Numerical Analysis/Topics

Causes of Errors w: Loss of Significance, Loss of Significance Numerical Linear Algebra w:Matrix norm, exercises w:LU decomposition, exercises, concept quiz w:Power iteration, exercises, examples w:Inverse iteration, exercises shifted inverse iteration w:Householder transformation, exercises Topic:Numerical Analysis/Matrix norm Iterative Refinement

Interpolation w: Polynomial interpolation Using the Vandermonde matrix, example, exercise w: Lagrange polynomial, example, exercise w: Newton polynomial w: Divided differences, proofs and examples Polynomial example, exercise w: Neville's algorithm, examples, quiz, code Interpolation_and_Extrapolation Comparison of the methods, concept quiz Cubic Spline Interpolation

Finding roots of nonlinear equations Rootfinding for nonlinear equations The bisection method Exercises on the bisection method Solution of the exercises on the bisection method The Newton's method Resources about rootfinding for nonlinear equations The Secant Method w: Fixed-point iteration, Fixed Point Iteration

Optimization

Integration and Differentiation Differentiation, examples Error of Analysis of Newton-Cotes formulas w: Romberg's method, Romberg's Integration method, Sample Code, Example, Exercise, Quiz w: Gaussian Quadrature, Gaussian Quadrature

Ordinary Differential Equations w: Truncation error (numerical integration), Truncation Errors w:Euler_method w:Runge-Kutta stability of RK methods exercises quiz Order of RK methods w:Multistep_methods Adams-bashforth and Adams-moulton methods stability of Multistep methods ODE Exercises ODE in vector form Exercises Quiz