Scalar-Input Vector-Output Function

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A Scalar-Input Vector-Output Function is a Real-Input Function that is a Vector-Output Function.



References

2009

  • (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Vector-valued_function
    • A vector-valued function is a mathematical function that maps real numbers to vectors. Vector-valued functions can be defined as:
        • \mathbf{r}(t)=f(t)\mathbf{{\hat{i+g(t)\mathbf{{\hat{j or
        • \mathbf{r}(t)=f(t)\mathbf{{\hat{i+g(t)\mathbf{{\hat{j+h(t)\mathbf{{\hat{k
      • where f(t), g(t) and h(t) are the coordinate functions of the parameter t, and \mathbf{{\hat{i, \mathbf{{\hat{j, and \mathbf{{\hat{k are unit vectors. r(t) is a vector which has its tail at the origin and its head at the coordinates evaluated by the function.
    • Properties: The domain of a vector-valued function is the intersection of the domain of the functions f, g, and h.


  • http://ltcconline.net/greenl/courses/202/vectorFunctions/vecfun.htm
    • A vector valued function is a function where the domain is a subset of the real numbers and the range is a vector.
    • In two dimensions: r(t) = x(t)i + y(t)j
    • In three dimensions: r(t) = x(t)i + y(t)j + z(t)k
    • You will notice the strong resemblance to parametric equations. In fact there is an equivalence between vector valued functions and parametric equations.


Domain
Range
Name
R R One variable Function
R R2 Parametric Equations
R2 R Function of 2 Variables
R Vectors Vector Valued Function