Functions and Operators in MAPLE and in MATLAB

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Functions and Operators in MAPLE and in MATLAB

• Matthias Kawski
• Dept of Math Statistics
• Arizona State University
• Tempe, AZ. U.S.A.

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Also, thanks for generous support by

• Department of Mathematics
• Center for Research in Education of Science,
• Mathematics, Engineering, and Technology
• Arizona State University
• INTEL Corporation through grant 98-34
• National Science Foundation through the grants
• DUE 97-52453 Vector Calculus via Linearization
• Visualization and
  Modern Applications
• DMS 00-72369 Algebra and Geometry of Nonlinear
  Control Systems
• EEC 98-02942 Engineering Foundation Coalition

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Vision (M.K., Odense 2000)

• We are at the beginning of a new era in which an
• interactive visual language not only complements,
  
• but often supersedes the traditional, almost
  exclusively
• algebraic-symbolic language which for generations
  
• has often been confused with mathematics itself,
• (and which may be largely responsible for the
  isolation,
• poor public perception, and extremely difficult
  re-entry
• into mathematics due to the imposed vertical
  structure).

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The power of interactive visualization

• stems from

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Zoom for derivative of vector field
Subtract the drift, and magnify domain and range
at equal rates,
compare
Definition A linear map (DF)(x) is the
derivative of F at x if
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Summary and conclusion

• Highly visual representations / metaphors
  that allow for fast, interactive
  manipulation
• facilitate doing math, understood as the
  process of
• experiment, make observations, conjecture,
  further test,
• formulate theorem, prove ? make
  definition, axiomatize
• are ideally suited to serve as roots around
  which to build rich concept
  images to be remembered for life
  (as opposed to memorize formula for next
  exam only)
• help make connections, avoid fragmentation of
  knowledge, provide coherence very
  few fundamental concepts
• mesmerize through their intrinsic beauty, invite
  to math

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Summary and conclusion

• Highly visual representations / metaphors
  that allow for fast, interactive
  manipulation
• facilitate doing math, understood as the
  process of
• experiment, make observations, conjecture,
  further test,
• formulate theorem, prove ? make
  definition, axiomatize
• are ideally suited to serve as roots around
  which to build rich concept
  images to be remembered for life
  (as opposed to memorize formula for next
  exam only)
• help make connections, avoid fragmentation of
  knowledge, provide coherence very
  few fundamental concepts
• mesmerize through their intrinsic beauty, invite
  to math

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Summary and conclusion

• Highly visual representations / metaphors
  that allow for fast, interactive
  manipulation
• facilitate doing math, understood as the
  process of
• experiment, make observations, conjecture,
  further test,
• formulate theorem, prove ? make
  definition, axiomatize
• are ideally suited to serve as roots around
  which to build rich concept
  images to be remembered for life
  (as opposed to memorize formula for next
  exam only)
• help make connections, avoid fragmentation of
  knowledge, provide coherence very
  few fundamental concepts
• mesmerize through their intrinsic beauty, invite
  to math

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Summary and conclusion

• Highly visual representations / metaphors
  that allow for fast, interactive
  manipulation
• facilitate doing math, understood as the
  process of
• experiment, make observations, conjecture,
  further test,
• formulate theorem, prove ? make
  definition, axiomatize
• are ideally suited to serve as roots around
  which to build rich concept
  images to be remembered for life
  (as opposed to memorize formula for next
  exam only)
• help make connections, avoid fragmentation of
  knowledge, provide coherence very
  few fundamental concepts
• mesmerize through their intrinsic beauty, invite
  to math

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Summary and conclusion

• Highly visual representations / metaphors
  that allow for fast, interactive
  manipulation
• facilitate doing math, understood as the
  process of
• experiment, make observations, conjecture,
  further test,
• formulate theorem, prove ? make
  definition, axiomatize
• are ideally suited to serve as roots around
  which to build rich concept
  images to be remembered for life
  (as opposed to memorize formula for next
  exam only)
• help make connections, avoid fragmentation of
  knowledge, provide coherence very
  few fundamental concepts
• mesmerize through their intrinsic beauty, invite
  to math

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