Class Mathematics I

The Mathematics I curricular unit (CU) was designed with a specific focus on the demands of Aeronautical Management—an area that operates in a highly dynamic, complex environment that is sensitive to small variations in the strategic and operational environment, where decisions must be based on realistic and robust quantitative models. The CU focuses on developing applied skills in linear and nonlinear dynamical modeling, which are essential both for the aeronautical industry context and for other CUs involving risk analysis and decision-making, developing key quantitative points of Risk Mathematics, Chaos Theory, and Complexity Sciences, aimed at: Understanding nonlinear and volatile decision-making environments; Analyzing complex networks and supply chains; Strategic management in turbulent contexts requiring analysis of nonlinear scenario evolution (e.g., the impact of a pandemic or systemic failures).

Not applicable

CP1. Principles of Mathematical Dynamical Modeling CP1.1. Dynamical systems modeling CP1.2. Concept of iteration and dynamical equations CP1.3. Fixed points, periodic and quasi-periodic dynamics CP1.4. Bifurcations, stability analysis, and transitions to chaos CP1.5. Deterministic chaos CP2. Mathematical Chaos Theory and Complexity in Aeronautical Management CP2.1. Impact of noise in nonlinear systems and stochastic chaos CP2.2. Concept of edge of chaos and its relevance to Aeronautical Management CP2.3. Chaos in nonlinear dynamical networks CP2.4. Empirical tools from chaos theory applied to Aeronautical Management (performance monitoring, detection of unstable patterns, and assessment of operational predictability)

Structuring of the Mathematics I curricular unit designed with a theoretical-practical approach with problem-based learning methodology focused on developing competencies in Mathematical Modeling, Risk Mathematics, Dynamical Simulation, and Mathematical Methods in Complexity Sciences. This is directly linked to the international R&D umbrella project for scientific and technological development, 'Chaos Theory and Complexity Sciences' (https://sites.google.com/view/chaos-complexity), in collaboration with international platforms and using advanced technological tools both in class and for individual student study: Northwestern University's  Center for Connected Learning and Computer-Based Modeling (CCL)'s Modeling Commons Platform with the project: http://modelingcommons.org/projects/190  Github: https://github.com/cpgoncalves/chaos-theory-complexity 

Ott, E. (2002). Chaos in Dynamical Systems (2nd ed.). Cambridge University Press. Kaplan, D. & Glass, L. (1995). Understanding Nonlinear Dynamics . New York, Springer, ISBN: 0-387-94440-0. Strogatz, S. H. (2018). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (2nd ed.). CRC Press. Sprott, J. C. (2014). Chaos and Time-Series Analysis. Oxford University Press. Liu, X., & Li, Y. (2021). Complex network analysis and modeling for aeronautical logistics systems. Journal of Air Transport Management, 94, 102066. https://doi.org/10.1016/j.jairtraman.2021.102066 Ribeiro, L., & Lopes, J. (2023). Stochastic Chaos in Aeronautical Decision-Making: A Model-Based Approach. Applied Mathematical Modelling, 122, 790-805. https://doi.org/10.1016/j.apm.2023.01.041 Grebogi, C., & Ott, E. (2020). Chaos theory and its applications to risk management in complex systems. Risk Analysis, 40(9), 1775-1790. https://doi.org/10.1111/risa.13545