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Equations

Bridges through History with Maths. Equations. E = mc 2. Carmen Margarida Fernandes Machado. Equations.

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Equations

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  1. Bridges through History with Maths Equations E = mc2 Carmen Margarida Fernandes Machado

  2. Equations An equation is a mathematical statement that two expression are equal: it is either an identity, in which the variables assume any value, or a conditional equation, in which the variables have only certain values (roots).

  3. For an equation to be true it is necessary that its unknowns assume certain values. Those will be the: Solution or Root of that equation

  4. Example: 52=x2+32 To make this statemente a true one: x=4 or x=-4

  5. How to solve an equation with one unknown? • The unknown should be placed on one memeber of the equation; • All the calculus should be done in order to the unknown.

  6. Considering the case above: 52=x2+32 x2=25-9 x=√16 x=4 x=-4 <=> <=> <=> ^

  7. So, to solve an equation more easily we must take numbers/expressions from one member to another and vice versa. But when numbers/expressions are placed on the other member, they will do exactly the inverse operation.

  8. So that: When a number is...on one member It will be...on the other one Summing Subtracting Multiplying Dividing Subtracting Summing Dividing Multiplying

  9. When an unknown as an exponent, the way to solve it is to apply to both members the root of that exponent: xn=y n√xn=n√y x=n√y <=> <=>

  10. Equations have several types, each one of them with specific ways to solve: • Linear; • Polynominal; • Algebraic; • Functional; • Transcendental; • Integral • ...

  11. Applications Despite in mathematics equations may seem too abstract, when applied to physics (for example) they have a meaning and their result will applied to reality.

  12. Example: The equation of positions of the uniform rectilinear movment is x=xo+vot, which in maths is more known as y=mx+b. They can also represent fuctions.

  13. References http://en.wikipedia.org/wiki/Equation Visited on December 2011 Collins English Dictionary – third edition

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