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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.
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.
Black holes and gravitational radiation are two of the most
dramatic predictions of general relativity. The quest for rotating
black holes - discovered by Roy P. Kerr as exact solutions to the
Einstein equations - is one of the most exciting challenges facing
physicists and astronomers. Gravitational Radiation, Luminous Black
Holes and Gamma-Ray Burst Supernovae takes the reader through the
theory of gravitational radiation and rotating black holes, and the
phenomenology of GRB-supernovae. Topics covered include Kerr black
holes and the frame-dragging of spacetime, luminous black holes,
compact tori around black holes, and black-hole spin interactions.
It concludes with a discussion of prospects for gravitational-wave
detections of a long-duration burst in gravitational-waves as a
method of choice for identifying Kerr black holes in the Universe.
This book is ideal for a special topics graduate course on
gravitational-wave astronomy and as an introduction to those
interested in this contemporary development in physics.
In this decade, the Transient Universe will be mapped out in great
detail by the emerging wide-field multiwavelength surveys, and
neutrino and gravitational-wave detectors, promising to probe the
astronomical and physical origin of the most extreme relativistic
sources. This volume introduces the physical processes relevant to
the source modeling of the Transient Universe. Ideal for graduate
students and researchers in astrophysics, this book gives a unified
treatment of relativistic flows associated with compact objects,
their dissipation and emission in electromagnetic, hadronic and
gravitational radiation. After introducing the source classes, the
authors set out various mechanisms for creating magnetohydodynamic
outflows in winds, jets and blast waves and their radiation
properties. They then go on to discuss properties of accretion
flows around rotating black holes and their gravitational wave
emission from wave instabilites with implications for the emerging
gravitational wave experiments. Graduate students and researchers
can gain an understanding of data analysis for gravitational-wave
data.
Black holes and gravitational radiation are two of the most
dramatic predictions of general relativity. The quest for rotating
black holes - discovered by Roy P. Kerr as exact solutions to the
Einstein equations - is one of the most exciting challenges
currently facing physicists and astronomers. Gravitational
Radiation, Luminous Black Holes and Gamma-Ray Burst Supernovae
takes the reader through the theory of gravitational radiation and
rotating black holes, and the phenomenology of GRB-supernovae.
Topics covered include Kerr black holes and the frame-dragging of
spacetime, luminous black holes, compact tori around black holes,
and black-hole spin interactions. It concludes with a discussion of
prospects for gravitational-wave detections of a long-duration
burst in gravitational-waves as a method of choice for identifying
Kerr black holes in the Universe. This book is ideal for a special
topics graduate course on gravitational-wave astronomy and as an
introduction to those interested in this contemporary development
in physics.
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