Download or read book Ecuaciones de Laplace y Helmholtz written by Juan Carlos Herrero and published by . This book was released on 2016-11-07 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: El objeto de este libro es la soluci�n detallada de las ecuaciones de Laplace y de Helmholtz, con un inter�s muy especial en el estudio de la ortogonalidad, normalizaci�n y completitud de las soluciones. En este libro aparecen con todo detalle y de modo pr�ctico los m�todos de resoluci�n de ecuaciones diferenciales en general, tales como la separaci�n de variables, la resoluci�n por series de potencias o el m�todo de Frobenius, y los m�todos particulares para la resoluci�n de otras ecuaciones tales como las de Bessel, Legendre, la hipergeom�trica o la de Sturm-Liouville. Se explican y se muestran de modo pr�ctico toda una serie de herramientas matem�ticas, desde las m�s sencillas a las m�s complicadas, como el teorema del binomio, los cambios de �ndices en sumatorios, las simplificaciones de expresiones mediante t�cnicas que van desde las m�s evidentes a las m�s ingeniosas, las demostraciones por inducci�n, los criterios de convergencia para series, incluyendo las series de potencias y su radio de convergencia, la f�rmula de Leibniz, la integraci�n por partes, el producto interno de funciones, la extensi�n anal�tica de una funci�n, el desarrollo en serie de Taylor y MacLaurin, la transformada de Laplace y de Fourier, el m�todo "steepest descent", el cambio de variable de integraci�n, las integrales de funciones de variable compleja, entre las que podemos citar las de Euler, Hankel, Weber y Schafheitlin, o la de Barnes, a lo largo de contornos de diversa �ndole, incluyendo los de Hankel y Pochhammer, abordando el estudio de la convergencia de dichas integrales e involucrando directamente el teorema del residuo o el teorema integral de Cauchy, entrando en el estudio, m�s o menos extenso, de otras funciones, como la funci�n exponencial y logar�tmica, los polinomios de Bernoulli, la f�rmula de Rodrigues, los polinomios de Legendre, la funci�n gamma (lo que implica un estudio de la f�rmula de Stirling y �sta de la f�rmula de Euler-MacLaurin), la funci�n gamma rec�proca, la funci�n digamma, la funci�n beta, las funciones hipergeom�tricas), y se abordan con especial atenci�n aspectos tales como la ortogonalidad, normalizaci�n y completitud de las soluciones de las ecuaciones de Laplace, Lagrange y Helmholtz, en las cuales se ve involucrada la teor�a de Sturm-Liouville y el espacio de Hilbert. El problema de la soluci�n de las ecuaciones de Laplace y Helmholtz, as� como el estudio de la ortogonalidad y completitud de las soluciones, se ha dividido en dos vol�menes. El primer volumen se dedica a las ecuaciones de Laplace y Helmlholtz en coordenadas esf�ricas, as� como su ortogonalidad y normalizaci�n, dejando para el segundo volumen el caso de las coordenadas cil�ndricas, polares y cartesianas de ambas ecuaciones, y el estudio de la completitud de todas las soluciones obtenidas en ambos vol�menes, abordando para ello el estudio de la teor�a de Sturm-Liouville y el espacio de Hilbert.

Download or read book Ecuaciones de Laplace y Helmholtz written by Juan Carlos Herrero and published by . This book was released on 2016-11-07 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: El objeto de este libro es la soluci�n detallada de las ecuaciones de Laplace y de Helmholtz, con un inter�s muy especial en el estudio de la ortogonalidad, normalizaci�n y completitud de las soluciones. En este libro aparecen con todo detalle y de modo pr�ctico los m�todos de resoluci�n de ecuaciones diferenciales en general, tales como la separaci�n de variables, la resoluci�n por series de potencias o el m�todo de Frobenius, y los m�todos particulares para la resoluci�n de otras ecuaciones tales como las de Bessel, Legendre, la hipergeom�trica o la de Sturm-Liouville. Se explican y se muestran de modo pr�ctico toda una serie de herramientas matem�ticas, desde las m�s sencillas a las m�s complicadas, como el teorema del binomio, los cambios de �ndices en sumatorios, las simplificaciones de expresiones mediante t�cnicas que van desde las m�s evidentes a las m�s ingeniosas, las demostraciones por inducci�n, los criterios de convergencia para series, incluyendo las series de potencias y su radio de convergencia, la f�rmula de Leibniz, la integraci�n por partes, el producto interno de funciones, la extensi�n anal�tica de una funci�n, el desarrollo en serie de Taylor y MacLaurin, la transformada de Laplace y de Fourier, el m�todo "steepest descent", el cambio de variable de integraci�n, las integrales de funciones de variable compleja, entre las que podemos citar las de Euler, Hankel, Weber y Schafheitlin, o la de Barnes, a lo largo de contornos de diversa �ndole, incluyendo los de Hankel y Pochhammer, abordando el estudio de la convergencia de dichas integrales e involucrando directamente el teorema del residuo o el teorema integral de Cauchy, entrando en el estudio, m�s o menos extenso, de otras funciones, como la funci�n exponencial y logar�tmica, los polinomios de Bernoulli, la f�rmula de Rodrigues, los polinomios de Legendre, la funci�n gamma (lo que implica un estudio de la f�rmula de Stirling y �sta de la f�rmula de Euler-MacLaurin), la funci�n gamma rec�proca, la funci�n digamma, la funci�n beta, las funciones hipergeom�tricas), y se abordan con especial atenci�n aspectos tales como la ortogonalidad, normalizaci�n y completitud de las soluciones de las ecuaciones de Laplace, Lagrange y Helmholtz, en las cuales se ve involucrada la teor�a de Sturm-Liouville y el espacio de Hilbert. El problema de la soluci�n de las ecuaciones de Laplace y Helmholtz, as� como el estudio de la ortogonalidad y completitud de las soluciones, se ha dividido en dos vol�menes. El primer volumen se dedica a las ecuaciones de Laplace y Helmlholtz en coordenadas esf�ricas, as� como su ortogonalidad y normalizaci�n, dejando para el segundo volumen el caso de las coordenadas cil�ndricas, polares y cartesianas de ambas ecuaciones, y el estudio de la completitud de todas las soluciones obtenidas en ambos vol�menes, abordando para ello el estudio de la teor�a de Sturm-Liouville y el espacio de Hilbert.

Download or read book Laplace and Helmholtz Equations written by Juan Carlos Herrero and published by . This book was released on 2016-11-07 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this book is the solution to the Laplace and Helmholtz equations with a special interest in the study of the solutions' orthogonality, normalization, and completeness. This book deals in detail and in a practical manner with the methods to solve differential equations in general, like separation of variables, power series, or Frobenius, and the particular methods to solve equations like Bessel's, Legendre's, or Sturm-Liouville's. A series of mathematical tools are explained practically, from the most simple ones to the most complicated ones, like the binomial theorem, the changes of index in summations, the simplification of expressions by means of techniques from obvious to ingenious, the proof by induction, the convergence tests for series, including the power series and the radius of convergence, the Leibniz formula, the integration by parts, the inner product of functions, the analytic continuation of a function, the expansion of a function in terms of Taylor or MacLaurin series, the Laplace transform, the Fourier transform, the steepest descent method, the change of integration variable, the evaluation of integrals by complex variable methods, like the integrals of Euler, Hankel, Weber and Schafheitlin, or Barnes, along different integration contours, like Pochhammer's or Hankel's, studying the convergence of the integrals, and involving the residue theorem, or Cauchy's integral theorem, approaching the study of other functions, like the exponential and logarithmic functions, the Bernoulli polynomials, the Rodrigues formula, the Legendre polynomials, the gamma function (involving the Stirling's formula and Euler-MacLaurin formula), the reciprocal gamma function, the digamma function, the beta function, the hypergeometric function (and the hypergeometric equation). The orthogonality, normalization, and completeness of Laplace, Lagrange, and Helmholtz equation solutions are dealt with in depth, involving the Sturm-Liouville theory, and Hilbert Space. The solution to the Laplace and Helmholtz equations, as well as the study of the orthogonality and completeness of the solutions is split into two volumes. The first volume deals with the Laplace and Helmholtz equations in spherical coordinates, and the orthogonality and normalization of the solutions. The second volume deals with the Laplace and Helmholtz equations in cylindrical, polar, and Cartesian coordinates, with a study on the completeness of all the solutions obtained in both volumes, based on Sturm-Liouville theory, and Hilbert Space.

Download or read book Modern Solvers for Helmholtz Problems written by Domenico Lahaye and published by Birkhäuser. This book was released on 2017-03-02 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to be more detailed and, therefore, lead to numerical problems of a larger scale. To solve these three dimensional problems fast and robust, iterative solvers are required. However for standard iterative methods the number of iterations to solve the system becomes too large. For these reason a number of new methods are developed to overcome this hurdle. The book is meant for researchers both from academia and industry and graduate students. A prerequisite is knowledge on partial differential equations and numerical linear algebra.

Download or read book Singular Integral Equations and Discrete Vortices written by I. K. Lifanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Download or read book Ecuaciones en Derivadas Parciales written by Fuente Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuente: Wikipedia. Paginas: 48. Capitulos: Condiciones de frontera, Ecuaciones elipticas en derivadas parciales, Ecuaciones hiperbolicas en derivadas parciales, Ecuaciones parabolicas en derivadas parciales, Teoria del potencial, Potencial electrico, Ecuacion del calor, Ecuacion de Dirac, Ecuacion de Schrodinger, Ecuacion de onda, Atomo de hidrogeno, Desarrollo multipolar, Armonicos esfericos, Ecuacion de Laplace, Ecuacion de Hamilton-Jacobi, Ecuacion en derivadas parciales, Teoria clasica de campos, Ecuacion de Mason-Weaver, Campo gravitatorio, Problema de Dirichlet, Ecuacion de la eikonal, Condicion de frontera de Cauchy, Ecuacion de Poisson, Ecuacion de Fokker-Planck, Sistema de reaccion-difusion, Condicion de frontera de Robin, Ecuacion de Rarita-Schwinger, Ecuacion de Helmholtz, Nucleo de Poisson, Aplicacion de la ecuacion de Poisson en macromoleculas, Ecuacion biarmonica, Formula de d'Alembert, Numero de Courant-Friedrich-Levy, Condicion de frontera de Dirichlet, D'Alambertiano, Condicion de frontera de Neumann, Ecuacion de difusion, Adveccion, Solucion fundamental, Condicion de frontera mixta, Ecuacion de conveccion-difusion, Ecuacion eliptica en derivadas parciales, Ecuacion parabolica en derivadas parciales, Problema de Stefan, Ecuacion hiperbolica en derivadas parciales, Momento multipolar. Extracto: La ecuacion del calor es una importante ecuacion diferencial en derivadas parciales que describe la distribucion del calor (o variaciones de la temperatura) en una region a lo largo del transcurso del tiempo. Para el caso de una funcion de tres variables en el espacio (x, y, z) y la variable temporal t, la ecuacion del calor es donde es la difusividad termica, que es una propiedad el material. La ecuacion del calor es de una importancia fundamental en numerosos y diversos campos de la ciencia. En las matematicas, es las ecuaciones parabolicas en derivadas parciales por antonomasia. En la.

Download or read book Shifted Laplace Preconditioners for the Helmholtz Equations written by C. Vuik and published by . This book was released on 2003 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Symmetry and Separation of Variables written by Willard Miller and published by Westview Press. This book was released on 1977 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Functional Analysis Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Download or read book Application of Green s Functions in Science and Engineering written by Michael D. Greenberg and published by Prentice Hall. This book was released on 1971 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partial Differential Equations for Scientists and Engineers written by Stanley J. Farlow and published by Courier Corporation. This book was released on 2012-03-08 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical text shows how to formulate and solve partial differential equations. Coverage includes diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Solution guide available upon request. 1982 edition.

Download or read book Linear Partial Differential Equations for Scientists and Engineers written by Tyn Myint-U and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.

Download or read book Multidisciplinary Mathematical Modelling written by Francesc Font and published by Springer Nature. This book was released on 2021-04-13 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a selection of the talks resulting from research carried out by different groups at the Centre de Recerca Matemàtica and presented at the International Congress on Industrial and Applied Mathematics, held in Valencia in 2019. The various chapters describe a wide variety of topics: cancer modelling, carbon capture by adsorption, nanoscale diffusion and complex systems to predict earthquakes. These mathematical studies were specifically aided via collaborations with biomedical engineers, physicists and chemists. The book is addressed to researchers in all of these areas as well as in general mathematical modelling.

Download or read book Partial Differential Equations of Applied Mathematics written by Erich Zauderer and published by Wiley-Interscience. This book was released on 1998-08-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only comprehensive guide to modeling, characterizing, and solving partial differential equations This classic text by Erich Zauderer provides a comprehensive account of partial differential equations and their applications. Dr. Zauderer develops mathematical models that give rise to partial differential equations and describes classical and modern solution techniques. With an emphasis on practical applications, he makes liberal use of real-world examples, explores both linear and nonlinear problems, and provides approximate as well as exact solutions. He also describes approximation methods for simplifying complicated solutions and for solving linear and nonlinear problems not readily solved by standard methods. The book begins with a demonstration of how the three basic types of equations (parabolic, hyperbolic, and elliptic) can be derived from random walk models. It continues in a less statistical vein to cover an exceptionally broad range of topics, including stabilities, singularities, transform methods, the use of Green's functions, and perturbation and asymptotic treatments. Features that set Partial Differential Equations of Applied Mathematics, Second Edition above all other texts in the field include: Coverage of random walk problems, discontinuous and singular solutions, and perturbation and asymptotic methods More than 800 practice exercises, many of which are fully worked out Numerous up-to-date examples from engineering and the physical sciences Partial Differential Equations of Applied Mathematics, Second Edition is a superior advanced-undergraduate to graduate-level text for students in engineering, the sciences, and applied mathematics. The title is also a valuable working resource for professionals in these fields. Dr. Zauderer received his doctorate in mathematics from the New York University-Courant Institute. Prior to joining the staff of Polytechnic University, he was a Senior Weitzmann Fellow of the Weitzmann Institute of Science in Rehovot, Israel.

Download or read book An Introduction to Partial Differential Equations with MATLAB written by Matthew P. Coleman and published by CRC Press. This book was released on 2016-04-19 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,

Download or read book Mathematical and Numerical Foundations of Turbulence Models and Applications written by Tomás Chacón Rebollo and published by Springer. This book was released on 2014-06-17 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.