Tricki

## Equation-solving front page

### Quick description

There are several different kinds of equations, and techniques for solving them vary considerably. So this page consists mainly of links to pages about solving particular kinds of equations.

There are a few general principles, however.

### Generic equation-solving techniques

Transform equation to reach a solved pattern Brief summary ( Make logically equivalent rearrangements of the equation until it, or the "hard" part of it, matches a pattern you already know how to deal with. )

### Articles about different kinds of equations

How to solve linear equations in one variable Brief summary ( These are equations like . This equation is called linear because the graph of is a straight line. )

How to solve linear equations in two variables Brief summary ( Things get slightly more complicated if you have two unknowns, and two equations to help you to determine them. For example, the equations could be and . However, there are various systematic ways of solving such pairs of equations and determining and . )

How to solve linear equations in many variables Brief summary ( The methods used to solve linear equations in two variables can be generalized to any number of variables. At this point it becomes fruitful to think of the unknown as a vector rather than as a sequence of many individual variables. )

How to solve quadratic equations Brief summary ( A quadratic equation is something like , which involves as well as . There are several techniques for solving them: which is best varies from example to example. )

How to solve cubic and quartic equations Brief summary ( These are like quadratic equations, but now they also involve cubes and fourth powers, respectively. For instance, the equation is a quartic equation. Cubic and quartic equations can be solved systematically, but they are much harder than quadratic equations. )

What makes some equations so much easier to solve than others? Brief summary ( There are several answers one might give to this question but here is one: if you can work something out on your calculator without using any memory, then the resulting equation will be easy to solve. A few examples will make clear what this means. )

How to solve polynomial equations in several variables

How to solve linear Diophantine equations

How to solve quadratic Diophantine equations

Diophantine equations front page

Differential equations front page Brief summary ( Differential equations are equations where the unknown involves a function (or more than one function) and the equation involves not just the function but also some of its derivatives. If the function is of more than one variable, then these may be partial derivatives. There are many importantly different kinds of differential equation. This page gives some initial guidance. )

How to solve functional equations