Using Technology as a Teaching/Research Tool in a Special Topics Course in Differential Equations

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Using Technology as a Teaching/Research Tool in
a Special Topics Course in Differential Equations

• Lawrence E. Levine
• Stevens Institute of Technology
• and
• West Point Military Academy
• llevine_at_stevens-tech.edu

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Using Technology in Teaching

• Web and Distance Learning
• Use in classroom
• State of the art classroom
• Laptops
• Wireless connections
• Software to monitor students laptops
• Scientific Notebook

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What Do You Do With All of This?

• Prepare lecture notes using SNB
• Have students work in class and monitor their
  work
• Project the work of a student for all to see
• Have students make presentations
• Involve the student

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Course Use of Technology I

• Presentation of material
• Review of basic techniques to solve Des
• Infinite series
• Series solution near an ordinary point
• Method of Frobenius
• Boundary value problems, Fourier series
• Separation of variables for PDEs

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Course Use of Technology II

• Research Tool
• Polynomial solutions of nonhomogeneous DEs
• Chebyshev, Hermite, Legendre, Laguerre equations
  with right hand side
• What initial conditions yield a polynomial
  solution?
• Maple kernel in SNB will solve initial value
  problem
• By looking at examples one attempts to guess the
  general case
• Then one proves that this is indeed the result.

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Another Approach

• Want a polynomial solution
• In these equations recurrence relation has step
  2
• Set expression for equal to zero
• Work backwards to get the initial conditions.