
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
1st Cycle Studies

Recommended Prerequisites

High School Mathematics.

Teaching Methods

The theoretical lectures are predominantly expository. In practical classes the students will solve exercises under the guidance of the instructor. In the theoretical classes it will prevail a strong interaction between concepts and their practical application. The transformation of concepts into working tools will be achieved by encouraging personal work. The formal lectures will be complemented by periods of individual attendance.

Learning Outcomes

The main goal of the course is to introduce the basic concepts of Linear Algebra and Analytic Geometry, and provide the students with mathematical tools that are necessary for applications in other areas of mathematics and in engineering. The course will help students to develop logic reasoning and critical thinking and to learn basic methods of proof making.

Work Placement(s)

No

Syllabus

  1. Matrices and Systems of Linear Equations.
  2. Determinants.
  3. Vector Spaces.
  4. Linear Transformations.
  5. Vector Spaces with Inner Product.
  6. Eigenvalues, Eigenvectors and Diagonalization of Matrices.
  7. Geometric Applications in R2 and R3 (applications to classification of conics and quadrics). 

Head Lecturer(s)

Carlos Alberto de Carvalho Duarte Gamas

Assessment Methods

Final assessment
Exam: 100.0%

Continuous assessment
Mini Tests: 20.0%
Frequency: 80.0%

Bibliography

- Ana Paula Santana e João Filipe Queiró, "Introdução à Álgebra Linear", Gradiva Publicações, 2010.

- Luís T. Magalhães, "Álgebra Linear como Introdução a Matemática Aplicada", Texto Editora, 1989.

- Gilbert Strang , “Linear Algebra and its Applications”, Harcout Brace Jovanovich, San Diego, 1988.