Maple worksheets on linear systems |

Numerical methods topics:

- Introduction - errors
- Root-finding
- Interpolation
- Numerical integration
- 1st order differential equations
- 2nd order differential equations
- Linear systems
- Finite difference methods
- The Duffing equation
- Approximation of functions
- The numerical evaluation of mathematical functions
- Special inverse functions
- The derivation of Runge-Kutta schemes
- Interpolation for Runge-Kutta schemes

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

Introduction-matintro.mws

- Maple data structures for vectors and matrices - new and old
- Shortcuts for entering vectors and matrices
- Operations on matrices using Maple
- Solving linear systems of equations with Maple
- Constructing random vectors and matrices
- Calculations involving matrices with floating point entries

Gaussian elimination-gauss.mws

- A procedure for performing Gaussian elimination:
GaussElimination.- Use of partial pivoting in Gaussian elimination

Gauss-Jordan elimination-gaussj.mws

- Elementary row operations and reduced echelon form
- A procedure for performing Gaussian elimination:
GaussElimination.

An introduction to LU decomposition-LUintro.mws

- Finding an LU decomposition from first principles.
- Using Gauss and Gauss-Jordan elimination to find an LU decomposition
- Using LU decomposition to solve a linear system of equations

Solution of linear systems by LU decomposition-LUdecomp.mws

- LU decomposition and its application in solving linear systems.
- A procedure for constructing the LU decomposition of a non-singular matrix:
LU_decomposition.- Use of the Maple procedure
LUdecompositionin the "LinearAlgebra" package.

Matrix inversion by Newton's method-newtoninv.mws

- How to divide using multiplication.
- A procedure for performing matrix inversion by Newton's method:
newtoninverse.

Tridiagonal matrices- tridiag.mws

- Compact storage of tridiagonal matrices.
- A procedure which expands the compact form of a tridiagonal matrix:
Tridiagonal.- A procedure for multiplying a vector by a tridiagonal matrix in compact form:
MultVector.- A procedure for solving a linear system with a tridiagonal coefficient matrix:
TridiagSolve.

Construction of Matrices with random entries-randmat.mws

- Procedures for generating random numbers:
randuniform,randnormal.- Using Maple procedures in "stats[random,...]" to generate random numbers.
- A procedure for constructing random data distributions:
distributiondata.- Graphing distributions.
- Constructing random vectors and matrices.

Procedures for linear systems- linsys.zip