Computational methods for physicists: compendium for students

Description

Since this is a 2nd Edition, we are giving below the topics we wish to add/update/revise in roughly the same chapter sequence as we had in the existing 1st Edition of the book. In addition to a general revision of the text, we propose the following major modifications (the asterisks denote the amount of text added/modified and/or or the difficulty level of the topics being discussed): Chapter 2 - Subsection 2.1.2: add discussion on how to find all zeros by means of the Newton method (*) Chapter 3 - Expand Subsection 3.2.7 on solving the A*x = b equations with sparse matrices to a full Section (**) - Expand Subsection 3.4.5 on solving the eigenvalue problem A*x = lambda*x to a full Section (**) - Discuss the exponentiation of a matrix, exp(A) (*) - Add a Subsection on Pseudospectra (**) - in general, enhance the "sparse" aspect of the chapter Chapter 4 - Add a new Section on Sparse FFT (following present Sec. 4.2), add corresponding Exercise (**) - Expand Subsection 4.6.2 on the Discrete Wavelet Transform to a full Section, add Exercise (***) - Add a Section on image denoising (**) - Add Section on Radon transformation (**) Chapter 5 - Rewrite Sections 5.1-5.5 to better distinguish between general discussion of distributions and the techniques involving samples, and to bring the notation in line with the book "Probability for Physicists" (***) - Introduce Bayesian data analysis and inference (***) - Expand Subsection 5.5.8 on Non-linear Regression to a full Section, add Exercises (**) Chapter 6 - Expand Section 6.5 on Noise, add Exercise (**) - Add Section on Takens Theorem and its applications: phase space reconstruction and optimal size determination (**) - Add discussion on signal entropies (**) - Update discussion on autoregressive models (optimal order) (*) - Add discussion on signal directionality / causality (**) Chapter 7 - Expand Section 7.10 on Stiff Problems of ODE, add Exercise (**) Chapter 8 - Expand Subsection 8.7.4 on Singular SL Problems to a Section, add Exercise (**) - Motivated by Section 8.8, write a new chapter on Inverse Problems (***) Chapter 10 - Expand Section 10.8, add Exercise (**) Chapter 11 - Expand Sections 11.7 and 11.8, add Exercises (**) New Chapter on Inverse Methods (***) New short Chapter or Appendix on minimization (**) - with derivatives or without them - with constraints or without them - deterministic and quasi-deterministic (MC methods) New Appendix on spline methods: B-splines, Bezier splines (**)