Linear Algebra and Analytical Geometry I

Recommended Prerequisites

Good knowledge of High School Mathematics.

Teaching Methods

Theoretical-practical classes are mainly expository and include examples and exercises to apply the material being taught.

In practical classes students are given exercises and examples which should be worked during classes with the help of the teacher.

Extensive tutorial time is offered to the students to clarify their difficulties with the theory and to help them with the homework assignments and preparation for the exams.

Learning Outcomes

The main goal of this curricular unit is to teach  students concrete Linear Algebra. The more computational aspects of Linear Algebra (matrices, linear systems, Rn) are introduced, preparing students for more advanced courses. We expect that with this Linear Algebra course students understand the need of correct reasoning and of proofs in Mathematics.

The main competences to be developed are: ability for  generalization and abstraction; ability to formulate and solve mathematical problems; design and correctly use of  mathematical  models; logical reasoning; critical thinking; correct mathematical writing.

Work Placement(s)

No

Syllabus

1. Matrices. Basic operations.

2. Linear systems. Gaussian Elimination. Gauss-Jordan algorithm.

3. Determinants.

4. The vector space structure of Rn.

5. Inner product in Rn. Projections onto subspaces. Least squares approximations. Cross product in R3.

6. Analytic Geometry.

Head Lecturer(s)

João Filipe Cortez Rodrigues Queiró

Assessment Methods

Asseessment
Approval in this course unit requires to score at least 10 (out of 20). The students that perform, along the semester, the mid-term exams and the tests may be exempted from final examination. The sum of percentages corresponding to these two components is 100%. The other students have to be evaluated at the end of the semester through a written examination (exam). : 100.0%

Bibliography

A. P. Santana, J. F. Queiró, Introdução à Álgebra Linear, Gradiva, 2010