Mathematics for economics and management II

Recommended Prerequisites

NA

Teaching Methods

The classes will include a theoretical exposition part illustrated through examples (using slides and programs with algebraic and graphic functions), as well as a practical part, in which exercises and problems will be carried out. The articulation between theory and practice is enhanced through this type of classes, which can be complemented by the occasional realization of theoretical conceptual questionnaires. Additionally, the ability to develop autonomous work will be encouraged, through weekly work plans, with adequate tutorial monitoring.

Learning Outcomes

This curricular unit aims to present the basics of Linear Algebra and Differential Calculus of functions of several variables usually applied in the different areas of Economics and Management. Specifically, concerning Linear Algebra, it is expected that the student knows and understands the concepts of vector and matrix and the rudiments of matrix algebra, the methods of solving systems of linear equations, highlighting the Gaussian elimination, the concept of determinant, its properties and applications, the concept of quadratic form and its classification. Regarding Calculus, it is expected that the student knows and understands the main concepts related to real functions of several real variables, as well as those related to the double integral. It is also expected that the student demonstrates mastery of these concepts, using techniques that derive from them and their properties in exercises and problems, with particular emphasis on applications to Economics and Management.

Work Placement(s)

No

Syllabus

1. Linear algebra

1.1. Vectors and matrices

1.2 Linear systems of equations

1.3 Determinants

1.4 Quadratic forms

2. Calculus

2.1 Differential calculus of real valued functions in several variables

2.1.1 Definition, domains, graphic representation. Topologic notions in Rn.

2.1.2 Partial derivatives, gradient vector and Hessian matrix. Interpretations.

2.1.3 Diferenciability, tangent plane and linear approximation, directional derivative.

2.1.4 Homogeneous functions.

2.1.5 Chain rule and implicit functions.

2.1.6 Quadratic Taylor polynomial.

2.1.7 Otimization without and with restrictions.

2.2 Double integrals

2.2.1 Definition, computation and interpretation.

2.2.2 Inversion in the order of integration.

2.2.3 Change of variables in the double integral.

Head Lecturer(s)

Pedro Manuel Cortesão Godinho

Assessment Methods

Assessment
Periodic or by final exam as given in the course information: 100.0%

Bibliography

BINMORE, Ken; DAVIES, Joan: Calculus: concepts and methods. Cambridge: Cambridge University Press, 2007.

LARSON, Ron; HOSTETLER, Robert P.; EDWARDS, Bruce H.: Cálculo. Vols. 1 e 2, 8ª ed.. São Paulo: McGraw-Hill Interamericana do Brasil, 2006.

LIMA, T. P.: Lições de álgebra linear, 2ª ed., Imprensa da Universidade de Coimbra, 2014.

LIMA, Teresa Pedroso de; MARQUES, Jorge: Lições de Matemática II. Coimbra: Imprensa da Universidade de Coimbra, 2017.

SARAIVA, Maria dos Anjos Fonseca ; SILVA, Maria Aldina Carvalho: Cálculo diferencial em Rn : resumo da teoria, exercícios resolvidos, exercícios para resolver. 2ª ed., reimp.. Coimbra : Livraria Almedina, 2000

SARAIVA, Paulo: Cálculo I: apontamentos teóricos e folhas práticas. Coimbra: FEUC, 2022.

SARAIVA, Paulo: Cálculo II: apontamentos teóricos e folhas práticas. Coimbra: FEUC, 2022.

SYDSAETER, Knut; HAMMOND, Peter J.: Essential mathematics for economic analysis. Harlow: Pearson Education, 3rd ed., 2008.