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Lawrence E. Levine Stevens Institute of Technology and West Point Military Academy

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@stevens-tech.edu. Using Technology in Teaching. Web and Distance Learning Use in classroom

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Lawrence E. Levine Stevens Institute of Technology and West Point Military Academy

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  1. 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@stevens-tech.edu

  2. 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

  3. 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

  4. 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

  5. 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.

  6. 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.

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