Sunday, January 1, 2012

Doing (some) calculus without knowing calculus

It is common to have 2 "first year" physics courses.  One uses calculus, a "university physics" course, and one only uses algebra, a "college physics" course.  With physics enrollments lower than adminstrators would like there has been pressure to combine these into 1 single first year course.

Numerical methods allow at least some of the calculus to be done by students who only know algebra (plus some computer programming skills). The velocity component in the x direction is then the change in x devided by the time change, vx = dx/dt. The acceleration component in the x direction is then the change in vx devided by the time change, ax = d(vx)/dt.  One can then do integration on the computer with the simple assignment statements:

LET vx = vx + ax*dt

LET x = x + vx*dt

A simple planetary or satellite orbit program is then something like:

We can then explore elliptical orbits by increasing vy from 1 toward 1.414.
Beyond that we get parabolic and hyperbolic trajectories.            

Of course there are other issues with trying to make a single "size" course that would "fit" all students.  The lab component for one thing.                                                             

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