Differential Equations Applied to Macroeconomics
Cod: 21185
Department: DCET
Scientific area: Mathematics
Total working hours: 156
Total contact time: 15

In this course we study ordinary differential equations and some applications to Macroeconomics. Basic techniques for the solution of first order linear, as well as for separable equations, and also for some systems and  higher order equations, are studied having as motivation and as concrete application situations origination in Mathematics modelling of Economics.

Ordinary differential equations
Macroeconomic models

Upon completion of this course the student should be able to:
  • solve linear first order scalar ODE, as well as autonomous higher order linear ones
  • study the behavior of autonomous scalar 1st order ODE using qualitative theory methods
  • study autonomous 2-dim systems of linear ODE; know how and when to apply some mathematical tools to the study of nonlinear systems
  • know Economics models mathematically modelled by ODE and interpret, in the Economics context, the results obtained

  • Introduction: examples of ordinary differential equations and models in economics
  • ODE: 1st order linear equations and systems
  • ODE: higher order linear autonomous equations
  • ODE: nonlinear first order equations
  • Linear and nonlinear ODE systems: basic theory and elements of qualitative theory

F. Pestana da Costa: Equações Diferenciais Ordinárias, 2ª Edição; Colecção Ensino da Ciência e da Tecnologia vol. 1, IST Press, Lisboa, 2011. ISBN  978-972-8469-00-9

J. Banasiak: Modelação Matemática em Dimensão Um: Uma Introdução Via Equações Diferenciais e às Diferenças; Coleção Ensino da Ciência e da Tecnologia vol. 58, IST Press, Lisboa, 2017. ISBN 987-989-8481-56-6
W.-B. Zhang: Differential Equations, Bifurcations and Chaos in Economics; Series on Advances in Mathematics for Applied Sciences vol. 68, World Scientific, Singapore, 2005. ISBN 981-256-333-4


Continuous assessment is privileged: 2 digital written documents (e-folios) during the semester (40%) and a final digital test, Global e-folio (e-folio G) at the end of the semester (60%). In due time, students can alternatively choose to perform one final exam (100%).

Students enrolled in this course must have studied Linear Algebra and Mathematical Analysis at levels similar to those of the courses 21002, 21030, and 21031.