Computational methods for physicists: compendium for students

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 (**)