Numerical Analysis 

Introduction (What is numerical analysis?, Direct or iterative methods, Floating-point arithmetic, Fixed-point numbers)

Introduction (Floating-point numbers, Significant figures, Rounding error, Loss of significance)

Nonlinear Equations (Bisection method)

Nonlinear Equations (False position methods)

Nonlinear Equations (Newton-Raphson method)

Nonlinear Equations (Secant methods)

Nonlinear equations (Simple fixed-point iteration)

Polynomial Interpolation (Polynomial interpolation, Taylor series)

Polynomial Interpolation (Lagrange form, Newton/divided-difference form)

Polynomial Interpolation (Inverse interpolation, Interpolation error)

System of Equations (System of linear equations, Direct methods, Gaussian elimination)

System of Equations (Gauss-Jordan methods, and Cramer's rule)

System of Equations (Basic iterative methods, Jacobi method)

System of Equations (Gauss-Seidel method)

System of Equations (System of nonlinear equations, Newton's method)

Numerical Integration (Newton-Cotes formula)

Numerical Integration (The Trapezoidal rule, Error of the Trapezoidal rule)

Numerical Integration (Simpson’s rules, Composite Simpson’s rule)

Numerical Integration (Higher-Order Newton-Cotes formulas)

Numerical Integration (Romberg integration)

Numerical Integration (Gaussian quadrature formulas)

Numerical Differentiation ‎(High-accuracy differentiation formulas, Richardson extrapolation)

Numerical Differentiation (Taylor series methods)

Numerical Differentiation (Euler’s method)

Numerical Differentiation (Improvements of Euler’s method)

Numerical Differentiation (Taylor series method of higher order)

Numerical Differentiation (Second-order Runge-Kutta methods)

Numerical Differentiation (Fourth-order Runge-Kutta method)

Numerical Differentiation (First-order system)

Numerical Differentiation (Higher-order system)

Introduction (What is numerical analysis?, Direct or iterative methods, Floating-point arithmetic, Fixed-point numbers)

Introduction (Floating-point numbers, Significant figures, Rounding error, Loss of significance)

Nonlinear Equations (Bisection method)

Nonlinear Equations (False position methods)

Nonlinear Equations (Newton-Raphson method)

Nonlinear Equations (Secant methods)

Nonlinear equations (Simple fixed-point iteration)

Polynomial Interpolation (Polynomial interpolation, Taylor series)

Polynomial Interpolation (Lagrange form, Newton/divided-difference form)

Polynomial Interpolation (Inverse interpolation, Interpolation error)

Polynomial Interpolation (Convergence and the Chebyshev nodes, Derivative conditions)

Linear Equations (Gaussian elimination, Triangular systems)

Linear Equations (LU factorization, Cholesky factorization)

Linear Equations (Pivoting, Vector norms, Matrix norms, Condition Number and Conditioning)

Linear Equations (Basic iterative methods, Jacobi method, Gauss-Seidel method )

Numerical Integration (Newton-Cotes formula)

Numerical Integration (The Trapezoidal rule, Error of the Trapezoidal rule)

Numerical Integration (Simpson’s rules, Composite Simpson’s rule)

Numerical Integration (Higher-Order Newton-Cotes formulas)

Numerical Integration (Romberg integration)

Numerical Integration (Gaussian quadrature formulas)

Numerical Differentiation ‎(High-accuracy differentiation formulas, Richardson extrapolation)

Numerical Differentiation (Taylor series methods)

Numerical Differentiation (Euler’s method)

Numerical Differentiation (Improvements of Euler’s method)

Numerical Differentiation (Taylor series method of higher order)

Numerical Differentiation (Second-order Runge-Kutta methods)

Numerical Differentiation (Fourth-order Runge-Kutta method)

Numerical Differentiation (First-order system)

Numerical Differentiation (Higher-order system)

Introduction (What is numerical analysis?, Direct or iterative methods, Floating-point arithmetic, Fixed-point numbers)

Introduction (Floating-point numbers, Significant figures, Rounding error, Loss of significance)

Nonlinear Equations (Bisection method)

Nonlinear Equations (False position methods)

Nonlinear equations (Simple fixed-point iteration)

Nonlinear Equations (Newton-Raphson method)

Nonlinear Equations (Secant methods)

Polynomial Interpolation (Polynomial interpolation, Taylor series)

Polynomial Interpolation (Lagrange form, Newton/divided-difference form)

Polynomial Interpolation (Inverse interpolation, Interpolation error)

Polynomial Interpolation (Convergence and the Chebyshev nodes, Derivative conditions)

Linear Equations (Gaussian elimination, Triangular systems)

Linear Equations (LU factorization, Cholesky factorization)

Linear Equations (Pivoting, Vector norms, Matrix norms, Condition Number and Conditioning)

Linear Equations (Basic iterative methods, Jacobi method, Gauss-Seidel method )

Numerical Integration (Newton-Cotes formula)

Numerical Integration (The Trapezoidal rule, Error of the Trapezoidal rule)

Numerical Integration (Simpson’s rules, Composite Simpson’s rule)

Numerical Integration (Higher-Order Newton-Cotes formulas)

Numerical Integration (Romberg integration)

Numerical Integration (Gaussian quadrature formulas)

Numerical Differentiation ‎(High-accuracy differentiation formulas, Richardson extrapolation)

Numerical Differentiation (Taylor series methods)

Numerical Differentiation (Euler’s method)

Numerical Differentiation (Improvements of Euler’s method)

Numerical Differentiation (Taylor series method of higher order)

Numerical Differentiation (Second-order Runge-Kutta methods)

Numerical Differentiation (Fourth-order Runge-Kutta method)

Numerical Differentiation (First-order system)

Numerical Differentiation (Higher-order system)