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Numerical Methods
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.
- Author
- Jeffrey R. Chasnov
- Publisher
- Hong Kong University of Science and Technology
- Source
- LibreTexts
- License
- CC BY
- Language
- EN
- Category
- Basic Sciences
Contents· 42 sections
- 01: IEEE Arithmetic
- 1.01: Definitions
- 1.02: Numbers with a Decimal or Binary Point
- 1.03: Examples of Binary Numbers
- 1.04: Hex Numbers
- 1.05: 4-bit Unsigned Integers as Hex Numbers
- 1.06: IEEE Single Precision Format
- 1.07: Special Numbers
- 1.08: Examples of Computer Numbers
- 1.09: Inexact Numbers
- 1.10: Machine Epsilon
- 1.11: IEEE Double Precision Format
- 1.12: Roundoff Error Example
- 02: Root Finding
- 2.01: Bisection Method
- 2.02: Newton's Method
- 2.03: Secant Method
- 2.04: Order of Convergence
- 03: System of Equations
- 3.01: Gaussian Elimination
- 3.02: LU Decomposition
- 3.03: Partial Pivoting
- 3.04: Operation Counts
- 3.05: System of Nonlinear Equations
- 04: Least-Squares Approximation
- 4.01: Fitting a Straight Line
- 4.02: Fitting to a Linear Combination of Functions
- 05: Interpolation
- 5.01: Polynomial Interpolation
- 5.02: Piecewise Linear Interpolation
- 5.03: Cubic Spline Interpolation
- 5.04: Multidimensional Interpolation
- 06: Integration
- 6.01: Elementary Formulas
- 6.02: Composite Rules
- 6.03: Local Versus Global Error
- 6.04: Adaptive Integration
- 07: Ordinary Differential Equations
- 7.01: Examples of Analytical Solutions
- 7.02: Numerical Methods - Initial Value Problem
- 7.03: Numerical Methods - Boundary Value Problem
- 7.04: Numerical Methods - Eigenvalue Problem