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Complements of Mathematical Calculation

Code 13993
Year 1
Semester S2
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements None.
Mode of delivery Face-to-face
Work placements Not applicable
Learning outcomes This course aims to promote the development of mathematical skills already acquired in the field of Matrix calculus, differential and integral, allowing the student 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:identify Linear Functions of Several Variables and solve practical problems involving this kind of functions; understand the notion of the Limit of a Real-Valued Function of Several Variables at a point; understand the notion of a Continuous Real-Valued Functions of Several Variables; compute Partial Derivatives and use them to solve practical problems; apply the Method of Lagrange Multipliers to extremum problems; solve pratical problems involving the Integral Calculus of Real-Valued Functions of Several Variables.
Syllabus 1. Vector Spaces: Definition and Examples; Subspaces and Spanning Sets; Linear Independence; Basis and Dimension;
2. Linear Functions of Several Variables: Definition and Examples; Matrix Representation of a linear function; Eigenvalues and Eigenvectors;
3. Real-Valued Functions of Several Variables: Domain and its geometric representation; Limits and Continuity; Partial Derivatives; Tangent Plane; Chain Rule; Extreme Values; Method of Lagrange multipliers;
4. Integration of Real-Valued Functions of Several Variables.
Main Bibliography 1. Main:
-Apontamentos de Matemática I, Ana Catarina Carapito, 2005.
-Textos de Apoio sobre Espaços Vectoriais e Aplicações Lineares, Rogério Serôdio.
-Introdução à Álgebra Linear, Reginaldo Santos (2010).
-Álgebra Linear, Isabel Cabral, Cecília Perdigão e Carlos Saiago. Escolar Editora, 2008.
-Cálculo Diferencial e Integral em R e Rn . Acilina Azenha e Maria Amélia Jerónimo. McGraw-Hill, 1995
2. Additional:
-Álgebra Linear com Aplicações, Howard Anton e Chris Rorres, 2001, 8ª Edição, Bookman.
-Cálculo para Economistas, Cesaltina Pires, McGraw-Hill, 2001.
-Cálculo, Volumes I e II, James Stewart, Thomson Learning, 2001.
Applied Mathematics for Business, Economics and Social Sciences, Frank S. Budnick,
McGraw-Hill, 1993.
-Funções Reais definidas em Rn: Exercícios e Aplicações, António Cerqueira e Paulo Vasconcelos, Litexa Editora, 1996.
-Introdução à Análise Matemática, J. Campos Ferreira, Fundação Calouste Gulbenkian, 1997.
Teaching Methodologies and Assessment Criteria Final grade: arithmetic mean grade of two written partial tests.

Each partial written test: 0-20.

Dates of the assessment
1st test: April 12th
2nd test: to be announced

Language Portuguese. Tutorial support is available in English.


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Eduardo Castro


Last updated on: 2024-04-16

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