Teaching Methodologies
The classes for this curricular unit are of a theoretical-practical nature.
Initially, the classes will have a more expository character, aiming to establish the theoretical foundations of the topics covered, followed by
the practical component, which involves solving proposed problems and exercises. The presentation and exploration of techniques and
concepts will be supported, whenever possible, by appropriate software to enhance understanding of the topics.
In parallel, applications of theoretical concepts to the fields of social and human sciences will be presented, with a particular focus on
economics and management.
ME1. Expository: Presentation of theoretical concepts with illustrative examples.
ME2. Participatory: Analysis, discussion, and resolution of proposed exercises.
ME3. Active: Solving tests, exams, and group work.
ME4. Autonomous Work: Reading and understanding the recommended bibliography and solving exercises provided by the instructor.
Learning Results
This unit aims to equip students with key tools in matrix calculus and calculus of functions of two variables, emphasizing applications in
economics and management, while building essential mathematical foundations for future courses.
The specific learning objectives are:
OA1. Introduce matrix language as a calculation tool; familiarize students with various techniques for solving systems of linear equations
that allow for alternative approaches in problem-solving within the field of study.
OA2. Understand the fundamental concepts related to the study of real functions of two real variables enabling students to apply these
concepts in practical real-life situations, particularly in their field of study; enhance students’ skills in abstract and logical reasoning, as well
as their ability to express themselves clearly and precisely using rigorous language.
Program
1. CP1. Matrix Calculus
1.1. Definition of a matrix. Generalities
1.2. Operations with matrices
1.3. Matrix condensation and characteristics. Gauss elimination method
1.5. Invertible matrices. Gauss-Jordan method
1.6. Systems of linear equations. Discussion and resolution using matrices
1.7. Determinants
2. CP2. Differential Calculus in IR2
2.1. Preliminary concepts
2.2. Limits and continuity of a function of two real variables
2.3. Partial derivatives
2.4. Chain rule
2.5. Differentials. Calculation of approximate values
2.6. Unconstrained extrema
2.7. Constrained extrema. Lagrange multipliers method
2.8. Optimization problems
Internship(s)
NAO
Bibliography
Bibliografia fundamental:
Borges, I., Textos de apoio e fichas práticas disponibilizados na plataforma NONIO, Edição do Autor.
Bibliografia complementar:
Cabral, I., Perdigão, C., Saiago, C. (2021). Álgebra Linear (6ª ed.). Escolar Editora
Giraldes, E., Fernandes, V. H. e Smith, M. P. M. (1997). Curso de Álgebra Linear e Geometria Analítica. McGraw-Hill
Harshbarger, R. J., Reynolds, J. J. (2018). Mathematical Applications for the Management, Life and Social Sciences. (12th ed.). Cengage
Learning
Larson, Holstetler and Edwards, (2006). Cálculo. Vol I e II, São Paulo. Ed McGraw Hill
Lay, D., Lay, S., McDonald , J. (2021). Linear algebra and its applications (6th edition). Pearson
Stewart, J. (2015). Calculus: Metric Version. Cengage Learning Brooks Cole
Swokowski, E.,(1979). Calculus with Analytic Geometry. Taylor & Francis.
Sydsæter, K., Hammond, P., Strøm, A. (2021). Essential Mathematics for Economic Analysis. (6th ed.). Pearson Education Limited