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Mathematics


Fitting of a Polynomial using Least Squares Method
Fitting of a Polynomial using Least Squares Method

Approximating a dataset using a polynomial equation is useful when conducting engineering calculations as it allows results to be quickly updated when inputs change without the need for manual lookup of the dataset. The most common method to generate a polynomial equation from a given data set is the least squares method. This article demonstrates how to generate a polynomial curve fit using the least squares method.


Exponent Laws
Exponent Laws

Algebraic expressions can often be simplified and subsequently solved through the use of the exponent laws (also called laws of indices or power laws). These laws allow an equation to be manipulated into a form which provides enhanced readability or opens up potential simplifications and substitutions. This article provides a reference for these laws.


Algebraic Factoring
Algebraic Factoring

When developing algebraic expressions it is often useful to factorise the expression to familiar components. Through factorisation, one can increases both the readability and manipulability of the expression. This article summarises the common algebra factorisation relationships.


Basics Of Affine Transformation
Basics Of Affine Transformation

Affine transformations are a class of transformations fundamental to modelling objects in three dimensions. This article presents the transformation and inverse transformation matrices for translating, scaling and rotating.


Converting Between Spherical and Cartesian Co-ordinate Systems

When working on problems in three dimensional space it is often required convert between two or more co-ordinate systems. This article presents the formulae to convert between Cartesian and Spherical co-ordinate systems.