Introduction To Methods Of Approximation In Physics And Astronomy
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| Author | : Maurice H. P. M. van Putten |
| Publisher | : Springer |
| Total Pages | : 347 |
| Release | : 2017-04-07 |
| Genre | : Science |
| ISBN | : 9811029326 |
This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based on their usefulness and educational value, their applicability to a broad range of problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals an evolving universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data-analysis. The book is organized to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. Some of the topics highlighted introduce the reader to selected problems with comments on numerical methods and implementation on modern platforms including CPU-GPU computing. Developed from lectures on mathematical physics in astronomy to advanced undergraduate and beginning graduate students, this book will be a valuable guide for students and a useful reference for practicing researchers. To aid understanding, exercises are included at the end of each chapter. Furthermore, some of the exercises are tailored to introduce modern symbolic computation.
| Author | : Peter Bodenheimer |
| Publisher | : CRC Press |
| Total Pages | : 360 |
| Release | : 2006-12-13 |
| Genre | : Science |
| ISBN | : 9780750308830 |
Numerical Methods in Astrophysics: An Introduction outlines various fundamental numerical methods that can solve gravitational dynamics, hydrodynamics, and radiation transport equations. This resource indicates which methods are most suitable for particular problems, demonstrates what the accuracy requirements are in numerical simulations, and suggests ways to test for and reduce the inevitable negative effects. After an introduction to the basic equations and derivations, the book focuses on practical applications of the numerical methods. It explores hydrodynamic problems in one dimension, N-body particle dynamics, smoothed particle hydrodynamics, and stellar structure and evolution. The authors also examine advanced techniques in grid-based hydrodynamics, evaluate the methods for calculating the gravitational forces in an astrophysical system, and discuss specific problems in grid-based methods for radiation transfer. The book incorporates brief user instructions and a CD-ROM of the numerical codes, allowing readers to experiment with the codes to suit their own needs. With numerous examples and sample problems that cover a wide range of current research topics, this highly practical guide illustrates how to solve key astrophysics problems, providing a clear introduction for graduate and undergraduate students as well as researchers and professionals.
| Author | : George B. Rybicki |
| Publisher | : John Wiley & Sons |
| Total Pages | : 402 |
| Release | : 2008-09-26 |
| Genre | : Science |
| ISBN | : 352761818X |
Radiative Processes in Astrophysics: This clear, straightforward, and fundamental introduction is designed to present-from a physicist's point of view-radiation processes and their applications to astrophysical phenomena and space science. It covers such topics as radiative transfer theory, relativistic covariance and kinematics, bremsstrahlung radiation, synchrotron radiation, Compton scattering, some plasma effects, and radiative transitions in atoms. Discussion begins with first principles, physically motivating and deriving all results rather than merely presenting finished formulae. However, a reasonably good physics background (introductory quantum mechanics, intermediate electromagnetic theory, special relativity, and some statistical mechanics) is required. Much of this prerequisite material is provided by brief reviews, making the book a self-contained reference for workers in the field as well as the ideal text for senior or first-year graduate students of astronomy, astrophysics, and related physics courses. Radiative Processes in Astrophysics also contains about 75 problems, with solutions, illustrating applications of the material and methods for calculating results. This important and integral section emphasizes physical intuition by presenting important results that are used throughout the main text; it is here that most of the practical astrophysical applications become apparent.
| Author | : Tai L. Chow |
| Publisher | : Cambridge University Press |
| Total Pages | : 575 |
| Release | : 2000-07-27 |
| Genre | : Science |
| ISBN | : 1139427962 |
This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the reader has an adequate preparation in general physics and calculus. The book bridges the gap between an introductory physics course and more advanced courses in classical mechanics, electricity and magnetism, quantum mechanics, and thermal and statistical physics. The text contains a large number of worked examples to illustrate the mathematical techniques developed and to show their relevance to physics. The book is designed primarily for undergraduate physics majors, but could also be used by students in other subjects, such as engineering, astronomy and mathematics.
| Author | : Kenneth Franklin Riley |
| Publisher | : |
| Total Pages | : 1008 |
| Release | : 1997 |
| Genre | : |
| ISBN | : |
| Author | : James F. Epperson |
| Publisher | : John Wiley & Sons |
| Total Pages | : 579 |
| Release | : 2013-06-06 |
| Genre | : Mathematics |
| ISBN | : 1118626230 |
Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
| Author | : Tao Pang |
| Publisher | : Cambridge University Press |
| Total Pages | : 414 |
| Release | : 2006-01-19 |
| Genre | : Computers |
| ISBN | : 9780521825696 |
This advanced textbook provides an introduction to the basic methods of computational physics.
| Author | : Dan Maoz |
| Publisher | : Princeton University Press |
| Total Pages | : 310 |
| Release | : 2016-02-23 |
| Genre | : Science |
| ISBN | : 0691164797 |
The ideal one-semester astrophysics introduction for science undergraduates—now expanded and fully updated Winner of the American Astronomical Society's Chambliss Award, Astrophysics in a Nutshell has become the text of choice in astrophysics courses for science majors at top universities in North America and beyond. In this expanded and fully updated second edition, the book gets even better, with a new chapter on extrasolar planets; a greatly expanded chapter on the interstellar medium; fully updated facts and figures on all subjects, from the observed properties of white dwarfs to the latest results from precision cosmology; and additional instructive problem sets. Throughout, the text features the same focused, concise style and emphasis on physics intuition that have made the book a favorite of students and teachers. Written by Dan Maoz, a leading active researcher, and designed for advanced undergraduate science majors, Astrophysics in a Nutshell is a brief but thorough introduction to the observational data and theoretical concepts underlying modern astronomy. Generously illustrated, it covers the essentials of modern astrophysics, emphasizing the common physical principles that govern astronomical phenomena, and the interplay between theory and observation, while also introducing subjects at the forefront of modern research, including black holes, dark matter, dark energy, and gravitational lensing. In addition to serving as a course textbook, Astrophysics in a Nutshell is an ideal review for a qualifying exam and a handy reference for teachers and researchers. The most concise and current astrophysics textbook for science majors—now expanded and fully updated with the latest research results Contains a broad and well-balanced selection of traditional and current topics Uses simple, short, and clear derivations of physical results Trains students in the essential skills of order-of-magnitude analysis Features a new chapter on extrasolar planets, including discovery techniques Includes new and expanded sections and problems on the physics of shocks, supernova remnants, cosmic-ray acceleration, white dwarf properties, baryon acoustic oscillations, and more Contains instructive problem sets at the end of each chapter Solutions manual (available only to professors)
| Author | : Yale University |
| Publisher | : |
| Total Pages | : 1284 |
| Release | : 1924 |
| Genre | : |
| ISBN | : |
| Author | : Boris Mikhailovich Karnakov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 180 |
| Release | : 2012-08-28 |
| Genre | : Science |
| ISBN | : 3642315585 |
This book has evolved from lectures devoted to applications of the Wentzel - Kramers – Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N −expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.
