MATH 1920 Lecture Notes - Lecture 7: Product Rule
8 Sep 2017
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Lecture 7 - calculus of vector valued functions. 14. 2 calculus of vector valued functions r(t) = lim(t -> t0) r(t) = t0) x(t), lim(t -> t0) y(t), lim(t -> t0) z(t)> Recall: for f(x), df/dt = lim(h -> 0) (f(x+h) - f(x))/h. The derivative of r(t) is given by dr/dt = lim(h -> 0) (r(t + h) - r(t))/h. Since the limit passes to each component, so does the derivative: dr/dt = Example: r(t) = r"(t) = If the derivative exists, then we say the vector valued function is differentiable. Note: differentiable space curves do not have sharp points where the derivative is undefined. The tangent vector: the derivative of a vector valued function is also a vector valued function and is called the tangent vector.
