Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems.Originally published in 1957.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Integrals, Generalized. --- Numerical integration.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies,ranging from mathematics and physics to computer science.

Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Fractional calculus. --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- Fractional dynamics. --- fractional calculus. --- nonlinear analysis. --- nonlinear dynamics.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Calculus. --- Calculus, Integral. --- Integrals. --- Calculus, Integral --- Integral calculus --- Differential equations --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph presents design methodologies for (robust) fractional control systems. It shows the reader how to take advantage of the superior flexibility of fractional control systems compared with integer-order systems in achieving more challenging control requirements. There is a high degree of current interest in fractional systems and fractional control arising from both academia and industry and readers from both milieux are catered to in the text. Different design approaches having in common a trade-off between robustness and performance of the control system are considered explicitly. The text generalizes methodologies, techniques and theoretical results that have been successfully applied in classical (integer) control to the fractional case. The first part of Advances in Robust Fractional Control is the more industrially-oriented. It focuses on the design of fractional controllers for integer processes. In particular, it considers fractional-order proportional-integral-derivative controllers, because integer-order PID regulators are, undoubtedly, the controllers most frequently adopted in industry. The second part of the book deals with a more general approach to fractional control systems, extending techniques (such as H-infinity optimal control and optimal input‒output inversion based control) originally devised for classical integer-order control. Advances in Robust Fractional Control will be a useful reference for the large number of academic researchers in fractional control, for their industrial counterparts and for graduate students who want to learn more about this subject.

Engineering. --- Control. --- Industrial Chemistry/Chemical Engineering. --- Industrial and Production Engineering. --- Chemical engineering. --- Industrial engineering. --- Ingénierie --- Génie chimique --- Génie industriel --- Cluster analysis. --- Mechanical Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Robust control --- Fractional calculus. --- Matrhematical models. --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Control engineering. --- Production engineering. --- Calculus --- Control and Systems Theory. --- Management engineering --- Simplification in industry --- Engineering --- Value analysis (Cost control) --- Chemistry, Industrial --- Engineering, Chemical --- Industrial chemistry --- Chemistry, Technical --- Metallurgy --- Manufacturing engineering --- Process engineering --- Industrial engineering --- Mechanical engineering --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume presents selected aspects of non-integer, or fractional order systems, whose analysis, synthesis and applications have increasingly become a real challenge for various research communities, ranging from science to engineering. The spectrum of applications of the fractional order calculus has incredibly expanded, in fact it would be hard to find a science/engineering-related subject area where the fractional calculus had not been incorporated. The content of the fractional calculus is ranged from pure mathematics to engineering implementations and so is the content of this volume. The volume is subdivided into six parts, reflecting particular aspects of the fractional order calculus. The first part contains a single invited paper on a new formulation of fractional-order descriptor observers for fractional-order descriptor continuous LTI systems. The second part provides new elements to the mathematical theory of fractional-order systems. In the third part of this volume, a bunch of new results in approximation, modeling and simulations of fractional-order systems is given. The fourth part presents new solutions to some problems in controllability and control of non-integer order systems, in particular fractional PID-like control. The fifth part analyzes the stability of non-integer order systems and some new results are offered in this important respect, in particular for discrete-time systems. The final, sixth part of this volume presents a spectrum of applications of the non-integer order calculus, ranging from bi-fractional filtering, in particular of electromyographic signals, through the thermal diffusion and advection diffusion processes to the SIEMENS platform implementation. This volume's papers were all subjected to stimulating comments and discussions from the active audience of the RRNR'2014, the 6th Conference on Non-integer Order Calculus and Its Applications that was organized by the Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland.

Engineering. --- Control. --- Complexity. --- Signal, Image and Speech Processing. --- Physics. --- Ingénierie --- Physique --- Dynamics -- Mathematics -- Congresses. --- Dynamics -- Mathematics. --- Fractals -- Congresses. --- Fractional calculus -- Congresses. --- Fractional calculus. --- Mechanical Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Fractional calculus --- Dynamics --- Mathematics --- Dynamical systems --- Kinetics --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Construction --- Industrial arts --- Technology --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Calculus --- Control and Systems Theory. --- Control engineering. --- Computational complexity. --- Signal processing. --- Image processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Complexity, Computational --- Electronic data processing --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers