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.