The
Parabolic Arc: A subtle step forward
A
Course Structure
Linear
Approximations
Fitting
parabolas (rather than lines) to sets of points
Finding
the parabola
Integration
Uniform
partitions … Simpson's Rule
Errors
in Trapezoidal vs Simpson's Rule
Differentiation
Meaningful
Symbolic Manipulation
|
Errors
in Central Difference Approximation
Fitting
parabolas with slope and curvature information
Finding
the parabola
Euler's
Method … Taylor approximations
Errors
in Euler's Method vs Quadratic Taylor poly.
Zeros
of a function … poor results from fitting points
Zeros
of a function … good results from Taylor poly.
Newton's
Method vs Quadratic polynomials
Lessons
for Students and Instructors |