Teaching Methodologies
The lessons will be held in class. Informatics means will be used. Lecturing is divided into two components:
classes dedicated to the presentation of theoretical concepts; lessons devoted to the resolution of practical
problems, including the use of software. The classes will be interspersed in a sequence that optimizes the
acquisition of skills.
The evaluation involves the accomplishment of a final exam. The final exam evaluation can be substituted by
the accomplishment of a set of partial tests, requiring mandatory a attendance rate of at least 75% over the
whole number of lessons.
Learning Results
The objectives of the discipline involve three chapters. All these chapters are strongly committed with
applications in the areas of management and enterprise sciences. In the first chapter, dedicated to numerical
methods, we study numerical techniques for finding zeros, maximums and minimums of functions on a single
variable. The resource to numerical techniques for the determination of extreme points is particularly important
in functions that do not present an exact form for the associated derivative function. The second chapter
focuses on matrix calculus, being mainly dedicated to efficiently solve systems of linear equations. The third
chapter is devoted to functions on two variables, aiming the calculation of maximums and minimums.
We intend that the student can acquire analytical and calculus tools in the scope of the proposed subjects, with
sight to the treatment and study of problems in the area of management and enterprise sciences.
Program
1. Numerical Methods for Functions on a Single Variable
Zeros
Bisection method
Newton’s method
Extreme points
Bisection method
Newton’s method
Practical applications to management sciences
2. Matrix Calculus
Matrices
Definitions
Matrix types
Operations with matrices. Inverse
Matrix condensation
GaussJordan
elimination method
Calculation of the inverse
Systems of linear equations
Definitions
Systems’ discussion and resolution
Systems’ resolution through the Gauss method
Determinants
Definition
Properties
Determinant calculation
Laplace’s theorem
Determinants applications
Matrix inverse calculation
Systems’ resolution. Cramer’s rule
3. Function on Two Variables
Definitions
Limits and continuity
1st order partial derivatives and nth order derivatives
Derivatives of composed functions
Optimization
Unconstrained extreme points
Equality constrained extreme points. Lagrange multipliers Practical applications to management sciences
Internship(s)
NAO
Bibliography
A.d’A. Breda e J.N. da Costa, Cálculo com Funções de Várias Variáveis, McGrawHill,1996.
L.J. Goldstein, D.C. Lay e D.I. Schneider, Matemática Aplicada: Economia, Administração e Contabilidade,Bookman, Porto Alegre, 8ª Edição, 2000.
R.J. Harshbarger e J. J. Reynolds, Matemática Aplicada: Administração, Economia e Ciências Sociais e
Biológicas, McGraw Hill Interamericana do Brasil, Ltda., 7ª Edição, 2006.
J.Leite, M. Carvalho, C. Neves, A.C. Amaro e P.C. Martins, Sebenta de Matemática I, 2006.
E.W. Swokowski, Cálculo com Geometria Analítica, Volume 1, Makron Books, Ltda., São Paulo, 2ª Edição,1994.
E.W. Swokowski, Cálculo com Geometria Analítica, Volume 2, Makron Books, Ltda., São Paulo, 2ª Edição,1994.