  This paper establishes calculus upon two physical facts: (1) any average
velocity is always between two instantaneous velocities, and (2) the motion of
an object is determined once its velocity has been determined. It directly
defines derivative and definite integral on an ordered field, proves the
fundamental theorem of calculus with no auxiliary conditions, easily reveals
the common properties of derivatives, and obtains differentiation formulas for
elementary functions. Further discussion shows that the new definitions are in
accord with the traditional concepts for continuously differentiable functions.
This is a result of the authors' research in the field of educational
mathematics, which hopes to provide a more elementary and effective way to
teach calculus.
