Numerical Methods & Computational Analysis
Root finding algorithms, linear systems, ODE/PDE solvers, regression, and applied engineering computing.
Theory Modules
Study the theory, review the governing formula, and test your knowledge with interactive questions.
Bisection Method
The bisection method repeatedly halves a continuous sign-change interval to find a root.
Error Analysis
Error analysis quantifies how far a computed or measured value deviates from a true or reference value. It distinguis...
Euler Method
The Euler method is the simplest numerical technique for solving first-order ordinary differential equations (ODEs) w...
Gauss Elimination
Gaussian elimination is a direct numerical method for solving systems of linear equations of the form [A]{x} = {b}. T...
Interpolation
Interpolation is a numerical method used to estimate unknown values that fall within the range of a discrete set of k...
MATLAB / Python Engineering Applications
MATLAB and Python are widely used to turn engineering equations, experimental data, and numerical models into repeata...
Newton-Raphson
The Newton-Raphson method (also called the Newton method) is an iterative technique for finding a root of a nonlinear...
Numerical Derivatives
Numerical differentiation is the process of estimating derivatives of a function using discrete data points rather th...
Numerical Integrals
Numerical integration (quadrature) approximates definite integrals ∫ₐᵇ f(x) dx when analytical integration is impossi...
Ordinary Differential Equations (ODE)
An Ordinary Differential Equation (ODE) is a mathematical equation that relates an unknown function of a single indep...
Optimization
Optimization is the mathematical process of finding the best possible design among a set of feasible alternatives. It...
Partial Differential Equations (PDE)
A partial differential equation (PDE) describes a dependent field variable as a function of two or more independent v...
Regression
Regression is the process of fitting a mathematical model to a set of measured data so that the model can describe th...
Root Finding
Root finding is the numerical process of determining values of x that satisfy f(x) = 0. It is fundamental in engineer...
Runge-Kutta Methods
Runge-Kutta (RK) methods are a family of numerical techniques for solving first-order initial-value ODEs of the form...
Systems of Linear Equations
A system of linear equations consists of multiple linear equations with the same set of unknowns, typically expressed...