2023
Mathematics Applied to Economics and Management I
Name: Mathematics Applied to Economics and Management I
Code: MAT02312L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
Objectives of the curricular unit: Introduction to mathematical methods applied to Economics and Management, in particular applied mathematical methods in modeling, static analysis of equilibrium, solving systems of linear equations, and calculus and prediction of growth and change.
Competences to develop: The acquisition of theoretical content of the program will enable the students to use and interpret specific concepts and symbols of mathematics, to present strategies for solving problems, interpreting and criticizing the results. Making connections between mathematical concepts and economic concepts, being able to solve problems in economic context by applying mathematical methods.
Acquired mathematical skills will be sufficient to read, understand and interpret some existing economic literature.
Competences to develop: The acquisition of theoretical content of the program will enable the students to use and interpret specific concepts and symbols of mathematics, to present strategies for solving problems, interpreting and criticizing the results. Making connections between mathematical concepts and economic concepts, being able to solve problems in economic context by applying mathematical methods.
Acquired mathematical skills will be sufficient to read, understand and interpret some existing economic literature.
Contents
I - Motivation
1.1 Supply, Demand and Profit in Terms of Price. Equilibrium
1.2 Partial Market Equilibrium and General Market Equilibrium
1.3 Equilibrium in National-Income Analysis
II - Comparative-Static Analysis
1.0 Revisions about Functions. Exp and Log
1.1 Rate of Change and the Derivative. Geometric Interpretation
1.2 Limits, Continuity and Differentiability
1.3 Rules of Differentiation
1.4. Marginal-Revenue and and Average-Revenue Functions. Marginal-Revenue and Average-Revenue Curves
1.5 Partial Derivatives
1.6 Applications
III - Static (or Equilibrium) Analysis
1.1 Matrices and Vectors
1.2 Matrix and Vector Operations
1.3 Vector Spaces
1.4 Transpose Matrix and Inverse Matrix
1.5 Conditions for Non-Singularity of a Matrix
1.6 Solving Linear Systems of Equations
1.7 Determinants. Application to the Computation of Inverse matrix. Cramers Rule
1.8 Applications: Market and National-Income Models; Leontief Input-Output Models
1.9 Matrices and partial derivatives
1.1 Supply, Demand and Profit in Terms of Price. Equilibrium
1.2 Partial Market Equilibrium and General Market Equilibrium
1.3 Equilibrium in National-Income Analysis
II - Comparative-Static Analysis
1.0 Revisions about Functions. Exp and Log
1.1 Rate of Change and the Derivative. Geometric Interpretation
1.2 Limits, Continuity and Differentiability
1.3 Rules of Differentiation
1.4. Marginal-Revenue and and Average-Revenue Functions. Marginal-Revenue and Average-Revenue Curves
1.5 Partial Derivatives
1.6 Applications
III - Static (or Equilibrium) Analysis
1.1 Matrices and Vectors
1.2 Matrix and Vector Operations
1.3 Vector Spaces
1.4 Transpose Matrix and Inverse Matrix
1.5 Conditions for Non-Singularity of a Matrix
1.6 Solving Linear Systems of Equations
1.7 Determinants. Application to the Computation of Inverse matrix. Cramers Rule
1.8 Applications: Market and National-Income Models; Leontief Input-Output Models
1.9 Matrices and partial derivatives
Teaching Methods
This is a course with 2x2,5 hours of theoretical-practical lessons per week. In there will be a structured exposition of the subjects using examples, when possible, with emphasis on applications to Economics and Management. Given the pedagogical model adopted, the exposure of such knowledge is complemented with the resolution of exercises that are provided in the previous week. For a proper understanding of the syllabus and for the course successful, students should develop regular work outside the classroom, particularly in the study of concepts and solving exercises.
Evaluation methods:
Continued evaluation (two mid-terms), final exam and resort exam.
Evaluation methods:
Continued evaluation (two mid-terms), final exam and resort exam.
Teaching Staff
