Vector valued Function

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A vector-valued function is a mathematical function which depends on a single real number parameter t, often representing time, producing a vector v(t) as the result. Whereas for scalar-valued functions there is only a single possible reference frame, to take the derivative of a vector-valued function requires the choice of a reference frame (at least when a fixed Cartesian coordinate system is not implied as such). Once a reference frame has been chosen, the derivative of a vector-valued function can be computed using techniques similar to those for computing derivatives of scalar-valued functions. A different choice of reference frame will, in general, produce a different derivative function. The derivative functions in different reference frames have a specific kinematical relationship.