Quantitative Methods I

Base Knowledge

12º ano de Matemática A

Teaching Methodologies

The teaching will have two components: exposition of the subjects and resolution of exercises in class. There will also be the possibility for students to have sessions to clarify doubts.

Learning Results

Develop and expand the skills of numerical and symbolic manipulation of expressions and develop the skills of formulating and solving problems in mathematical terms, stimulating critical capacity and the clear and rigorous presentation of the process and results.

Provide students with mathematical concepts and techniques within the scope of matrices and determinants, calculus in R and real functions of a real variable and series, which allow them to understand mathematics and its application to problem solving, namely in the areas of accounting , management and economics.

Implement the use of the graphical application GEOGEBRA to support the calculation and study of graphical representations of functions.


Introduction – language issues

1 Calculus in R (short review)

1.1 Numbers and stones

1.2 From N to R

1.3 The real line and the concept of the modulus of a number

1.4 Letters and Variables

1.5 Arithmetic

1.6 Fractions

1.7 Powers and radicals

1.8 Rounding

1.9 Percentages

1.9.1 Valuations and devaluations

1.10 Solving equations with one variable

2 Matrix Calculus

2.1 Matrix definition. Generalities

2.2 Operations with matrices. Invertible matrices

2.3 Condensation of matrices

2.3.1 Gauss-Jordan Elimination Method

2.3.2 Calculation of the inverse of a matrix

2.4 Systems of Linear Equations

2.4.1 Definitions. Generalities

2.4.2 Discussion and resolution of systems

2.5 Determinants

3 Real functions of real variables

3.1 Generalities

3.1.1 Elementary definitions

3.1.2 Cartesian references and graphical representations

3.1.3 Injectivity and zeros

3.1.4 Composition of functions and inverse function. Operations with functions

3.1.5 Monotony and extremes

3.2 Polynomial functions. Lines and parabolas

3.2.1 Constant function

3.2.2 Linear function

3.2.3 Linear models in economics

3.2.4 Quadratic function

3.3 Limits and continuity

3.3.1 Limits

3.3.2 Continuity

3.3.3 Limits at infinity and infinite limits

3.4 Exponential function and logarithmic function

3.4.1 Calculation of continuously compounded interest

3.5 Derivation of functions

3.5.1 Geometric definition and interpretation

3.5.2 Calculation of approximate values. Differentials

3.5.3 Marginal cost

3.5.4 Average change and instantaneous change

3.5.5 Derivative calculation. Derived function

3.6 Basic rules of derivation

3.7 Monotony, extremes and concavities

3.8 L’Hôpital’s Rule

3.9 Some examples applied to management and economics

4. Series

4.1 Sums and summations.

4.2 Numerical series: definitions and properties.

4.3 Arithmetic series and geometric series. Applications in finance.

4.4 Dirichlet series.

4.5 Convergence criteria

4.6 Polynomial approximation of functions – Taylor polynomial.

4.7 Applications to the area of ​​accounting and management.

Curricular Unit Teachers




– Bennett, J., Briggs, W., Using & Understanding Mathematics_ A Quantitative Reasoning Approach, Pearson (2015)

– Breda, A.d´A., Costa, J.N., Cálculo com Funções de Várias Variáveis, McGraw-Hill, 1996.

– Caraça, B. , Conceitos Fundamentais da Matemática, Ed. Gradiva, 1998 (2ª ed.).

– Carvalho, M., Métodos Quantitativos I, ISCAC – IPC, 2021(*)

– Goldstein, L.J., Lay, D.C., Schneider, D.I., Matemática Aplicada: Economia, Administração e Contabilidade, 8ª Edição, Bookman, 2000.

– Leon, S. J., Linear Algebra with Applications, Prentice Hall, New Jersey, 2002.

– J. Stewart, single variable calculus, Brooks/Cole Cengage Learning, ©2012 [2012]

– Silva, Jaime Carvalho e – Princípios de análise matemática aplicada. Lisboa : Editora McGraw-Hill de Portugal, 1994.

– Harshbarger, R. J. and Reynolds, J. J., Mathematical Applications for the Management, Life, and Social Sciences, 11th edition, Cengage Learning Brooks Cole, 2016.

– Stewart, J., Calculus: metric version, London: Cengage Learning Brooks Cole, 2015.

– Sydsæter, K., Hammond P., with Strøm, A., Essential mathematics for economic analysis, 4th ed., Pearson Education Limited, 2012.

(*) Basic bibliography.