What is the equation?
In our article about what is the equation, we not only give the definition, but also give different classifications of equations with examples.
What is the equation: general concepts so the equation is a kind of equality with an unknown referent Latin letter. When the numerical value of the letters, allowing you to get the right equality, called a root of the equation more details about this you can read in our article what is a root of the equation, we will continue to talk about the equations.
Arguments of the equation (or variables) are unknown, and the solution of the equation is called finding all its roots or the lack of roots. Types of equations:
Equations are divided into two large groups: algebraic and transcendental.
Algebraic is called such equation, in which to find the root of the equation uses only the algebraic steps-4 arithmetic as well as exponentiation and extracting natural root.
Transcendental equation is called, where to find the root of the function are used: for example, trigonometric, logarithmic, and other.
Among algebraic equations secrete: entire — with two parts, consisting of integers of algebraic expressions in relation to unknown; fractional algebraic expressions contain numerator and denominator; irrational — algebraic expressions here are under the sign of the root.
Note also that the fractional and irrational equations can be reduced to the solution of integral equations. Transcendental equations are divided into: exponential equations are those that contain variable in exponent. They are solved by moving to a single base or measure, the overall multiplier for brace, decomposition of the multipliers and some other means; logarithmic equations with logarithms — then there are equations where the unknowns are within of logarithms.
To solve such equations are difficult (unlike, say, most algebraic), as this would require solid mathematical preparation. The most important thing here is to move from the equation with logarithms to the equation, that is, to simplify the equation. Of course, the logarithmic equation can be only if they have identical numerical basis and do not have conversion rates; trigonometry is the equation with variables under the signs of trigonometric functions.
Their solution requires the initial development of trigonometric functions; mixed is a differential equation with parts belonging to different types (for example, parabolic and elliptic parts or elliptical and hyperbolic, etc.). With regard to the classification by the number of unknowns, everything is simple here: distinguishes equations with one, two, three and so on.
There is also another classification, which is based on the degree of which is available on the left side of the polynomial. On the basis of this distinguished linear, quadratic and cubic equations.
Linear equations can also be called 1-degree equations, square is 2, and cubic 3, respectively.
Well to solve almost any equation will require not only knowledge of algebra and trigonometry, but also, and often very deep knowledge.