Nonlinear Ordinary Differential Equations

Author: Dominic Jordan
Publisher: Oxford University Press on Demand
ISBN: 0199208247
Format: PDF, ePub, Mobi
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Thoroughly updated and expanded 4th edition of the classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences it is published alongside a separate Problems and Solutions Sourcebook containing over 500 problems and fully-worked solutions.

Nonlinear Ordinary Differential Equations An Introduction for Scientists and Engineers

Author: Dominic Jordan
Publisher: OUP Oxford
ISBN: 0199208247
Format: PDF, Kindle
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This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinicbifurcation and Liapunov exponents.Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007).Both texts cover a wide variety of applications whilst keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

Nonlinear Ordinary Differential Equations

Author: Martin Hermann
Publisher: Springer
ISBN: 813222812X
Format: PDF, ePub, Docs
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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.

Ordinary and Partial Differential Equations

Author: Victor Henner
Publisher: CRC Press
ISBN: 1466515031
Format: PDF, Mobi
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Covers ODEs and PDEs-in One TextbookUntil now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn't exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as

Mathematical Methods for Geophysics and Space Physics

Author: William I. Newman
Publisher: Princeton University Press
ISBN: 1400882826
Format: PDF, Mobi
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Graduate students in the natural sciences—including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy—need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors

Integral Transforms and Their Applications

Author: Lokenath Debnath
Publisher: CRC Press
ISBN: 9781420010916
Format: PDF, ePub, Mobi
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Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.

Nichtlineare Finite Element Methoden

Author: Peter Wriggers
Publisher: Springer-Verlag
ISBN: 3642568653
Format: PDF, Docs
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Die Anwendung der Finite-Element-Methode auf nichtlineare technische Probleme hat in den letzten Jahren - auch wegen der stark angestiegenen Rechnerleistung - erheblich zugenommen. Bei nichtlinearen numerischen Simulationen sind verschiedene Aspekte zu berücksichtigen, die das Wissen und Verstehen der theoretischen Grundlagen, der zugehörigen Elementformulierungen sowie der Algorithmen zur Lösung der nichtlinearen Gleichungen voraussetzen. Hierzu soll dieses Buch beitragen, wobei die Bandbreite nichtlinearer Finite-Element-Analysen im Bereich der Festkörpermechanik abgedeckt wird. Das Buch wendet sich an Studierende des Ingenieurwesens im Hauptstudium, an Doktoranden aber auch an praktisch tätige Ingenieure, die Hintergrundwissen im Bereich der Finite-Element-Methode erlangen möchten.