Computational Physics

by Y. D. Chong

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An introductory course in computational physics for upper-level undergraduates. Topics covered include numerical linear algebra, eigenvalue problems, sparse matrix problems, numerical integration and initial-value problems, Fourier transforms, and Monte Carlo simulations. Programming examples are based on Scientific Python.

Description from LibreTexts.

Publisher
Nanyang Technological University
Subjects
Physics, Mathematical Physics and Pedagogy
Licence
CC BY-SA 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Scipy Tutorial
  7. 1.1: Preliminaries
  8. 1.2: Getting Started
  9. 1.3: Modularizing the Code
  10. 2: Scipy Tutorial (Part 2)
  11. 2.1: Sequential Data Structures
  12. 2.2: Improving the Program
  13. 3: Numbers, Arrays, and Scaling
  14. 3.1: A Model of Computing
  15. 3.2: Integers and Floating-Point Numbers
  16. 3.3: Arrays
  17. 3.4: Exercises
  18. 4: Numerical Linear Algebra
  19. 4.1: Array Representations of Vectors, Matrices, and Tensors
  20. 4.2: Linear Equations
  21. 4.3: Exercises
  22. 5: Gaussian Elimination
  23. 5.1: The Basic Algorithm
  24. 5.2: Matrix Generalization
  25. 5.3: Pivoting
  26. 5.4: LU Decomposition
  27. 6: Eigenvalue Problems
  28. 6.1: Basic Facts about Eigenvalue Problems
  29. 6.2: Numerical Eigensolvers
  30. 7: Finite-Difference Equations
  31. 7.1: Derivatives
  32. 7.2: Discretizing Partial Differential Equations
  33. 7.3: Higher Dimensions
  34. 8: Sparse Matrices
  35. 8.1: Sparse Matrix Algebra
  36. 8.2: Sparse Matrix Formats
  37. 8.3: Using Sparse Matrices
  38. 8.4: Example- Particle-in-a-Box Problem
  39. 9: Numerical Integration
  40. 9.1: Mid-Point Rule
  41. 9.2: Trapezium Rule
  42. 9.3: Simpson's Rule
  43. 9.4: Gaussian Quadratures
  44. 9.5: Monte Carlo Integration
  45. 10: Numerical Integration of ODEs
  46. 10.1: Example- Equations of Motion in Classical Mechanics
  47. 10.2: Forward Euler Method
  48. 10.3: Backward Euler Method
  49. 10.4: Adams-Moulton Method
  50. 10.5: Runge-Kutta Methods
  51. 10.6: Integrating ODEs with Scipy
  52. 11: Discrete Fourier Transforms
  53. 11.1: Conversion of Continuous Fourier Transform to DFT
  54. 11.2: Spectral Resolution and Range
  55. 11.3: The Split-Step Fourier Method
  56. 12: Markov Chains
  57. 12.1: The Simplest Markov Chain- The Coin-Flipping Game
  58. 12.2: General Description
  59. 12.3: The Ehrenfest Model
  60. 13: The Markov Chain Monte Carlo Method
  61. 13.1: Basic Formulation
  62. 13.2: The Ising Model
  63. Back Matter
  64. Index
  65. Glossary
  66. Detailed Licensing