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   STUDY GUIDE FOR MATH 3416 FINAL EXAM
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   1. Errors, loss of significance, Taylor series

   2. Bisection, Newton and secant methods for root finding.
      You should know how to derive them and do simple
      calculations using a calculator.

   3. Lagrange form for interpolating polynomials.
      Newton's form for interpolating polynomials using the
      Newon divided difference table.
      Errors in interpolation using given formulas for linear
      and quadratic interpolation.

   4. Deriving derivative approximations using Taylor series and
      Richardson extrapolation.

   5. One step trapezoidal rule and composite trapezoidal rule.
      You should know how to use these rules to approximate
      integrals with a calculator.
      Using the error formula.

   6. Same as 5 but for Simpson's rule.
      Deriving Simpson's rule from the trapezoidal rule using
      Richardson extrapolation.
 
   7. Using the Romberg table obtained from
      Richardson extrapolation.
      You should know how to construct the table by hand using
      a calculator

   8. The naive gaussian elimination algorithm with back
      substitution.
      How to improve this algorithm.

   9. Obtaining the LU factorization without row exchanges
      and using it to solve a linear system.
      What modifications are needed if row exchanges are used.

   10.Using Euler's method to solve a differential equation.
      Deriving higher order methods using Taylor series.