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Complements of Mathematical Calculation

Complements of Mathematical Calculation

Code	12679
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.
Language	Portuguese. Tutorial support is available in English.