Learning Results
The first chapter one involves the study of matrices, including matrix algebra and the resolution of linear equation
systems. This chapter aims at supplying the students with the knowledge of several resolution techniques of the
linear equation systems which allow them to follow other approaches in the resolution of problems in the field of
their graduation.
The second chapter aims at analysing real functions with two variables, involving definitions and properties, the
study of limits and continuity, the derivative computation, differentials and extremes, subject or not to equality
constraints. The main purpose is to allow students to be able to perform the study of real functions with two real
variables, in particular functions involved in problems of Management.
The last chapter focuses on the study of some numerical methods for the determination of zeros and extremes of
the functions, using namely the bisection method, the Newton’s method and the method of the golden number.
Program
I. Matrix algebra
1. Matrices
1.1. Matrix definition. Generalities
1.2. Operations with matrices
1.3. Transposing matrices
1.4. Condensing matrices and characteristic of a matrix. Gauss’s elimination method
1.5. Invertible matrices. Gauss-Jordan’s method
2. Linear equation systems
2.1. Definition. Generalities
2.2. Solving systems by the Gauss’s elimination method
2.3. Discussing systems
2.4. Solving systems by the inverse method
3. Determinants
4. Applications to Management
II. Real functions with two real variables
1. Definitions
2. Limits and continuity
3. Partial derivatives of the 1st order and 2nd order
4. Differentials. Computing approximate values
5. Derivative of the composed function
6. Derivative of the implicit function
7. Constrained extremes. Application of the method of Lagrange multiplier
8. Applications to Management
III. Numerical methods for real functions with real variable
1. Computing roots
2. Determination of extreme points
3. Applications to Management
Internship(s)
NAO
Bibliography
Os docentes da unidade curricular disponibilizam no moodle os textos de apoio de carácter teórico usados nas
aulas, assim como as folhas práticas e respectivas soluções.
Como bibliografia complementar, são aconselhados:
– A. P. Santana e J. F. Queiró, Introdução à Álgebra Linear, Gradiva, 2010
– M. Carvalho, Cálculo Matricial, ISCAC, Coimbra, 2005
– Larson, Holstetler and Edwards, Cálculo. Vol I e II, São Paulo. Ed McGraw Hill, 2006
– A.d’A. Breda e J.N. da Costa, Cálculo com Funções de Várias Variáveis, McGraw-Hill, 1996
– L.J. Goldstein, D.C. Lay e D.I. Schneider, Matemática Aplicada: Economia, Administração e Contabilidade,
Bookman, Porto Alegre, 8ª Edição, 2000
– C. Pires, Cálculo para Economistas, McGraw-Hill, 2001
– E. W. Swokowski, Cálculo com Geometria Analítica, Volume 1 e 2, Makron Books, Ltda., São Paulo, 2ª Edição, 1994
– R. L. Burden e J. D. Faires, Numerical Analysis, Thomson Brooks/Cole, 8th Edition, 2005