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Maple worksheets on linear systems |
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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 LUdecomposition in 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
