A Brief Annotated Bibiolography on Newton's
Method
Dr. Therese Shelton
1. Boyce, W. & DiPrima, R. Calculus
John Wiley & Sons. 1988. ISBN: 0-471-09333-5. pp. 214-220.
A good, traditional development. Gives graphical
and numerical evidence. Also applies to piecewise-defined functions. No
specific technology used. Multiple problems for students.
2. Cohen, M. et. al. Student Research Projects
in Calculus. Mathematical Association of America. 1991. ISBN: 0-88385-503-8.
pp. 90-91, 107-108, 121, 144-145.
Project outlines: 1) a straightforward root
of a polynomial through which students discover Newton's Method; 2) a narrative
with evidence from a court case that requires the mean value theorem and
the intermediate value theorem; 3) a difficult problem involving noncommutativity
of exponents that requires parametric equations; and 4) a problem that
requires parametric equations and involves a ball thrown at a moving ferris
wheel.
3. Edwards, C. & Penney, D. Single Variable
Calculus with Analytic Geometry and Early Transcendentals. Prentice
Hall. 1998. ISBN: 0-13-793092-5. pp. 197-205.
A thorough development. Gives graphical and
numerical evidence. Concise coding TI-85, HP-48SX, Mathematica, and Maple.
Extension to computations with complex numbers to generate color computer
graphics. Multiple problems and a project for students.
4. Harvey, J. G. & Kenelly, J. W. Explorations
with the TI-85. Academic Press, 1993. ISBN: 0-12-329070-8. pp. 193-195
Concise introduction with specific instructions
for the TI-85. No exercises.
5. Smith, R. & Minton, R. Discovering Calculus
with the HP-28 and HP-48. McGraw-Hill. 1992. ISBN: 0-07-059185-7. pp.
138-147.
Gives graphical and numerical evidence. Discusses
sensitivity to initial guesses. No problems for students.
6. Solow, A., editor and principal author of this
lab. "Newton's Method." Learning by Discovery: A Lab Manual for Calculus.
Volume 1 of Resources for Calculus. MAA Notes Number 27. Mathematical
Association of America. 1997. ISBN: 0-88285-083-4. pp. 46-51.
Graphical development. Several exercises for
students. Discussion of sensitivity to initial guess and chaotic behavior.
Coding for Maple, single command for Mathematica, and coding for Derive.
sensitivity to initial guesses. No problems for
students.
7. Straffin, P., editor and principal author of this
lab. "Newton's Method and Fractal Patterns." Applications of Calculus.
Volume 3 of Resources for Calculus. MAA Notes Number 29. Mathematical
Association of America. 1993. ISBN: 0-88285-085-0. pp. 68-84.
Elementary and extended development. Several
exercises for students; includes answers. Discussion of sensitivity to
initial guess, chaotic behavior, error estimates, connection of function
roots to super-attracting fixed points, and other theorems. Includes black
and white computer graphics. Includes references. Version of this lab appeared
in the UMAP Journal 12, 1991, pp. 143-164.