# Numerical Analysis Topics

## 1. Computer Numbers

- The Decimal and Binary Number Systems
- Arithmetic with Binary Numbers
- Converting Binary Numbers to Decimal Numbers
- Converting Decimal Numbers to Binary Numbers
- Floating Point Numbers
- Storage of Numbers in IEEE Single-Precision Floating Point Format ( Examples 1 )
- Accuracy of Floating Point Representations of Numbers
- Truncation of Floating Point Numbers
- Rounding of Floating Point Numbers

## 2. Error

## 3. Root-Finding Methods

- The Bisection Method for Approximating Roots
- The Algorithm for The Bisection Method for Approximating Roots
- Applying The Bisection Method
- Newton's Method for Approximating Roots
- Error Estimation and Error Verification of Newton's Method
- The Convergence of Newton's Method
- The Algorithm for Newton's Method for Approximating Roots
- Applying Newton's Method
- Error Analysis of Newton's Method for Approximating Roots
- Fixed Points ( Examples 1 )
- The Fixed Point Method for Approximating Roots
- The Convergence of The Fixed Point Method
- The Algorithm for The Fixed Point Method
- Applying The Fixed Point Method ( Examples 1 )

## 4. Interpolation Polynomials

- Linear Lagrange Interpolating Polynomials ( Examples 1 )
- Quadratic Lagrange Interpolating Polynomials ( Examples 1 )
- Higher Order Lagrange Interpolating Polynomials
- Bounds of Error in Higher Order Lagrange Interpolating Polynomials
- Divided Differences
- Newton's Divided Differences Interpolation Formula
- Natural Cubic Spline Function Interpolation ( Examples 1 )
- Cubic Splines for Interpolating Functions
- Error in Polynomial Interpolations

## 5. Systems of Linear Equations

- Matrix Arithmetic
- Properties of Matrix Arithmetic
- Elementary Row Operations on Matrices
- The Invertibility of a Matrix
- The Determinant of a Matrix
- Linear Equations and Systems of Linear Equations
- The Gaussian Elimination Algorithm
- Partial Pivoting in Gaussian Elimination
- The Algorithm for Gaussian Elimination with Partial Pivoting
- Computing the Inverse of a Matrix with Gaussian Elimination
- Counting Operations in Gaussian Elimination
- The LU Decomposition of a Matrix ( Examples 1 | Examples 2 )
- Doolittle's Method for LU Decompositions
- The Algorithm for Doolittle's Method for LU Decompositions
- LU Decompositions for Tridiagonal Matrices
- Error in Solutions to Systems of Linear Equations
- Vector Norms
- Matrix Norms
- The Residual Correction Method
- Error Analysis in Solutions to Systems of Linear Equations
- The Jacobi Iteration Method
- The Algorithm for The Jacobi Iteration Method
- Applying The Jacobi Iteration Method
- The Gauss-Seidel Iteration Method
- The Algorithm for The Gauss-Seidel Iteration Method
- Applying The Gauss-Seidel Iteration Method

## 6. Eigenvalues

## 7. Methods for Solving Systems of Nonlinear Equations

- Newton's Method for Solving Systems of Two Nonlinear Equations
- The Algorithm for Newton's Method for Solving Systems of Two Nonlinear Equations
- Applying Newton's Method for Solving Systems of Two Nonlinear Equations
- Newton's Method for Solving Systems of Many Nonlinear Equations
- The Fixed Point Method for Solving Systems of Two Nonlinear Equations
- Convergence of The Fixed Point Method for Solving Systems of Two Nonlinear Equations
- The Algorithm for The Fixed Point Method for Solving Systems of Two Nonlinear Equations
- Applying The Fixed Point Method for Solving Systems of Two Nonlinear Equations

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