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This library shelf holds tutorials and utilities on fundamental and
applied mathematics.

Included are such topics as Fourier Series, linear algebraic
equations, nonlinear graphic transforms, chain codes, digital
filters, halftone techniques, vectors and similar subjects.

Primarily by authors Don Lancaster or Jim Fitzsimons.

Note that additional math topics also appear in the Wavelets, the
Cubic Spline, and our Magic Sinewave library pages.

Most library files require an Adobe Acrobat 4.0 plug in for online
viewing.  Offline, these may be accessed by an Acrobat Reader or
an eBook Reader or any other .pdf" accepting program.  

  Featured "Must Read" File: .
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   The Saga of the Dripping Stalactites STALAC.PDF" #35
      Celebrating the beauty of applied mathematics, first through a catalog
      of our more obscure "fun with long strings of numbers" topics and
      then by way of the Magic Sinewave timeline history.

Click here for the Magic Sinewave library.
Click here for a Magic Sinewave intro.
Click for a Magic Sinewave development proposal.
Click here to Order MSD-28X chips & source code.

  Tutorials: .
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   Pixel Interpolation Algorithms PIXINTPLPDF #83
     A review of popular pixel interpolation schemes including Bilinear,
     Nearest Neighbor, Bilinear with lookup, Modified 3x3, and Bicubic.
     Includes detailed bicubic math derivation. .

Click here for the Pixel Interpolation utility.
Click here for the Pixel Interpolation
demo..

Click here for the PostScript library.
Click here for the GuruGram 83
source code.
Click here to Contact the Author
directly.

   Drawing a circle through 3 points CIRC3PTS.PSL 
     
Brief Don Lancaster tutorial and PostScript demo of drawing a
     circle through three points.
Finding the slope at the midpoint
     leads to less tedious improved curvetracing routines.

Click here for the CIRC3PTS.pdf" demo.
Click here for new CURVETR2.PSL sourcecode.
Click here fornew CURVETR2.pdf" demo.

   Fitting 3 points to a quadratic curve PARAFIT.PSL 
    
Brief Don Lancaster tutorial and PostScript demo of fitting three
    data points to a parabola and quickly finding the x and y values of
    the minimum. For curve fitting and minimization.

Click here for Custom Research assistance.

   Vector-to-step conversion tutorial VECTSTEP.PDF
      Introduction and tutorial shows how to convert slanty lines into
     
 stepper steps or screen pixels. Basic conversion. Breshenham's
      method.
Table lookup. Adding dimensions. Cardinal moves.

Click here for Banner Advertsing opportunities.

   Binomial Goes Binary ONESWORD.HTML
       A PostScript utility to generate all possible binary words of length
      
"n" having "k" ones in them. Use for magic sinewaves & exploration.
       
of the binomial theorm. Requires two way recordable com.

Click here for energy efficient Magic Sinewaves.

   Binary Chain Code Intro CHAIN01.HTML
     A Don Lancaster tutorial and Jim Fitzsimons math program that
      
explores binary chain codes,. Unique self-positioning sequences.
      
Includes BASIC listing and chain codes for order 2 through 16.

Click here for Cubic Spline tutorials.

   Tech Musings #107  MUSE107.PDF
     SX laser printer repairs, linear phase digital filters, home theater
      
opportunities and resources , debunking some technomyths,
       
improved access to government surplus electronics.

Click here for more Tech Musings columns.

   Tech Musings #102  MUSE102.PDF
     A "colorizer" for PostScript; Using bionomial coefficients;
       
Laser printer repair resources; magnetic field intensity paper;
      
HP 5SiMX Book-on-demand printer, more.

Click here to view our Bargain Pages.

  PS 4x4 Linear Equation Solver LINEQ04.PSL 
     
Tutorial and test demo solves n=4 linear algebraic equations by
    
first using Gaussian Elimination followed by back substitution. This
     
can easily be extended to other orders.

Click here for additional Gauss-Jordan theory.

   Fun With Fields FUNFIELD.PDF" #39
     Using PostScript to quickly solve advanced field problems
     with astonishingly simple math. Gradients, Equipotentials, Laplacians.

Click here for the FUNFIELD.PSL source code.
Click here for the FIELDS01.pdf" field generator.
Click here for the FIELDS01.pdf" field frmo.

Click here to reach the GuruGram library.
Click here to reach the PostScript library.
Click here for additional Consulting
services.
Click here to Contact the Author
directly.

   Tech Musings #148  MUSE148.PDF
   
  Algae hydrogen source. Applying Taylor Series. Surplus and auction
     update. Lithium polymer batteries. Understanding nonlinearity. Some
     Battery books. Cave radio site, Maxim chargers, more...

Click here for Patent Avoidance info.

   Tech Musings #152  MUSE152.PDF  
        
Fundamentals of power and energy. 52 LED's from one port!
       
Shuffling alogrithms and pitfalls. Multi-banner auto rotator.
       
Thermodynamic Books. n-connectedness math.

Click here for Live Auction bargains.

  Linear Equation Solver LINEAREQ.PS 
      A group of PostScript utilities and demos that use determinants to
       solve high order linear algebraic equations
. Explicit examples shown
      
to 10x10. Includes linear phase digital filter design examples.

Click for Auctions & Surplus library page.

   Tech Musings #151 MUSE151.PDF 
      
Radio Shack Wireless Humidity Data Format. Exergy and energy
      
quality. JavaScript Bouncy Buttons. Chebycheff polynomonials.
       
Fluxgate & magnetometry books. Plastics suppliers. More..

Click for our Pseudoscience Bashing library page.

   Tech Musings #106 MUSE106.PDF
      
Secrets of math determinants, Power generation efficiencies, Solving
      larger linear equations
, induction heating fundamentals, new BOD
      
Book-on-demand binding opportunities.

Click here for Product Development tutorials.

   Bezier curve through four points BEZ4PTS.PDF
      Jim Fitzsimmons TEX tutorial shows how to fit a Bezier curve
      
through two end points and two intermediate points, all of which
      
are on the desired cubic polynomial curve.

Click for the PostScript Sourcecode utility.

    Tech Musings #148 MUSE148.PDF 
      Algae hydrogen source. Applying Taylor Series. Surplus and auction
     
update. Lithium polymer batteries. Understanding nonlinearity.
      Battery
books. Cave radio site, Maxim chargers, more

Click here for Custom Research assistance.

   Tech Musings #105 MUSE105.PDF
      
H-P 5SiMx laser printer hard drive interface, new video and audio
      
chips, navigation resources update, understanding digital filters,
      
triple tri-sample building blocks, linear phase techniques.

Click here to view our Bargain Pages.

   Secrets of  Nonlinear Graphics Transformations
     
From Circuit Cellar for August of 1995. Reviews both linear and
     
nonlinear transforms such as Isometric, Perspective, Tuna Can,
     
Star Wars, Root Beer, Spherical , Glyph Path, and Scribble.

Click here for more Circuit Cellar tutorials.

    Book Scanning "Gutter Math" GUTTER01.PDF  #103
       An analysis of the typical shape of an open book as may be
      encountered during scanning. Along with correction flattening
      procs. Often a sparce Taylor Series will suffice.                            12/09

Click here to reach the PostScript library..
Click here for the PS Gonao Utilities..

Click here for the GuruGram 103 source code.
Click here to Contact the Author directly.

   A nonlinear "Tuna Can" transform  TUNACAN.HTML
     
Tutorial on a quick and dirty Tuna Can transform that lets you
     
wrap lettering around a tilted can or cylinder. Also an example of
     
how to use Don's Gonzo utilities and Acrobat as PostScript interpreter.

Click here for Patent Avoidance info.

   Hyperbolic Cubic Spline Fitting  HYSPLINE.PDF
      
Don Lancaster Acrobat tutorial shows the steps involved in
      
approximating a 1/x hyperbola with a pair of cubic splines, done
      
to exceptional accuracy.

Click here for more Cubic Spline info.

   Tech Musings #90 MUSE90.PDF
     
 Fourier Series analysis, alternatives to plated through holes,
      
classic computer resources, a $200 GPS receiver, Newtek's
      
new video toaster for Windows.

Click here for Fourier Series example.

   PS Bezier curve through fuzzy data!  FUZZYBEZ.HTML
      
Don Lancaster tutorial shows how to fit a Bezier curve to fuzzy
     data points
. While preserving end points and optionally the exit and
     entry
angles. Read PS source in editor, modify , send to Distiller.

Click here for the PostScript Sourcecode.
Click here for the Acrobat PDF Demo.

   Tech Musings #142 MUSE142.PDF
       
Contact-free battery chargers. Gage and SPS machine tool interface.
       
Useful energy resources. Some induction heating books.
       
Using Gauss Jordan Elimination to solve linear equations.

Click here for Custom Research assistance.

   Hardware Hacker #83 HACK83.PDF
      Halogen cycle mysteries, Science versus pseudoscience, some new
      
books, Vector-to-step conversion, Hacker PostScript, interconnects,
      
Weather satellite resources, EITD phone directory, more...

Click here for more Vector to Step tutorials.

   Hardware Hacker #62 HACK62.PDF
      
Using cubic splines. Switchmode resources. Electrorheological
      
fluids. National's simple switcher. Colorized avuncular sleezoids.
      
Curvetracing contest. Non-ionizing radiation safety.

Click here for more Cubic Spline info.

   Tech Musings #122 MUSE122.PDF
     
Atmel's PIC Challenger. HP's ScanJet 6100C. Finding satellite
     i
imagery. Understanding quadrature. Broadband phase shifters.
     
Using Hilbert transforms. Hydraulic rams. PostScript transparency.

Click here for Live Auction bargains.

   Tech Musings #89 MUSE89.PDF
      
BASIC Stamp Manuals. Secrets of Fibonacci sunflowers.
      
New Bezier cubic spline book. Adobe's elegant Acrobat.
      
E-field ac voltage sensing.

Click for PostScript or Acrobat assistance.

   Tech Musings #112 MUSE112.PDF
        A.C. power measurement tutorial and basics. Aerogel resources
       
and developments. 99 cent Telephone extension lockouts.
       
Understanding RMS currents. Several column corrections.

Click here for more Tech Musings columns.

   RMS current & voltage finder FINDRMS.PS
   A PostScript utility to find the rms and average values of any complex
   waveform
. Especially triac phase controls. Also investigates recent
   
outrageous lighting efficiency claims.

Click here for Custom Research assistance.

   Ken Shiriff:  VCRPlus Codes
      
Shows the six bit encoding and decoding of the VCRplus
      time and date codes
. Tutorial text, figure, and sourcecode combined
      
into single .pdf" file from November 1993 original.

Click here for other Third Party tutorials.

   Hardware Hacker #59 HACK59.PDF
     
High side FET drivers. Drawing semilog plots. Laser printer
     
repair kits. Fundamentals of resonance. Far East computing
     
resources. Semiconductor manufacturer resources.

Click here for more PostScript info.

   Hardware Hacker #65 HACK65.PDF
      
Short haul telemetry and comm links. Max-Min slope theory.
     
SETI books and resourses. Unique new optical link. Understanding
     
the Maximum Power Transfer Theorem. Gerber file formats.

Click here for more Hardware Hacker columns.

   Bubble Sort Utility BUBLSORT.PS
      
Simple stack-oriented utility that bubble sorts up to several
      
thousand values. Read tutorial first as textfile, then test and
       
modify as runnable PostScript code.

Click here for additional PostScript resources.

   Insertion Sort Utility INSORT.PS
     
Simple stack-oriented utility that approximates an insertion sort
     
up to several thousand values. Read tutorial first as textfile, then
      
test and modify as runnable PostScript code.

Click here for Adobe Acrobat PDF info.

  Links: .
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    Resources from Math Links
      
This appears to be the defining site for all links mathematical
      currently on the web.

Click here for the Hotbot search engine.
Click here for the Google search engine.

Click here for Cubic Spline tutorials.
Click here for Custom Consulting assistance.
Click here for Magic Sinewave tutorials.
Click here for some Wavelet tutorials.

  Books: .
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Bezier Curves & Cubic Splines:

B-Spline Knot Insertion and Deletion Algorithms ( Roger Goldman )
Curves and Surfaces  ( Academic Press )
Curve and Surface Fitting  ( Peter Lancaster )
An Introduction to Nurbs  ( David Rodgers )
Geometric Modeling using Beta Splines  ( Brian Barsky )
Handbook of Splines  ( Gheorghe Micula )
Handbook of Splines for the User  ( Eugene Shikin )
Interpolating Cubic Splines  ( Gary Knott )
Methods of Shape; Preserving Spline Approximation ( Boris Kvasov )
The Nurbs Book  ( Les Piegelr )
Nurbs for Curves and Surface Design  ( Gerald Farin )
PostScript Language Reference Manual   ( Adobe Systems )
A Practical Guide to Splines ( Carl De Booer )
Spline Functions ( K. Bohmer )
Theory of Splines and Applications  ( J. Ahlberg )
Two Dimensional Spline Interpolation Algorithms  ( Helmuth Spath )

Error Correcting Codes:

Principles of Digital Communication ( Andrew Viterbi)
 
1997 Error Correcting Code Symposium (Harold Mattson)
Algebraic Algorithims and Error-Correcting... (John Alton)
Applicable Algebra, Error-Correcting Codes, ... (Beth Th)
CDMA; Principles of Spread Spectrum Comm (Andrew Viterbi)
Coded Modulation for Fading Channels (Hamidreza Jamali)
Data & Computer Communications (William Stallings)
Engineer's Error Coding Handbook (A Houghton)
Error Control Coding (Shu Lin)
Error Control Systems for Digital Comm... (Stephen Wicker)
Error Control Techniques for Digital Comm... (Arnold Michelson)
Error Correcting Codes (John Baylis)
First Course in Coding Theory (Raymond Hill)
Introduction to Error-Correcting Codes (Michael Purser)
Intro to Error Correcting Codes (Scott Vanstone)
Theory & Applications of Error-Correction Codes (Jiri Adamek)
Trellis Coding  (Christian Schlegel)
Voice & Data Communications Handbook (Regis Bates)
Understanding Data Communications (Gilbert Held)

Wavelets:

An Introduction to Wavelets ( Charles Chui )
Applied Wavelet Analysis with S-Plus ( Andrew Bruce )
Fourier and Wavelet Analysis  ( George Bachman )
Fractal and Wavelet Image Compression Technique  ( Stephen. Welstead )
Handbook of Wavelet Transform Algorithms ( Carl Taswell )
Introduction to Wavelet Transforms ( Ramesh Gopinath )
Multirate and Wavelet Signal Processing  ( Bruce Suter )
Multiscale Wavelet Methods for PDE ( Wolfgang Dahmen )
Signal and Image Representation in Combined... ( Y. Zeev )
Signal Processing With Wavelet-Based Fractals ( G. Wornell )
Wavelet Analysis for Image Processing ( L. Prasad )
Wavelet Analysis: Scalable Info Structure ( H. Resnikoff)
Wavelet Basics (Y. Chan )
Wavelet Theory and Pattern Recognition ( Yuan Y. Tan )
A Wavelet Tour of Signal Processing ( Stephane Mallat )
Wavelet Transforms & Applications ( Mysore Raghuveer )
Wavelets: A Tutorial in Theory & Applications ( Charles Chui )
Wavelets: Theory, Algorithms & Applications ( C. Chui )

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