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The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas. It presents for the first time in book form the theory of Pommaret bases, a special kind of Gröbner bases closely related to Koszul homology, and contains an extensive discussion of the existence and uniqueness of solutions of formally well-posed initial value problems and a novel presentation of Vessiot's dual version of the Cartan-Kähler

Evolution. --- Differential equations --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Differential equations. --- Computer algorithms. --- 517.91 Differential equations --- Mathematics. --- Computer science --- Algebra. --- Commutative algebra. --- Commutative rings. --- Partial differential equations. --- Physics. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Commutative Rings and Algebras. --- Theoretical, Mathematical and Computational Physics. --- Symbolic and Algebraic Manipulation. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Partial differential equations --- Rings (Algebra) --- Algebra --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Science --- Algorithms --- Differential equations, partial. --- Differential Equations. --- Data processing. --- Mathematical physics. --- Computer science—Mathematics. --- Physical mathematics --- Physics

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As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company they drew from each other fresh vitality and thenceforward marched on at rapid pace towards perfection Joseph L. Lagrange The theory of differential equations is one of the largest elds within mathematics and probably most graduates in mathematics have attended at least one course on differentialequations. But differentialequationsare also offundamentalimportance in most applied sciences; whenever a continuous process is modelled mathem- ically, chances are high that differential equations appear. So it does not surprise that many textbooks exist on both ordinary and partial differential equations. But the huge majority of these books makes an implicit assumption on the structure of the equations: either one deals with scalar equations or with normal systems, i. e. with systems in Cauchy-Kovalevskaya form. The main topic of this book is what happens, if this popular assumption is dropped. This is not just an academic exercise; non-normal systems are ubiquitous in - plications. Classical examples include the incompressible Navier-Stokes equations of uid dynamics, Maxwell's equations of electrodynamics, the Yang-Mills eq- tions of the fundamental gauge theories in modern particle physics or Einstein's equations of general relativity. But also the simulation and control of multibody systems, electrical circuits or chemical reactions lead to non-normal systems of - dinary differential equations, often called differential algebraic equations. In fact, most of the differentialequationsnowadaysencounteredby engineersand scientists are probably not normal.

Differential equations --- Equations différentielles --- Equations différentielles --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B

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This book constitutes the proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing, CASC 2016, held in Bucharest, Romania, in September 2016. The 32 papers presented in this volume were carefully reviewed and selected from 39 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.

Computer science. --- Arithmetic and logic units, Computer. --- Algorithms. --- Numerical analysis. --- Computer science --- Computer simulation. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Symbolic and Algebraic Manipulation. --- Simulation and Modeling. --- Numeric Computing. --- Arithmetic and Logic Structures. --- Mathematics. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Arithmetic and logic units, Computer --- Informatics --- Mathematics --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Mathematical analysis --- Algebra --- Arithmetic --- Computer arithmetic --- Electronic digital computers --- Science --- Foundations --- Circuits --- Computer software. --- Computational complexity. --- Electronic data processing. --- Data processing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Complexity, Computational --- Machine theory --- Software, Computer --- Computer systems --- Automation --- Computer science—Mathematics. --- Discrete mathematics. --- Computer arithmetic and logic units. --- Computer Modelling. --- Numerical Analysis. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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Chapter “Positive Solutions of Systems of Signed Parametric Polynomial Inequalities” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Computer software. --- Computer science. --- Software engineering. --- Computer network architectures. --- Logic design. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Computing. --- Special Purpose and Application-Based Systems. --- Computer System Implementation. --- Logic Design. --- Logics and Meanings of Programs. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Architectures, Computer network --- Network architectures, Computer --- Computer architecture --- Computer software engineering --- Engineering --- Informatics --- Science --- Software, Computer --- Computer systems --- Algorithms. --- Computer science—Mathematics. --- Special purpose computers. --- Architecture, Computer. --- Computer logic. --- Computer science logic --- Logic, Symbolic and mathematical --- Architecture, Computer --- Special purpose computers --- Computers --- Algorism --- Algebra --- Arithmetic --- Foundations --- Computers, Special purpose. --- Computer systems. --- Computer Science Logic and Foundations of Programming. --- ADP systems (Computer systems) --- Computing systems --- Systems, Computer --- Electronic systems --- Cyberinfrastructure

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This book constitutes the refereed proceedings of the 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, held in Moscow, Russia, in August 2019. The 28 full papers presented together with 2 invited talks were carefully reviewed and selected from 44 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CASs in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.

Computer science. --- Computer software. --- Software engineering. --- Information Systems. --- Mathematics of Computing. --- Algorithm Analysis and Problem Complexity. --- Software Engineering. --- Special Purpose and Application-Based Systems. --- Management of Computing and Information Systems. --- Computer software engineering --- Engineering --- Software, Computer --- Computer systems --- Informatics --- Science --- Software engineering --- Computer science --- Computer science—Mathematics. --- Algorithms. --- Special purpose computers. --- Management information systems. --- Computer-based information systems --- EIS (Information systems) --- Executive information systems --- MIS (Information systems) --- Sociotechnical systems --- Information resources management --- Management --- Special purpose computers --- Computers --- Algorism --- Algebra --- Arithmetic --- Communication systems --- Foundations --- Computers, Special purpose. --- Electronic data processing—Management. --- IT Operations.