Quantitative Methods Applied to Business Sciences I

• Operate on the set of real numbers.
• Elementary notions of real fuctions of a 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.

The goal of this curricular unit is to provide students with mathematical tools and skills that give them the ability to calculate, understand, interpret and solve questions, not only in the context of other curricular units that are part of the course’s syllabus, but also within the scope of the professional activity that they may perform, following the skills granted by the degree they propose.

1. Real Functions of Real Variable

1.1. Definitions and generalities.
1.2. Limits and continuity.
1.3. Applications in the context of finance and accounting.
1.4. Derivatives.

1.4.1. Definition and geometric interpretation.

1.4.2. Derivation rules.

1.4.3. Differentials – determination of approximate values.

1.4.4. Optimization problems.

1.4.5. Applications in the context of finance and accounting.

1.5. Taylor polynomial – determination of approximate values and applications in the context of finance and accounting.

2. Numerical methods – determination of approximate values of zeros andextremes of a real function of a real variable.

2.1 Bisection Method.
2.2 Newton’s Method
2.3 Applications in the context of finance and accounting.

NAO

Essential bibliography.

• Carvalho, Margarida Abreu de, Métodos Quantitativos I, ISCAC-IPC, 2019.
• Carvalho, Margarida Abreu de, Métodos Quantitativos II, ISCAC-IPC, 2019.
• Goldstein, L.J., Lay, D.C., Schneider, D.I., Matemática Aplicada: Economia, Administração e Contabilidade, 8ª Edição, Bookman, 2000.
• Harshbarger, R. J. and Reynolds, J. J., Mathematical Applications for the Management, Life, and Social Sciences, 11th edition, Cengage Learning Brooks Cole, 2016.
• Rocha, Conceição, Métodos Quantitativos Aplicados às Ciências Empresariais I, ISCAC-IPC, 2023.

Complementary bibliography.

• Bennett, J., Briggs, W., Using & Understanding Mathematics, A Quantitative Reasoning Approach, Pearson 2015.
• Caraça, B., Conceitos Fundamentais da Matemática, Ed. Gradiva, 1998 (2ª ed.).
• James Stewart, Calculus: metric version, 8th ed., London: Cengage Learning Brooks Cole, 2015. 
• Sydsæter, K., Hammond, P., Arne Strom, A., Essential Mathematics for Economic Analysis,  4th ed, Pearson, 2012.