Algebra

© Department of Physics, University of Guelph

The first topic to be reviewed is fractions. A fraction is expressed as , where a is called the numerator and b, the denominator.

Now we will investigate power laws. A number raised to a power is written as ax, where a is the base and x is the power or exponent.

Now let's look at proportionality. Often in physical problems, one deals with parameters that vary as certain other parameters are varied. These parameters are called variables.

We will now examine the solutions of a linear equation in one unknown, remember that an equation is simply a statement of equality.

Now how do we deal with common factors? Often the solution of an equation can be simplified by removing factors common to all terms.

Let's now turn our attention to the dimensionality of the equations. All terms in an equation, connected by a plus or minus sign must have the same dimensions and be in the same system of units.

Now let's look at the solutions of two simultaneous equations.

Finally let us look at the binomial expansion. Often it is necessary to calculate expressions of the following form, (1 + x)n, where n may be an integer or a fraction.

The format that we saw emerging, we can write in a general way as follows, .

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