File: http://www.math.villanova.edu/archives/maple/misc/0index.htm
Date: 21-nov-2009 By: bob jantzen, klaus volpert

VILLANOVA UNIVERSITY MATH DEPARTMENT

WEB FILE SERVER

Miscellaneous MAPLE files

Most of the files in this subdirectory are MAPLE V Release 4 and Release 5 worksheets, but someday they might be upgraded to Release 13 (probably not). No browsing of the underlying files is allowed because bob is tired of fighting with the web people to keep this option, but all the worksheets are listed in this file, although the actual filenames are all lowercase.

Shift clicking or clicking (whatever) on a MAPLE worksheet (.mws) file will prompt you for a location and name to download the file (your hard drive or diskette). You can then open the file using MAPLE. If you have difficulty with this archive you may contact the webmaster by e-mail:

robert.jantzen@villanova.edu

The nonlinear curvefitting files below were described in  The Maple Reporter Summer 1998 Edition (pp.6-7 article: Fit for Anything in this PDF file).

Directory of DEPART\MATH\MAPLE\MISC\:

Logistic and nonlinear curve fitting
[maple 6? recall the change maple5: " to maple6: % for the ditto operator;
require updating to maple12]

• LGTRUDSM.MWS
  True Least Squares Logistic Regression with Downhill Simplex Minimization by Les Wright using the MAPLE routine:
  DOWNHILL.M
  extracted from the worksheet
  DOWNHILL.MWS
  the downhill simplex minimization method in multidimensions, implementation by Dr Francis J. Wright. [seems to work better than Alshom's procedure for this problem]
• LOGDOWN.MWS
  Solving Logistic Regression Problems Using Downhill Simplex Minimization
• LOGISTI2.MWS
  Preliminary worksheet to the next one:
• LOGISTIC.MWS
  Logistic Curve Fitting via Linear Least Squares Applied to Transformed (linearized) Data.
• LOGISTRU.MWS
  True Least-Squares Logistic Regression by Les Wright using the following nonlinear regression procedure:
• NNLINFIT.MWS
  A nonlinear regression procedure by Preben Alsholm.
• LOGFIT.MWS
  An application of both the nonlinfit procedure and the downhill simplex minimization method to fitting a 3-parameter family of logarithmic curves to some data.
• MTC1093.HTML
  Interesting SIAM web article on the Levenberg-Marquardt nonlinear regression problem.
• NLINFIT3.MWS
  NONLINFIT3.MWS: The damped Gauss-Newton-fit procedure by Preben Alsholm, September 1, 1998 (original version: December 12, 1996)
• FITODES2.MWS
  FITODESYS2.MWS: Estimates of parameters in differential equations Preben Alsholm, August 28 1998
• LSQDDEM1.MWS
  Least Squares Nonlinear Regression and Downhill Simplex Minimization: A Marriage of the Two by Les Wright, January 1, 1999
• LSQD.M
  Accompanying Least Squares Nonlinear Regression .M file by Les Wright, January 1, 1999
• NLFIT.MWS
  Single Independent Variable Nonlinear Regression with Levenberg-Marquardt procedure by David Holmgren, November 29, 1999
• MNLFIT.MWS
  Multivariable Nonlinear Regression with Levenberg-Marquardt procedure by David Holmgren et al, November 29, 1999

LambertW function in pharmaceutical problem

• /lambert
  This arises in the simplest drug absorption model when trying to express one of the two decay coefficients in terms of the peak time and the remaining decay coefficient.

Miscellaneous stuff (filenames are actually all lower case):

• ANIMATE.MWS
  Some examples of animations with plottools.
  ANIMATE2.MWS
  An rotatable animated (rotating) 3d graphic.
• BIN2NORM.MWS
  Deriving the continuous normal distribution from the discrete binomial distribution in the limit of large n, by Les Wright. 
• CALCLPOP.MWS
  Finding the best-fitting logistic equation to given data is not easy, because the parameters in the equation are non-linear. This worksheet discusses a method, that first makes a `good guess' at the parameters, and then uses graphical methods and calculus to find a local minimum of the error function near this guess. Regarding this problem see also several worksheets above: LGTRUDSM.MWS, LOGDOWN.MWS, LOGISTIC.MWS etc.
• CHAOS1_5.MWS
  This is a comprehensive and well-written Maple notebook containing some tools for studying mathematical chaos. It was written by Ken Monks, who originally created this sheet for use in an undergraduate course on chaos and fractals which he developed and taught at the University of Scranton. [needs updating]
  chaos5to10.mws
  An amateur effort at coding iterations of functions, with animation of the iteration added with the Maple5 to Maple10 update.
• COLORS.MWS
  A discussion of the difference of two coloring systems that Maple uses: the RGB-spectrum and the HSV-spectrum.
• COMBINE.MWS
  A differential equation dsolve example which shows the importance of the combine command.
  competingspecies.mw
  Phase plane analysis of equilibrium points in the competing species nonlinear 2x2 system of ODEs
• conics_from_rectangle.mws
  [2009 update with trammel remarks: conics_from_rectangle.mw]
  A cute geometric construction for the conic sections arising from pushing on a simple teacher test question. Apparently this rectyangle construction has a hidden trammel in it [the "trammel of Archimedes"].
  [related to this: ellipseinspace.mws, another curious question about an ellipse in space, how to identify it]
  [a recent article on this topic:
   An Ancient Elliptic Locus
  By: John E. Wetzel
  j-wetzel@illinois.edu
  In the plane, two vertices P and Qof a triangular tile PQRmove respectively on two intersecting lines p and q. What is the locus of the third vertex R? Frans van Schooten the younger showed in 1646 that the locus is an ellipse. We present two proofs of this result, one an elegant deduction from the special case in which R lies on the line PQ that was given by John Casey in 1885, the other a clever argument using motions that John Sullivan included in a 1996 paper that has never been published.
• CUTSURF.MWS
  An incomplete worksheet showing the piece of a surface above a nonrectangular region of the plane.
• CYCLOID.MWS
  A neat worksheet written by Gerhard Bitsch that visualizes the creation of a cycloid by a point on a moving cycle.
• DATAIO.MWS
  How to read in or write out data from/to a file, which is then fit using least squares regression.
• DIPSTICK.MWS
  A very thorough discussion of the problem of calibrating a dipstick for a tank, that is of the shape of a surface of revolution. includes an interesting comment from MUG concerning the speed of numerical integration routines.
• DSOLICFM.MWS
  Patches the Maple V Release 5 differential equation solver to allow indexed function names to be used with initial conditions.
• DSOLVNR5.MWS
  Based on a discussion in MUG, this worksheet explains how to make MAPLE functions of the output of dsolve/numeric solutions which can themselves appear in other deq's or be integrated etc.
• ERRORBAR.MWS
  A procedure that draws an 'error plot' for given statistical data.
• FITODES2.MWS
  Estimates of parameters in differential equations (by Preben Alsholm): Given an initial value problem diff(y(x),x) = F(y(x),a,b,c); , y(x[0]) = y[0];, where a, b, c, ... are unknown constants. Two lists are given: One containing the x-values and one containing the corresponding y-values. We are to determine the constants a, b, c, ... such that the solution curve y = f(a,b,c, ... , x) in a 'best possible' way passes through the given points....
  frenetellipse.htm [see also the complete package]
  Finding the points on an ellipse such that the line segments from a given point in the plane to the ellipse are perpendicular to the tangent direction, i.e., coincide with normals to the ellipse. [see also ellipsoid_normals.mws, .mw, Arthur Cayley investigated the geometry of the ellipsoid, Jacobi solved the geodesic problem]
• FOURIER.MWS
  A nice procedure, written by Christine Wilson, that calculates the Fourier Series for a given function, and animates the successive approximations. As an example there is a very nice visualization of the Gibbs phenomenon.
• GRIDLINE. MWS
  Provides a procedure that plots the graph of a function together with a user-adjustable underlying grid.
• newtoncotes.mw
  Newton-Cotes coefficients generalize Simpson's rule (uses Vandermonde polynomial bases).
• PLTARY3D.MWS
  Displaying Arrays of Plots (still not entirely satisfactory in MAPLE V Release 4 or Release 5!): Either all 2D or all 3D plots.
• POLYCOLO.MWS
  Shows how to color a triangulated polygon (2D), and a polyhedra provided by the plottools or geom3d-package, using the commands polygonplot and polygonplot3d.
• rainbow.mw
  The Calculus of Rainbows from James Stewart: Calculus Concepts and Contexts 5e Page 282. Evaluating the various rainbow angles.
• RGB_Hue_and_HSV.mw
  Understanding the color parameters for nice effects in 3-D graphics especially
• sap6.mw
  James Stewart Calculus: Concepts and Contexts, Applied Project 6.4, p.472: Where to Sit at the Movies.
• SEQPTPLT.MWS
  Generating Sequences of Pairs of Points for Plotting.
• series.mw
  For those undergraduates who jump into multivariable calculus as freshmen and miss power series, a short review.
• SFPS3-16.MWS
  James Stewart Calculus: Concepts and Contexts, Focus on Problem Solving 3.16, p 265. Locus of points where pair of tangent lines to ellipse are perpendicular.
• SFPS5-1.MWS
  James Stewart Calculus: Concepts and Contexts, Focus on Problem Solving 5.1, p 444. Divide a 14 inch diameter pizza into (equal area) thirds by 2 parallel cuts.
• SFPS5-6.MWS
  James Stewart Calculus: Concepts and Contexts, Focus on Problem Solving 5.6, p 445. A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. If it is to be partially submerged in the liquid so as to maximize the exposed wetted area of the disk, show that the center of the disk should be positioned at a height r/sqrt(1+Pi^2) above the surface of the liquid. (Solution by Fritz Hartmann)
• SHADEIN.MWS [shadein.mw]
  Shading in the region between two function graphs in the plane over a specified interval, by Tim Feeman. This is partially outdated since the Maple plotting has gotten more sophisticated, but when the region between two curves also crosses the horizontal axis, it is more efficient than the following plot option which requires dividing the interval up into further subintervals in which the two curves are ordered on each subinterval, since the "filled = true" option shades between the curve and the horizontal axis.
  Here is a nice example using the simpler "filled = true" option which does not have this complication: cubicareaputnam.mw
  However, subtracting 1/2 from these functions being graphed leads to the additional problem.
• SOUND.MWS
  Uses a telephone number as the coefficients for a Fourier Series (=Sound). Shows how the telephone number can be retrieved via Fourier analysis. (part of CSC1024 demonstrations)
• trianglecentroid.mws
  Derives the centroid of a triangle and extends it to a polygon.
• transfercurve.mw
  Stewart Calculus 5e applications of curvature: transfer curve connecting straight pieces of railroad track.
• UMBTORUS.MWS [more about this]
  From the Larson et al Calculus (6th Edition) by Houghton Mifflin (Prentice Hall): The Umbilic Torus (an interesting 3-D plot)
• VALLEEP_BOB8.MWS
  Critical points of the Vallee-Poussin polynomials plotted in the complex plane for high n.