| Code |
13988
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Solid Mathematics knowledge of high school.
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Mode of delivery |
Face-to-face
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Work placements |
Not applicable
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Learning outcomes |
This course aims to promote the learning of mathematical concepts in the field of matrix and integral calculus, and the development of skills to enable students to understand and use mathematics as a tool to aid in solving practical problems.
At the end of curricular unit, the student should be able to: understand the concepts of the continuity and differentiability of a Function of One Variable and apply the standard results about continuous and differentiable Functions of One Variable; solve problems involving the Integral Calculus of Functions of One Variable; apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix and calculating the Determinant of a matrix; solve Systems of Linear Equations by using Gaussian Elimination and Cramer Rule.
Eigenvalues and eigenvectors.
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Syllabus |
1.. Functions of One Variable: Domain and Graph; Exponential and Logarithmic Function; Limits and Continuity; Differentiation: Rules; Cauchy Rule and Indeterminations; Weierstrass Theorem; Differential; Extreme Values;
2. Integration of Functions of One Variable: Indefinite Integral/Antiderivative; Integration Techniques; Applications of the Definite Integral; Improper integrals.
3. The Set of Complex Numbers: Definition and Examples, Geometric Representation, Operations with Complex Numbers;
4. Systems of Linear Equations and Matrices: Introduction to Systems of Linear Equations; Gaussian Elimination; Matrix Operations; Inverse Matrix; Diagonal, Triangular and Symmetric Matrices;
5. Determinants: Determinant Function; Properties of the Determinants; Cramer Rule.
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Main Bibliography |
-Cálculo Vol.I. James Stewart. 5. ed- São Paulo. Editor Cengage Learning 2006;
-Curso de Análise Vol. 1. Elon Lages Lima. Projeto Euclides 2004;
-Matemática para Economistas. Kevin Wainwright e Alpha C. Chiang.Editora Campus 2006;
-Matemática para Economistas. Carl.P.Simon, Lawrence Blume. Trad. Claus Ivo Doring. Bookman 2006.
-Álgebra linear com aplicações. Anton, Howard 8ª ed. Editor Porto Alegre. 2012.
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Teaching Methodologies and Assessment Criteria |
Students will have to attend at least 70% of classes. Students who were enrolled in the 22/33 academic year and student workers have automatic attendance.
The UC will operate under a continuous Assessment regime. Two written tests at 20 points each will be carried out. The final grade of the continuous assessment will be the arithmetic average of the test classification.
Students who fail the continuous assessment will be able to take the final exam as long as they attend the UC.
Students with a final grade greater than or equal to 18 points (through continuous assessment or final exam) must take a grade defense test. Failure to take this test implies a final grade of 17 points for the curricular unit.
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Language |
Portuguese. Tutorial support is available in English.
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