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Presentation
Presentation
Provides a wide range of basic mathematical knowledge, skills and tools essential for Engineering studies.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 5
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULHT39-61
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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
Properties of real numbers and complex numbers. Types of matrices. Matrix operations. Matrix algebra. Transposed, symmetrical, and hemi-symmetrical.
Systems of linear equations. Gauss elimination. Linear independence. Rank. Invertible matrices.
Determinants. Laplace's theorem. Cramer's Rule.
Eigenvectors and eigenvalues.
Vector spaces. Subspaces. Base and dimension.
Linear transformations. Injective and surjective transformations. Image and kernel. Matrix of a linear transformation. Vector spaces with internal product.
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Objectives
Objectives
Operate with matrixes. Master the properties of matrix operations. Distinguish several types of matrices and identify their properties. Condense and reduce matrices. Analyse the nature of systems of linear equations and solve them whenever possible. Determine eigenvalues and eigenvectors and take advantage of its properties. Recognize vector spaces and their properties. Know the concepts of linear independence and their properties. Learn how to analyse linear transformations. Determine properties of vector sets in internal product spaces.
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Teaching methodologies and assessment
Teaching methodologies and assessment
Series of exercises will be proposed with the aim of consolidating knowledge and stimulating problem-solving skills. The evaluation of the discipline, expressed on a scale from 0 to 20 points, will be made at different times, including 2 midterms (40% + 50%) and individual work to be developed outside the classroom (10%). If the weighted average of these evaluations is equal to or greater than 9.5, the student will be successful in the subject, otherwise the student will be able to attend a global frequency. In the final exam, the student can improve the grade. The minimum passing grade for these assessments is also 9.5. Assessment criteria are explained at the beginning of the semester.
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References
References
Cabral, I., Perdigão, C., Saiago, C. - Álgebra Linear., 5ª ed., Lisboa: Escolar Editora, 2018
Strang, G. - Linear Algebra, 5ª ed., MA: Wellesley-Cambridge Press, 2016
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Office Hours
Office Hours
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Mobility
Mobility
No