Function evaluation
Polynomials
Series
Continued fractions
Least squares fitting
Histograms
Interpolation:




Lagrange interpolation (formula)
o Linear interpolation (formula)
o Polynomial interpolation (algorithm)
Neville’s algorithm (formula and algorithm)
Cubic spline (definitions)
Rational function interpolation(formula, algorithm)
Solution of nonlinear equations (root finding):




Roots of polynomial
Bisection method (method, error)
Newton and Raphson method (method, error)
Method of secants (method, error)
Derivatives



Forward difference
Central difference and higher-order methods
Higher-order derivatives
Numerical integration



Rectangular integration
Trapezoid integration
Simpson method
Steepest descent




Least-squares fit to arbitrary function
Method of least squares
Grid search
Gradient search
Differential equations



Simple Euler method
Modified Euler method
Modified Euler method; predictor-corrector
Monte Carlo simulation



Uniform random number generation
Random number for non-uniform distributions
o Inversion method
o Accept and reject method
Monte Carlo integration
Linear regression



Constant errors
Weighting the fit
Estimate of sigma
Solution of simultaneous algebraic equations







Linear systems of equations
Gaussian elimination
Back substitution
Gaussian elimination used in determinant evaluation
Gaussian-Jordan elimination method
Matrix inversion
Eigenvalue problem
Partial differential equations



Elliptical partial differential equation
Parabolic partial differential equation
Hyperbolic partial differential equation
Ordinary differential equations: boundary-value problem


Trial-and-error method
Simultaneous-equation method