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Applied partial differential equations / J David Logan
New York : Springer, 2015
294 pages. : illustrations
Ký hiệu phân loại (DDC): 515.353
his text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.
Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory.
The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains.
Methods include eigenfunction expansions, integral transforms, and characteristics.
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Basic Concepts in Computational Physics / Benjamin A. Stickler and Ewald Schachinger
Cham : Springer, 2016
409 p. ; cm.
Ký hiệu phân loại (DDC): 530.1
This new edition is a concise introduction to the basic methods of computational physics. Readers will discover the benefits of numerical methods for solving complex mathematical problems and for the direct simulation of physical processes. The book is divided into two main parts: Deterministic methods and stochastic methods in computational physics. Based on concrete problems, the first part discusses numerical differentiation and integration, as well as the treatment of ordinary differential equations. This is extended by a brief introduction to the numerics of partial differential equations. The second part deals with the generation of random numbers, summarizes the basics of stochastics, and subsequently introduces Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. The final two chapters discuss data analysis and stochastic optimization. All this is again motivated and augmented by applications from physics. In addition, the book offers a number of appendices to provide the reader with information on topics not discussed in the main text. Numerous problems with worked-out solutions, chapter introductions and summaries, together with a clear and application-oriented style support the reader. Ready to use C++ codes are provided online.
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