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.
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
E-learning
Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based 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.
