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Computational Physics

Nguồn ngoài

Computational Physics

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.

Mathematical Physics and PedagogyPhysics
Tác giả
Y. D. Chong
Nhà xuất bản
Nanyang Technological University
Nguồn
LibreTexts
Giấy phép
CC BY-SA
Ngôn ngữ
EN
Danh mục
Khoa học cơ bản
Đọc trực tuyến Tải PDF (nguồn mở)
Mục lục· 57 mục
  1. 01: Scipy Tutorial
  2. 1.01: Preliminaries
  3. 1.02: Getting Started
  4. 1.03: Modularizing the Code
  5. 02: Scipy Tutorial (Part 2)
  6. 2.01: Sequential Data Structures
  7. 2.02: Improving the Program
  8. 03: Numbers Arrays and Scaling
  9. 3.01: A Model of Computing
  10. 3.02: Integers and Floating-Point Numbers
  11. 3.03: Arrays
  12. 3.04: Exercises
  13. 04: Numerical Linear Algebra
  14. 4.01: Array Representations of Vectors Matrices and Tensors
  15. 4.02: Linear Equations
  16. 4.03: Exercises
  17. 05: Gaussian Elimination
  18. 5.01: The Basic Algorithm
  19. 5.02: Matrix Generalization
  20. 5.03: Pivoting
  21. 5.04: LU Decomposition
  22. 06: Eigenvalue Problems
  23. 6.01: Basic Facts about Eigenvalue Problems
  24. 6.02: Numerical Eigensolvers
  25. 07: Finite-Difference Equations
  26. 7.01: Derivatives
  27. 7.02: Discretizing Partial Differential Equations
  28. 7.03: Higher Dimensions
  29. 08: Sparse Matrices
  30. 8.01: Sparse Matrix Algebra
  31. 8.02: Sparse Matrix Formats
  32. 8.03: Using Sparse Matrices
  33. 8.04: Example- Particle-in-a-Box Problem
  34. 09: Numerical Integration
  35. 9.01: Mid-Point Rule
  36. 9.02: Trapezium Rule
  37. 9.03: Simpson's Rule
  38. 9.04: Gaussian Quadratures
  39. 9.05: Monte Carlo Integration
  40. 10: Numerical Integration of ODEs
  41. 10.01: Example- Equations of Motion in Classical Mechanics
  42. 10.02: Forward Euler Method
  43. 10.03: Backward Euler Method
  44. 10.04: Adams-Moulton Method
  45. 10.05: Runge-Kutta Methods
  46. 10.06: Integrating ODEs with Scipy
  47. 11: Discrete Fourier Transforms
  48. 11.01: Conversion of Continuous Fourier Transform to DFT
  49. 11.02: Spectral Resolution and Range
  50. 11.03: The Split-Step Fourier Method
  51. 12: Markov Chains
  52. 12.01: The Simplest Markov Chain- The Coin-Flipping Game
  53. 12.02: General Description
  54. 12.03: The Ehrenfest Model
  55. 13: The Markov Chain Monte Carlo Method
  56. 13.01: Basic Formulation
  57. 13.02: The Ising Model