E77: INTRODUCTION TO COMPUTER PROGRAMMING FOR SCIENTISTS AND ENGINEERS

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E77 INTRODUCTION TO COMPUTER PROGRAMMING FOR
SCIENTISTS AND ENGINEERS

• Lecture Outline
• 1. Polynomials as arrays
• 2. Two-dimensional plots
• 3. Three-dimensional plots

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Polynomials as arrays

• 1. Polynomials as arrays
• Any one-dimensional polynomial of n-th degree can
  be
• expressed as
• Such a polynomial can be put in one-to-one
• correspondence with a one-dimensional array
• Note n-th degree polynomials correspond to
• n1-dimensional vectors!

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Polynomials as arrays

• All basic polynomial operations, such as
  addition, scalar
• multiplication and division can be rendered
  easily as
• vector operations. In particular
• Addition/subtraction is equivalent to
  element-wise addition/subtraction of equal-sized
  vectors.
• Scalar multiplication is equivalent to
  element-wise multiplication of a vector by a
  scalar.

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Polynomials as arrays

• Multiplication and division between polynomials P
  and Q is handled in MATLAB by the functions
  conv(P,Q) and deconv(P,Q).
• The evaluation of a polynomial P for a given
  argument x is handled in MATLAB by the function
  polyval(P,c)

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Polynomials as arrays

• Polynomial root-finding is handled by the
  function roots(P).
• Polynomial differentiation is handled by the
  function polyder(P).
• Polynomial integration is handled by the function
  polyint(P,c).

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Two-dimensional plots

• 2. Two-dimensional plots
• The effective visual representation of data is of
  great
• significance in science and engineering.
• Two-dimensional plots in MATLAB
• Simple x-y plots (plot)
• Pie charts (pie)
• Bar and stair charts (bar, stairs)
• Histograms (hist)
• Error bars (errorbar)
• Other special plots (area, fill, scatter)

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Three-dimensional plots

• 3. Three-dimensional plots
• Three-dimensional plots in MATLAB
• Simple x-y-z plots (plot3)
• Mesh plots (mesh, meshc, meshz)
• Surface plots (surf, surfc, surf1)
• Pie charts (pie3)
• Bar plots (bar3)
• Contour plots (contour, contour3)
• The view command controls the perspective of a
• plot.

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Three-dimensional plots

• Remarks on plots
• The type of data and the scope of their
  presentation dictates the choice of plot option.
• Always label the axes and put a title on each
  plot.
• Be sure to scale the axes as necessary (linear or
  logarithmic scales).
• Avoid extremely busy plots.
• Use subplots when plotting on the same plot
  becomes too busy.
• When producing plots always keep the target
  audience in mind.

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Summary

• What did we learn today?
• One dimensional polynomials can be treated
  equivalently as vectors.
• Basic polynomial operations readily reduce to
  corresponding vector operations.
• Two- and three-dimensional plots are effective
  visual mean of communicating technical
  information.
• The choice of plots is dictated by the type of
  data and the scope of the presentation.
• When generating plots, keep the target audiences
  needs and tastes in mind!