Class Mathematics I

The CU of Mathematics I develops fundamental skills in quantitative reasoning and mathematical modeling of problems in Aeronautical Management and Aeronautical Sciences, with emphasis in linear and nonlinear dynamics in continuous time, with applications to problems in Economics, Management and Aeronautical Sciences.

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SP1. Differential Equations and Dynamical Modeling SP1.1. Modeling of dynamical systems and System Dynamics. SP1.2. Concept of derivative: first and second derivative. SP1.3. Flow variables and stock variables. SP1.4. Concept of integral. SP2. Differential Equations applied to Dynamical Modeling in Economics, Management and Aeronautical Sciences. SP2.1. Main types of dynamics and their mathematical modeling. SP2.2. Solving of systems of differential equations with applications to Economics, Management and Aeronautical Sciences. SP2.3. Feedback and nonlinear dynamics. SP2.4. Differential equations and stock and flows diagrams. SP2.5. Numerical integration.

Structuring of the CU with theoretical-practical teaching, oriented around the development of skills in dynamical modeling based on the field of System Dynamics with applications to Aeronautical Management and Aeronautical Sciences. Connection of the CU to the international R&D project ?System Dynamics? ( https://sites.google.com/view/systemdynamics/ ) involving technological production and production of webinars (available in the Youtube playlist https://youtube.com/playlist?list=PLmLUR-kyF1qWvcss1voLDkirln3mjsmGk ), developed in connection with Northwestern University?s Center for Connected Learning and Computer-Based Modeling (CCL)'s platform Netlogo Modeling Commons, in the form of the project with code #MC Project 181 "'System Dynamics' project" http://modelingcommons.org/projects/181 , with direct connection between teaching and research in the context of dynamical systems modeling with application to Aeronautical Management and Aeronautical Sciences.

Cavana, R.Y., Dangerfield, B.C., Pavlov, O.V. , Radzicki, M.J., Wheat, I.D. (Eds.) (2021). Feedback Economics: Economic Modeling with System Dynamics . Switzerland, Springer, ISBN: 978-3030671891. Ogata, K. (2004). System Dynamics Fourth Edition . Pearson. US, Pearson, ISBN: 978-0131424623. Strogatz, S.H. (2015). Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity) . Boulder, Westview Press. ISBN: 978-0738204536. Walecka, J.D. (2020). Introduction To Classical Mechanics . Singapore, World Scientific, ISBN: 978-9811217432. NASA National Aeronautics and Space Administration (2020). Aeronautics: An Educator's Guide with Activities in Science, Mathematics, and Technology Education. USA, U.S. Federal Government, ASIN : B08KR7JPRH. Zabczyk, J. (2020). Mathematical Control Theory: An Introduction . Switzerland, Birkhäuser, ISBN: 978-3030447762.