This book collects the latest results and new trends in the application of mathematics to some problems in control theory, numerical simulation and differential equations.  The work comprises the main results presented at a thematic minisymposium, part of the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), held in Valencia, Spain, from 15 to 18 July 2019. The topics covered in the 6 peer-review contributions involve applications of numerical methods to real problems in oceanography and naval engineering, as well as relevant results on switching control techniques, which can have multiple applications in industrial complexes, electromechanical machines, biological systems, etc. Problems in control theory, as in most engineering problems, are modeled by differential equations, for which standard solving procedures may be insufficient. The book also includes recent geometric and analytical methods for the search of exact solutions for differential equations, which serve as essential tools for analyzing problems in many scientific disciplines.

Concepción Muriel is Professor of Mathematical Analysis at the University of Cádiz, Spain. She obtained a PhD in Mathematics at the University of Salamanca. She has participated in a large number of international congresses and has authored more than 50 scientific papers and book chapters, focusing on analytical and geometrical methods for differential equations.

Carmen Pérez-Martinez is Professor of Mathematical Analysis at the University of Cádiz. She received her PhD in Mathematics from University of Cádiz. She investigates in Control Theory, focusing on switched systems. She has authored several papers about stabilization of switched systems and their applications in real systems.

Numerical Simulation: J. Alonso, J. et al., The upwelling of the Colombian Caribbean Coasts: remote sensing, morphology and influence on the Lake Maracaibo.- J. Coronil, D. et al., Is it possible the use of discontinuous shapes in hydrodynamics?.-Control Theory: García-Gutiérrez, J.J et al., Stabilization of third order switched linear systems via invariant set.- Pérez, C. et al., Control of second-order switched systems with application to DC-DC converters.-Differential Equations: Mendoza, J. et al., Symbolic computation algorithms for second-order ODEs by using  two -symmetries.- Ruiz, A. and Muriel, C., Systems of vector fields for the integration of ordinary differential equations.