Numerical Analysis

These notes organize Burden and Faires, Numerical Analysis, 9th edition, into a practical wiki path for computation, analysis, and implementation. The emphasis is the central theme of the text: numerical algorithms are useful only when their approximation error, floating-point behavior, convergence, and stability are understood together.

The sequence starts with calculus-based error estimates and machine arithmetic, then moves through nonlinear equations, interpolation, differentiation, integration, ordinary differential equations, numerical linear algebra, approximation theory, eigenvalue problems, nonlinear systems, boundary-value problems, and finite-difference methods for partial differential equations. Each topic page follows the same study pattern: intuition, algorithm, convergence or stability analysis, a worked example, and executable Python/NumPy/SciPy-style code.

Use the pages in order for a first pass; later, jump directly to the method family needed for a computation.

1. Numerical Analysis
2. Mathematical Preliminaries and Error Analysis
3. Floating Point Conditioning and Stability
4. Bisection and Fixed Point Iteration
5. Newton Secant and Polynomial Roots
6. Lagrange Interpolation and Neville Method
7. Divided Differences and Hermite Interpolation
8. Cubic Splines and Parametric Curves
9. Numerical Differentiation and Richardson Extrapolation
10. Newton Cotes and Romberg Integration
11. Adaptive and Gaussian Quadrature
12. Euler Taylor and Runge Kutta Methods
13. Adaptive Runge Kutta and Multistep Methods
14. ODE Stability Stiffness and Systems
15. Gaussian Elimination Pivoting and LU
16. Matrix Factorizations and Special Systems
17. Jacobi Gauss Seidel and SOR
18. Conjugate Gradient and Iterative Refinement
19. Least Squares and Chebyshev Approximation
20. Rational Trigonometric Approximation and FFT
21. Eigenvalue Methods
22. Nonlinear Systems
23. Boundary Value Problems
24. Finite Difference Methods for PDEs