| Code |
12674
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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 and determine 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;
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. Eigenvalues and eigenvectors.
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Main Bibliography |
- Análise Real, Funções de uma variável, Volume 1. Elon Lages Lima. Oitava Edição. Coleção Matemática Universitária (2006).
-Matemática para Economistas. Kevin Wainwright e Alpha C. Chiang.Editora Campus 2006;
-Matemática para Economistas. Carl P. Simon, Lawrence Blume. Trad. Claus Ivo Doering. Bookman 2006;
-Cálculo Vol.I. James Stewart. 5. ed- São Paulo. Editor Cengage Learning 2006;
-Álgebra linear com aplicações. Anton, Howard 8ª ed. Editor Porto Alegre. 2012.
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Language |
Portuguese. Tutorial support is available in English.
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