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Ah yeaahhhh!!!! Calculus of V.V.F’s Derivatives and Integration of Vectors This will lead to applications of vectors involving calculus…which is the heart of all this vector stuff.

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Sketch the plane curve represented by: Sketch the vector r(1).

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Move the r’(1) vector to the terminal point of r(1) to interpret what it is. What does the slope of this vector represent? How is the slope of this vector just like p-metric dy/dx?

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Hmmmm….the magnitude of the vector representing instantaneous rate of change. Lock this away for a lil’ bit.

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If you can find the first derivative, then you can find the second derivative! What does each value mean? Do they jive with the graph?

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If we can differentiate we can integrate! COMPONENT INTEGRATION We will apply this practically when we discuss pos.,vel, accel., and bounce between all three.

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Integrate the following. Remember C! …Wait…what does C represent in this case?

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Definite Integral (Like going from velocity curve to finding displacement)

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Since we will be solving problems that give a velocity and initial height, it is important we can find particular solutions w/ an initial condition!!!

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Try this beast!

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Differentiability and Rates of Change. To be differentiable, a function must be continuous and smooth. Derivatives will fail to exist at: cornercusp vertical.

Differentiability and Rates of Change. To be differentiable, a function must be continuous and smooth. Derivatives will fail to exist at: cornercusp vertical.

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