Numerical Methods Step by Step
Error and Representation
Absolute and Relative Error
Rounding and Significant Figures
Stopping Criteria and Residual
Machine Epsilon by Halving
Root Finding — Bracketing
Bisection Method
False Position (Regula Falsi)
Bracketing and Sign Change
Root Finding — Open Methods
Newton-Raphson Method
Secant Method
Fixed-Point Iteration
Convergence Comparison
Interpolation
Linear Interpolation
Lagrange Interpolation
Newton Divided Differences
Numerical Integration
Trapezoidal Rule
Simpson's Rule
Composite Trapezoidal Rule
Integration Error Estimate
Numerical Differentiation
Forward Difference
Central Difference
Richardson Extrapolation
Linear Systems
Gaussian Elimination with Partial Pivoting
LU Decomposition
Jacobi Iteration
Gauss-Seidel Iteration
ODEs
Euler's Method
Improved Euler (Heun's Method)
Runge-Kutta (RK4)
![Three bisection steps for x squared minus 2 narrow [1, 2] to [1.375, 1.5], width 0.125; the exact root is sqrt(2), shown separately.](assets/numerical-methods-cover.svg)