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Algebras, Linear. --- Algebra, Homological. --- Ordered algebraic structures. --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Homological algebra --- Algebra, Abstract --- Homology theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology

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Algebra

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Fundamentals of Advanced Mathematics, Volume Three, begins with the study of differential and analytic infinite-dimensional manifolds, then progresses into fibered bundles, in particular, tangent and cotangent bundles. In addition, subjects covered include the tensor calculus on manifolds, differential and integral calculus on manifolds (general Stokes formula, integral curves and manifolds), an analysis on Lie groups, the Haar measure, the convolution of functions and distributions, and the harmonic analysis over a Lie group. Finally, the theory of connections is (linear connections, principal connections, and Cartan connections) covered, as is the calculus of variations in Lagrangian and Hamiltonian formulations. This volume is the prerequisite to the analytic and geometric study of nonlinear systems.

Mathematics

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The aim of this book is to propose a new approach to analysis and control of linear time-varying systems.  These systems are defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as they are actually.  The system equations, derived, e.g., from the laws of physics, are gathered to form an intrinsic mathematical object, namely a finitely presented module over a ring of operators.  This is strongly connected with the engineering point of view, according to which a system is not a specific set of equations but an object of the material world which can be described by equivalent sets of equations.  This viewpoint makes it possible to formulate and solve efficiently several key problems of the theory of control in the case of linear time-varying systems.  The solutions are based on algebraic analysis.   This book, written for engineers, is also useful for mathematicians since it shows how algebraic analysis can be applied to solve engineering problems.   Henri Bourlès is a Professor and holds the industrial automation chair at the Conservatoire national des arts et métiers in France. He has been teaching automation for over 20 years in engineering and graduate schools.   Bogdan Marinescu is currently research engineer at the French Transmission System Operator (RTE) and Associate Professor at SATIE-Ecole Normale Supérieure de Cachan.  .

Mechanical Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Adaptive control systems --- Linear systems --- Mathematical models. --- Systems, Linear --- Self-adaptive control systems --- Engineering. --- System theory. --- Control engineering. --- Robotics. --- Mechatronics. --- Control, Robotics, Mechatronics. --- Systems Theory, Control. --- Differential equations, Linear --- System theory --- Artificial intelligence --- Feedback control systems --- Self-organizing systems --- Systems theory. --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Systems, Theory of --- Systems science --- Science --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Machine theory --- Philosophy

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Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- mechatronica --- industriële robots --- automatisering --- systeemtheorie --- systeembeheer