Quantitative Methods Applied to Business Sciences II

• Operate on the set of real numbers.
• Elementary notions of real functions of real variable.

Classroom lessons.

Expository teaching method and practical component of solving exercises.

Proposed resolution of exercises with monitoring by the teacher.

Proposed exercise resolution autonomously.

Use of software that combines various mathematical concepts.

Goals:

The aim of this curricular unit is to provide students with mathematical tools and concepts that will give them the ability to calculate, understand, interpret and solve questions, not only in the context of other curricular units that make up the course syllabus, but also in the context of the professional activity they may carry out following the skills granted by the degree they are aiming for.

Skills:

In each topic of the programme, students develop skills such as:

• Evaluation of profit and loss areas;
• Evaluating financial investments;
• Organising, operating, manipulating and analysing data;
• Analysing financial graphs;
• Analysing the sensitivity of financial models;
• Maximising profits;
• Cost minimisation;
• Resource optimisation.

1. Integrals.

1.1 Definition and calculation.

1.2 Differential equations.

1.3 Area measurement of flat regions.

1.4 Calculation of approximate values: trapezoid rule.

1.5 Applications in the context of finance and accounting.

 2. Matrices.

2.1 Generalities about matrices:

2.1.1 Operations with matrices.

2.1.2 Characteristics of a matrix.

2.1.3 Inverse matrix: Gauss-Jordan method.

2.1.4 Determinant of a matrix.

2.2 Solving and discussing systems of linear equations.

2.3 Applications in the context of finance and accounting.

3. Real functions of two real variables.

3.1 Generalities.

3.2 Partial derivatives.

3.2.1 Geometric definition and interpretation.

3.2.2 Calculation of approximate values: differentials.

3.2.3 Applications in the context of finance and accounting.

3.3 Optimization

3.3.1 Determination of simple extremes.

3.3.2 Determination of conditioned extremes: Lagrange multipliers method.

3.3.3 Applications in the context of finance and accounting.

NAO

Essential bibliography.

• Breda, A.d´A., Costa, J.N., Cálculo com Funções de Várias Variáveis, McGraw-Hill, 1996.
• Carvalho, Margarida Abreu de, Métodos Quantitativos I, ISCAC-IPC, 2019.
• Goldstein, L.J., Lay, D.C., Schneider, D.I., Matemática Aplicada: Economia, Administração e Contabilidade, 8ª Edição, Bookman, 2000.

Complementary bibliography.

• Harshbarger, R. J. and Reynolds, J. J., Mathematical Applications for the Management, Life, and Social Sciences, 11th edition, Cengage Learning Brooks Cole, 2016.
• James Stewart, Calculus: metric version, 8th ed., London: Cengage Learning Brooks Cole, 2015.
• Leon, S. J., Linear Algebra with Applications, Prentice Hall, New Jersey, 2002.
• Silva, Jaime Carvalho e, Princípios de análise matemática aplicada, Lisboa: Editora McGraw-Hill de Portugal, 1994.
• Tan, S.T., Matemática Aplicada à Administração e Economia, Pioneira Thomson Learning, 2001.