Numerical Methods (Math 4300/7300)
Here is a list of Mathematica files that I use in my course. These
are designed to complement the text book Numerical Methods 5th Ed.,
Burden and Faires, ITP. In this manner, the names of the Mathematica
notebooks are exactly in line with the Chapter numbers from this book.
However, these notebooks present the material quite differently from
the book. They are designed to illustrate only certain aspects, particularly
those that Mathematica is well able to deal with.
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1.3.sequence.nb: This considers
the sequence given in Example 3 of Chapter 1.3, showing that floating point
errors can be very bad. This also provides an opportunity to consider
the difference between evaluating sequences recursively and iteratively
2.1.bisect.nb: A rough and
ready implementation of the bisection method.
the fixed point algorithm, including some rather pretty graphics.
the Newton-Raphson method, including the modified method of Chapter 2.4.
Nothing to do with the book, shows the fractal produced by applying Newton's
Method to x3-1 = 0.
of Taylor's series.
3.1.0.solve.nb: An introduction
to solving equations in Mathematica.
3.1.interp.nb: Shows how
to calculate interpolating polynomials. Includes graphs illustrating
how badly interpolating polynomials actually interpolate.
splines from their definition.
4.1.diff.nb: Derive formulae
for numerically evaluating derivatives, including the error term.
I think that this notebook really shows beautiful Mathematica can be.
It includes the derivation of a nine point formula.
4.5.adapt.nb: An implementation
of the adaptive quadrature method. It is implemented as a recursive
routine, and as such is much easier to understand, and much shorter than
the algorithm given in the text book.
5.2.euler.nb: Implement Euler's
method with y' = y (mainly to demonstrate
Prove that the Runge-Kutta Method given in the book is 4th order.
5.5.fehl.nb: Implement the
the Adams-Bashforth and Adams-Moulton Methods, including error terms.
5.9.euler.nb: Implement Euler's
method for systems of equations (mainly to demonstrate errors).
7 from Chapter 5.9.
5.10.stability.nb: Illustration of a
highly unstable numerical method for solving differential equations.