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.
 

• 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 in Mathematica.
• 2.1.bisect.nb:  A rough and ready implementation of the bisection method.
• 2.2.iterate.nb:  Illustrates the fixed point algorithm, including some rather pretty graphics.
• 2.3.newton.nb:  Illustrates the Newton-Raphson method, including the modified method of Chapter 2.4.
• 2.3.1.cube.newt.nb:  Nothing to do with the book, shows the fractal produced by applying Newton's Method to x³-1 = 0.
• 3.0.taylor.nb:  Plots 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.
• 3.3.hermite.nb:  Hermite interpolation.
• 3.4.splines.nb:  Calculates 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.
• 4.7.gauss.quad.nb:  Implement Gaussian Quadrature.
• 5.2.euler.nb:  Implement Euler's method with y' = y (mainly to demonstrate errors).
• 5.4.runge.kutta.nb:  Prove that the Runge-Kutta Method given in the book is 4th order.
• 5.5.fehl.nb:  Implement the Runge-Kutta-Fehlberg Method.
• 5.6.adams.bash.nb:  Derive 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).
• 5.9.pred.prey.nb:  Exercise 7 from Chapter 5.9.
• 5.10.stability.nb:  Illustration of a highly unstable numerical method for solving differential equations.