Mathematical Equation

A Mathematical Equation is a mathematical expression that is a formula/equation (that asserts mathematical information in form of a mathematical equality between two mathematical expressions.

• AKA: Math Formula.
• Context:
  • It can be expressed as [math]\displaystyle{ A=B }[/math], where [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] are mathematical expressions (that may contain unknown variables) and “[math]\displaystyle{ = }[/math]” denotes the equality binary relation.
  • It can be an input to an Equation Solving Task.
  • It can range from being an Abstract Mathematical Equation to being a Mathematical Equation Instance (such as a numbered mathematical equation).
• Example(s)
  • a Algebraic Equation, such as a linear equation, such as [math]\displaystyle{ 2.1x + 3 = 5 }[/math]
  • a Differential Equation.
  • …
• Counter-Example(s):
  • a Mathematical Function.
  • a Software Equation.
  • a Mathematical Variable.
  • a Software Variable Assignment.
  • a Chemical Formula.
• See: Chain Rule, Equality (Mathematics), Binary Relation, Proposition (Mathematics), Statement (Logic), Algebra, Identity (Mathematics), Necessarily True, Arithmetic, Relation (Mathematics), Volume, Sphere, Integral Calculus, Method of Exhaustion, Radius, Algebraic Expression, Closed-Form Expression, Analytical Expression.

---

---

References

• http://en.wikipedia.org/wiki/Category:Equations

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/formula Retrieved:2014-8-24.
  • In science, a formula is a concise way of expressing information symbolically as in a mathematical or chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities. The plural of formula can be spelled either as formulas or formulae (from the original Latin).

    In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion; but, having done this once, mathematicians can produce a formula to describe the volume in terms of some other parameter (the radius for example). This particular formula is:

    Having obtained this result, and knowing the radius of the sphere in question, we can quickly and easily determine its volume. …

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/equation Retrieved:2014-7-26.
  • In mathematics, an equation is a formula of the form A = B, where A and B are expressions that may contain one or several variables called unknowns, and "=" denotes the equality binary relation. Although written in the form of proposition, an equation is not a statement that is either true or false, but a problem consisting of finding the values, called solutions, that, when substituted for the unknowns, yield equal values of the expressions A and B. For example, 2 is the unique solution of the equation x + 2 = 4, in which the unknown is x.

    Historically, equations arose from the mathematical discipline of algebra, but later became ubiquitous. “Equations" should not be confused with “identities", which are presented with the same notation but have a different meaning: for example 2 + 2 = 4 and x + y = y + x are identities (which implies they are necessarily true) in arithmetic, and do not constitute a values-finding problem, even when variables are present as in the latter example.

    The term "equation” may also refer to a relation between some variables that is presented as the equality of some expressions written in terms of those variables' values. For example the equation of the unit circle is x² + y² = 1, which means that a point belongs to the circle if and only if its coordinates are related by this equation. Most physical laws are expressed by equations. One of the most famous ones is Einstein's equation E = mc².

    The = symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.

2012

• http://en.wikipedia.org/wiki/Equation
  • QUOTE: An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign (=), for example :[math]\displaystyle{ x + 3 = 5\, }[/math] asserts that x+3 is equal to 5. The = symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.

• http://en.wikipedia.org/wiki/Equation#Types_of_equations
  • Equations can be classified according to the types of operations and quantities involved. Important types include:
    • An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
    • A linear equation is an algebraic equation of degree one.
    • A polynomial equation is an equation in which a polynomial is set equal to another polynomial.
    • A transcendental equation is an equation involving a transcendental function of one of its variables.
    • A functional equation is an equation in which the unknowns are functions rather than simple quantities.
    • A differential equation is an equation involving derivatives.
    • An integral equation is an equation involving integrals.
    • A Diophantine equation is an equation where the unknowns are required to be integers.
    • A quadratic equation.

---