Computational Methods in Physics : Compendium for Students This book is intended to help advanced undergraduate graduate and postdoctoral students in their daily work by oﬀering them a compendium of numerical methods. The choice of methods pays signiﬁcant attention to error estimates stability and convergence issues as well as optimization of program execution speeds. Numerous examples are given throughout the chapters followed by comprehensive end of chapter problems with a more pronounced physics background while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations inverse Sturm Liouville problems as well as retrospective and recovery problems for partial diﬀerential equations. The revised text now includes an introduction to sparse matrix methods the solution of matrix equations and pseudospectra of matrices; it discusses the sparse Fourier non uniform Fourier and discrete wavelet transformations the basics of non linear regression and the Kolmogorov Smirnov test; it demonstrates the key concepts in solving stiﬀ diﬀerential equations and the asymptotics of Sturm Liouville eigenvalues and eigenfunctions. Among other updates it also presents the techniques of state space reconstruction methods to calculate the matrix exponential generate random permutations and compute stable derivatives Basics of numerical analysis Solution of nonlinear equations Matrix methods Transformations of functions and signals Statistical description and modeling of data Modeling and analysis of time series Initial value problems for ordinary differential equations Boundary value problems for ordinary differential equations Difference methods for one dimensional partial differential equations Difference methods for partial differential equations in more than one dim Spectral methods for partial differential equations Inverse methods