Computational Methods in Physics: Compendium for Students

Since this is a 2^nd 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

- Discuss the exponentiation of a matrix, exp(A) (*)

- Add a Subsection on Pseudospectra (**)

- in general

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 (**)

- 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

- Add Section on Takens Theorem and its applications: phase space

- Add discussion on signal entropies (**)

- Update discussion on autoregressive models (optimal order) (*)

- Add discussion on signal directionality / causality (**)

Chapter 7

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 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 (**)