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Maple in Mathematics Education and Research
This book constitutes refereed proceedings of the 4th Maple Conference, MC 2020, held in Waterloo, Ontario, Canada, in November 2020. The 25 revised full papers and 3 short papers were carefully reviewed and selected out of 75 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.
Computer Algebra in Scientific Computing
This book constitutes the proceedings of the 20th International Workshop on Computer Algebra in Scientific Computing, CASC 2018, held in Lille, France, in September 2018. The 24 full papers of this volume presented with an abstract of an invited talk and one paper corresponding to another invited talk were carefully reviewed and selected from 29 submissions. They deal with cutting-edge research in all major disciplines of computer algebra in sciences such as physics, chemistry, life sciences, and engineering. 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.
Pseudo-Complex General Relativity
This book explores the role of singularities in general relativity (GR): The theory predicts that when a sufficient large mass collapses, no known force is able to stop it until all mass is concentrated at a point. The question arises, whether an acceptable physical theory should have a singularity, not even a coordinate singularity. The appearance of a singularity shows the limitations of the theory. In GR this limitation is the strong gravitational force acting near and at a super-massive concentration of a central mass. First, a historical overview is given, on former attempts to extend GR (which includes Einstein himself), all with distinct motivations. It will be shown that the only pos...
The Accurate Finite-difference Scheme and Finite-element Method for some Partial Differential Equations
This monograph is intended for graduate students, researchers and teachers. It is devoted to the construction of high-order schemes of the finite difference method and the finite element method for the solution of multidimensional boundary value problems for various partial differential equations, in particular, linear Helmholtz and wave equations, and nonlinear Burgers' equation. The finite difference method is a standard numerical method for solving boundary value problems. Recently, considerable attention has been paid to constructing an accurate (or exact) difference approximation for some ordinary and partial differential equations. An exact finite difference method is developed for Helmholtz and wave equations with general boundary conditions (including initial condition for wave equation) on the rectangular domain in R2. The method proposed here comes from [4] and is based on separation of variables method and expansion of one-dimensional three-point difference operators for sufficiently smooth solution. The efficiency and accuracy of the method have been tested on several examples.
Nonlinear Partial Differential Equations for Scientists and Engineers
This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.
An Introduction to Nonlinear Partial Differential Equations
Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applicati...
Physics and Astrophysics of Ultra High Energy Cosmic Rays
The International School on Physics and Astrophysics of Ultra High Energy Cosmic Rays (UHECR2000) was held at the Observatoire de Paris–Meudon on June 26-29, 2000. This was the ?rst international school speci?cally dedicated to ultra high energy cosmic rays. Its aim was to familiarize with and attract students, physicists and astronomers into this quickly developing newresearch ?eld. The mysterious and currently unknown origin of the most energetic par- cles observed in Nature has triggered in recent years theoretical speculations ranging from electromagnetic acceleration to as yet undiscovered physics - yond the Standard Model. It has also lead to the development of several new detection ...
Atomic Collisions and Spectra
Atomic Collisions and Spectra provides an overview of the state of knowledge on atomic collision physics. The book grew out of lecture notes for a succession of courses at the University of Chicago in 1967-1979, which reported the new material as it was taking a definite form. It has been enriched since 1980, as the subject matured and continued to expand. The book is organized into four parts. Part A deals briefly with rather elementary items of general information. Part B then takes up in considerable detail those aspects of single-electron scattering whose mastery is essential for treating multielectron processes. Part C deals with multielectron processes with a residual—if often realistic—restriction, namely, that the multielectron interactions remain confined within a core region from which only a single electron escapes into alternative channels of a long-range field. Part D surveys studies of double (or multiple) escape of electrons from a core. The book is intended for multiple use as a graduate school text, a tool for independent study, or a reference for particular topics.
