Equation
A mathematical equation is an expression containing two mathematical objects connected by an equals sign (=) .[1][2][3][4] The equals sign says that both sides are exactly equal, or of the same value. An equation can be as simple as [math]\displaystyle{ x=0 }[/math], or as complex as [math]\displaystyle{ 4(3y^{99})+76=42+3x }[/math] or harder.
There are two kinds of mathematical equations:
- The kind of equation that is either true or false; these are also called identities. For example:
- [math]\displaystyle{ 2\cdot(x+4)=2x+8\rightarrow\text{true} }[/math]
- The kind of equation that is only true for certain values of the variable(s). The equation is only true if the variable(s) have that value. For example:
- [math]\displaystyle{ 2\cdot x=8\rightarrow x=4 }[/math]
The second kind is often used to solve problems in which finding the value of some variables is involved. For example, if
- [math]\displaystyle{ 2x=8 }[/math], [math]\displaystyle{ x=\frac82=4 }[/math]
The second kind of equation is used in algebra. For example, to solve the equation [math]\displaystyle{ 2x=8 }[/math] for [math]\displaystyle{ x }[/math], one would follow an algebraic rule to find that [math]\displaystyle{ x=4 }[/math].
Types of equations
Equations can be classified by the types of operations and quantities involved. For example:
- An algebraic equation is an equation in which both sides are polynomials. These are further classified by degree:
- Linear equation for degree one
- Quadratic equation for degree two
- Cubic equation for degree three
- Quartic equation for degree four
- Quintic equation for degree five
- A Diophantine equation is an equation where the unknowns are required to be integers
- A differential equation is a functional equation involving derivatives of the unknown functions, which include:
Equation Media
The first use of an equals sign, equivalent to 14x + 15 = 71 in modern notation. From The Whetstone of Witte by Robert Recorde of Wales (1557).
Illustration of a simple equation; x, y, z are real numbers, analogous to weights.
The solutions –1 and 2 of the polynomial equation x2 – x + 2 = 0 are the points where the graph of the quadratic function y = x2 – x + 2 cuts the x-axis.
The Nine Chapters on the Mathematical Art is an anonymous 2nd-century Chinese book proposing a method of resolution for linear equations.
The blue and red line is the set of all points (x,y) such that x+y=5 and -x+2y=4, respectively. Their intersection point, (2,3), satisfies both equations.
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius.
A strange attractor, which arises when solving a certain differential equation
Related pages
References
- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-09-01.
- ↑ "Equations and Formulas". www.mathisfun.com. Retrieved 2020-09-01.
- ↑ "A statement of equality between two expressions. Equations are of two types, identities and conditional equations (or usually simply "equations")". « Equation », in Mathematics Dictionary, Glenn James et Robert C. James (éd.), Van Nostrand, 1968, 3 ed. 1st ed. 1948, p. 131.
- ↑ Une équation est une égalité entre deux expressions mathématiques, donc une formule de la forme A = B, où les deux membres A et B de l'équation sont des expressions où figurent une ou plusieurs variables, représentées par des lettres. ÉQUATION, mathématique - Encyclopædia Universalis