Numerical Methods

by Jeffrey R. Chasnov

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These notes, taught at the Hong Kong University of Science and Technology with two lecture hours per week, are primarily for non-mathematics majors and were required by several engineering departments.

Description from LibreTexts.

Publisher
Hong Kong University of Science and Technology
Subjects
Mathematics, Applied Mathematics
Licence
CC BY, 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. Latex
  7. 1: IEEE Arithmetic
  8. 1.1: Definitions
  9. 1.2: Numbers with a Decimal or Binary Point
  10. 1.3: Examples of Binary Numbers
  11. 1.4: Hex Numbers
  12. 1.5: 4-bit Unsigned Integers as Hex Numbers
  13. 1.6: IEEE Single Precision Format
  14. 1.7: Special Numbers
  15. 1.8: Examples of Computer Numbers
  16. 1.9: Inexact Numbers
  17. 1.10: Machine Epsilon
  18. 1.11: IEEE Double Precision Format
  19. 1.12: Roundoff Error Example
  20. 2: Root Finding
  21. 2.1: Bisection Method
  22. 2.2: Newton's Method
  23. 2.3: Secant Method
  24. 2.4: Order of Convergence
  25. 3: System of Equations
  26. 3.1: Gaussian Elimination
  27. 3.2: LU Decomposition
  28. 3.3: Partial Pivoting
  29. 3.4: Operation Counts
  30. 3.5: System of Nonlinear Equations
  31. 4: Least-Squares Approximation
  32. 4.1: Fitting a Straight Line
  33. 4.2: Fitting to a Linear Combination of Functions
  34. 5: Interpolation
  35. 5.1: Polynomial Interpolation
  36. 5.2: Piecewise Linear Interpolation
  37. 5.3: Cubic Spline Interpolation
  38. 5.4: Multidimensional Interpolation
  39. 6: Integration
  40. 6.1: Elementary Formulas
  41. 6.2: Composite Rules
  42. 6.3: Local Versus Global Error
  43. 6.4: Adaptive Integration
  44. 7: Ordinary Differential Equations
  45. 7.1: Examples of Analytical Solutions
  46. 7.2: Numerical Methods - Initial Value Problem
  47. 7.3: Numerical Methods - Boundary Value Problem
  48. 7.4: Numerical Methods - Eigenvalue Problem
  49. Back Matter
  50. Index
  51. Detailed Licensing