Numerical Analysis

• Linear Equations:
  • [[Direct methods]] ([[Gaussian elimination]], [[LU decomposition]], [[Cholesky factorization]]).
  • [[Iterative methods (Gauss-Seidel and Jacobi)]] and their convergence for diagonally dominant coefficient matrices.
• Nonlinear Equations:
  • [[Bisection method]], [[secant method]], [[Newton-Raphson method]], [[fixed point iteration]].
• Interpolation:
  • [[Lagrange and Newton forms of interpolating polynomial]], [[Error in polynomial interpolation of a function]].
• Calculus & ODEs:
  • [[Numerical differentiation and error]].
  • [[Numerical integration]]: [[Trapezoidal and Simpson rules]], [[Newton-Cotes integration formulas]], [[composite rules]], [[mathematical errors involved in numerical integration formulae]].
  • [[Numerical solution of initial value problems for ordinary differential equations]]: [[Methods of Euler]], [[Runge-Kutta method of order 2]].