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Presentation
Presentation
The present curricular unit belongs to the curricular plan of this 1st cycle degree. The main goal of this curricular unit is to provide students with fundamental knowledge in the context of algebra and mathematical and logical reasoning, that are essential in learning the contents of other subsequent curricular units. It is intended that, through various theoretical and practical strategies, students can apply and solidify the knowledge gained throughout the semester on complex numbers, vector spaces, matrices, determinants, systems of linear equations, eigenvectors and eigenvalues and linear transformations.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 6
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULP732-61
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
1. Review of sets and complex numbers. MATLAB software environment. 2. Matrices: classification, properties, and operations. Matrix rank. Inverse of a matrix. Matrix equations. 3. Determinants: definitions and properties; calculation using Sarrus’ Rule, Laplace’s Theorem, and the triangularization method; finding the inverse using the adjugate. 4. Systems of equations: classification and methods of solution. 5. Vector spaces: vectors and operations; definition and properties; linear combination; linear dependence and independence; vector subspace; generating set; basis and dimension of a vector space; change of basis. 6. Eigenvalues and eigenvectors: definition, properties, and determination. Diagonalization. Quadratic form. Applications. 7. Linear transformations: kernel and image. Matrix representation of a linear transformation.
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Objectives
Objectives
At the end of this course, students should have acquired knowledge about: - Operate with complex numbers in different forms. - Operate with matrices to solve equations and calculate the matrix inverse of a matrix. - Calculate the value of the determinant of a matrix. - Solve a system of equations by applying the knowledge matrix. - Analyze a system of equations using the knowledge matrix and on vector spaces, assessing their possible solution. - Characterize real linear spaces, mastering the concept of linear dependence and independence of vectors, a basis to characterize and define the coordinates of a given vector basis. - Determine and work eigenvectors and eigenvalues. - Work with linear transformations. - To become familiar with the Matlab environment and learn how to apply it to analyze the topics covered in this course unit.
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Teaching methodologies and assessment
Teaching methodologies and assessment
This UC will use some active methodologies that promote greater student involvement in pedagogical activities, such as Flipped Classroom ans learning in a collaborative environment. In terms of digital technologies, Moodle and MATLAB will be used.
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References
References
- Giraldes, E., Fernandes, V., Smith, M. (2003), Curso de Álgebra Linear e Geometria Analítica, McGraw Hill, Portugal. - Kreyszig, E. (2011), Advanced Engineering Mathematics (tenth edition), McGraw Hill, United States of America. - Diversos textos de apoio a fornecer ao longo das sessões.
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Office Hours
Office Hours
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Mobility
Mobility
No
