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.
