Computational Methods in Physics

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 (**)