Algebraic Methods
Introduction
In this section, the first of four outcomes that make up the Mathematics for Technicians unit, you will be introduced to some of the basic rules, laws and methods needed to manipulate algebraic expressions, functions and equations.
Mastery of algebra is vitally important, because without the ability to manipulate equations and functions quickly and efficiently, the remainder of your mathematical and scientific topics become that much more difficult.
When students tell me that they are `unable to differentiate' or `unable to solve a problem involving trigonometry', the chances are that what they really mean is that they are unable to simplify or transpose the equations associated with these subjects, which require fluency in using algebra. You will, therefore, not be surprised to discover that we will spend some time studying the underpinning algebra necessary for the satisfactory resolution of mathematical, scientific and engineering problems.
We start by looking at factors, products, powers and indices (exponents) and use these algebraic tools to manipulate and simplify algebraic expressions and formulae. Then, although not strictly part of the outcome, we consider the methods necessary to transpose and evaluate formulae, these methods being of vital importance to those wishing to practice as technicians and engineers. The skills learnt in transposing and evaluating formulae may then be applied to the analytical solution of equations. Indeed, after the introduction of some graphical methods, we consider the analytical and graphical solution of linear and simultaneous equations together with the analytical solution of quadratic equations, using factorization and the quadratic formula. Finally, the nature and use of logarithms is considered, particularly with respect to the linearization of experimental and engineering data.
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