Linear Algebra and Analytical Geometry

Recommended Prerequisites

Knowledge and mastery of subjects taught in Mathematics Secondary Education.  

Teaching Methods

Expository lecture followed by exercises resolution: the presentation of theoretical material is followed by practical applications for a better understanding and consolidation of the material just taught. Whenever possible, exercises in the area of Electronic Engineering are used.

Learning Outcomes

As a first formal contact students have with mathematical abstraction, the issues developed in this course require that various familiar mathematical examples are presented (in the sets of real and complex numbers) to introduce their generalizations to the generic concepts of matrix, vector space and linear transformation. These are mathematical tools that students learn with the primary purpose of their use in other areas of mathematics and applications in engineering (determinants, Gaussian elimination and the least square methods in solving linear systems, matrix diagonalization, matrix decomposition using singular values, application to solving systems of linear differential equations). Simultaneously, students are encouraged to develop critical thinking, to solve problems, to express their ideas accurately, in writing and orally, to work in groups and individually and develop the ability to learn independently, upon presentation of work done at home and exposed in the classroom. 

Work Placement(s)

No

Syllabus

1. Matrices. Matrix operations.

2. Systems of linear equations - Gauss elimination method.

3. Matrix inversion - Gauss-Jordan algorithm.

4. Determinants.

5. Vector Spaces.

6. Linear Transformations.

7. Vector Spaces with inner product. Least Squares Method.

8. Diagonalization of matrices.

9. Decomposition of matrices using singular values.

10. Geometric applications in R2 and R3

11. Applications to solving systems of linear differential equations  

Head Lecturer(s)

Ana Paula Jacinto Santana Ramires

Assessment Methods

Final assessment
Exam: 100.0%

Continuous assessment
Mini Tests: 30.0%
Frequency: 70.0%

Bibliography

Introdução à Álgebra Linear, Ana Paula Santana e João Filipe Queiró, Gradiva, 2010

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