Introduction to Methods of Approximation in Physics and Astronomy

MAURICE H. P. M. VAN PUTTEN is a Professor of Physics and Astronomy at Sejong University and an Associate Member of the School of Physics, Korea Institute for Advanced Study. He received his Ph.D. from the California Institute of Technology and held postdoctoral research positions at the Institute for Theoretical Physics at the University of California, Santa Barbara, and the Center for Radiophysics and Space Research at Cornell University. He held faculty positions at the Massachusetts Institute of Technology, Nanjing University and the Institute for Advanced Studies at CNRS-Orleans. His current research focus is on multimessenger emissions from rotating black holes including gravitational radiation from core-collapse supernovae and long gamma-ray bursts, Ultra-High Energy Cosmic Rays (UHECRs) from Seyfert galxies, dynamical dark energy in cosmology and hyperbolic formulations of general relativity and relativistic magneto-hydrodynamics.

Preface.- Part I Preliminaries.- 1 Complex numbers.- 2 Complex function theory.- 3 Vectors and linear algebra.- 4 Linear partial differential equations.- Part II Methods of approximation.- 5 Projections and minimal distances.- 6 Spectral methods and signal analysis.- 7 Root finding.- 8 Finite differencing: differentiation and integration.- 9 Perturbation theory, scaling and turbulence.- Part III Selected topics.- 10 Thermodynamics of N-body systems.- 11 Accretion flows onto black holes.- 12 Rindler observers in astrophysics and cosmology.- A Some units and constant.- B Г(z) and Ϛ(z) functions.

“This is a thorough and rigorous introduction to the subject, intended for students at the graduate or very advanced undergraduate level. Van Putten (Sejong Univ., South Korea) presents a collection of problems that most readers will find quite challenging to solve. … Summing Up: Recommended. With reservations. Upper-division undergraduates through faculty and professionals.” (T. Barker, Choice, Vol. 55 (10), June 2018)