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The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.
Mathematics. --- Differential equations. --- Mathematical physics. --- Numerical analysis. --- Ordinary Differential Equations. --- Numerical Analysis. --- Mathematical Physics. --- Mathematical Applications in the Physical Sciences. --- Physical mathematics --- Physics --- 517.91 Differential equations --- Differential equations --- Math --- Mathematics --- Differential Equations. --- Mathematical analysis
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This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.
Mathematics. --- Differential equations. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Numerical analysis. --- Continuum mechanics. --- Ordinary Differential Equations. --- Numerical Analysis. --- Applications of Mathematics. --- Mathematical Applications in the Physical Sciences. --- Continuum Mechanics and Mechanics of Materials. --- Mathematical Physics. --- Differential Equations. --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Mathematical analysis --- Math --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- 517.91 Differential equations --- Differential equations --- Physical mathematics --- Engineering --- Engineering analysis --- Mathematics
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his commemorative volume honours the 65th birthday of Dr. Rolf Griebel, celebrating his service as General Director of the Bavarian State Library. The authors include major contributors to German and international library science from the realms of culture, academia, and politics. The essays explore the strategic challenges that face innovate library management practice, focusing on the future role of libraries in a digital world.
Libraries -- Information technology -- Planning. --- Libraries -- Information technology. --- Libraries and community. --- Libraries and the Internet. --- Social Sciences --- Library & Information Science --- Griebel, Rolf. --- Bayerische Staatsbibliothek. --- Bavarian State Library, Munich. --- Festschrift. --- Bavaria (Germany). --- Bavarian State Library --- Staatsbibliothek München --- Munich. --- Munich (Germany). --- Biblioteca del Estáu de Baviera --- Bayerische Staatsbibliothek München --- BSB --- دار الكتب الظاهرية --- Bayrische Staatsbibliothek --- Kgl. Hof- und Staatsbibliothek in München --- Germany. --- Alemania --- Ashkenaz --- BRD --- BuÌgd NaiÌramdakh German Uls --- Bundesrepublik Deutschland --- Deguo --- Deutsches Reich --- Deutschland --- Doitsu --- Doitsu RenpoÌ KyoÌwakoku --- Federal Republic of Germany --- Federalʹna Respublika Nimechchyny --- FRN --- GeÌrman --- German Uls --- Germania --- Germaniiï¸ a︡ --- Germanyah --- Gjermani --- Grossdeutsches Reich --- JirmaÌniÌya --- KhBNGU --- Kholboony BuÌgd NaiÌramdakh German Uls --- Nimechchyna --- Repoblika Federalin'i Alemana --- RepuÌblica de Alemania --- RepuÌblica Federal de Alemania --- Republika Federal Alemmana --- VaÌcijaÌ --- VeiÌmarskaiï¸ a︡ Respublika --- Weimar Republic --- Weimarer Republik --- Germany (East) --- Germany (West) --- Europe --- Bu̇gd Naĭramdakh German Uls --- Doitsu Renpō Kyōwakoku --- Federalʹna Respublika Nimechchyny --- Gėrman --- Germanii︠a︡ --- Jirmānīya --- Kholboony Bu̇gd Naĭramdakh German Uls --- República de Alemania --- República Federal de Alemania --- Vācijā --- Veĭmarskai︠a︡ Respublika
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Semitic languages --- Indo-European languages --- Consonants. --- Consonants.
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English language --- English language --- English language --- Dialects.
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