We started Vector Functions of a Single Variable [Transparancy 3]. Continuity and limits of vector functions are defined in terms of the components of the vector function. Using this, the derivative of a vector function was defined in terms of derivatives of its components.
Various derivative rules were proved [Transparancies 4 to 6]. The product rule transfers over to vectors in a straightforward way, including derivatives of dot-products and cross-products.
We finished off [Transparancy 6] with a brief discussion of space curves. I gave a demonstration of how to plot space curves using "Maple". The commands used were:
> with(plots): > spacecurve([sin(t),cos(t),t],t=0..8*Pi);The ">" is Maple's prompt -- you don't type that. You have to type with(plots) in order load the "plots" package which contains the "spacecurve" command, otherwise it will be inaccessible. Note also that each statement must end with a semi-colon, unless you want to suppress the output of a command, in which case you use a colon as I did with the "with(plots)" command.
This particular space curve is a spiral around the z-axis. Within Maple you can rotate the plot to view it at any desired angle.
I encourage you all to try plotting space curves in Maple. The class has been issued assignment lab accounts for this purpose. You can also find Maple in the drop-in labs on campus. Click here for more information on using computers in this course.
If you have a computer at home, you may wish to purchase Maple from the Microcomputer Store on campus. It is available for both Macintosh and MS Windows machines.
