# Numerical Computing with MATLAB

## by Cleve Moler.

**Introduction:**

This is an excellent textbook on basic numerical
methods, the MATLAB programming environment, and technical computing. The
problems are enjoyable and interesting. I would recommend it highly to
anyone who wanted .
Note: the entire book, chapter by chapter can be found online here

Here
are a few problems from the book I have had time to write the solutions to.

**Matlab Code For Various Problems:**

**Chapter 7 (Ordinary Differential Equations):**

- prob_7_2.m (a comparison of methods for computing compound interest numerically)

- prob_7_4.m (evaluating the error function using its differential equation)

- prob_7_4_fn.m (the error functions differential equation)

- prob_7_5.m (error experiments with RK4)

- prob_7_5_fn.m (the differential equation for a simple harmonic oscillator)

- myrk4.m (a fixed stepsize Runge-Kutta integrator (of global order 4))

- prob_7_6.m (experiments with stiff and non-stiff ODE solvers)

- prob_7_6_fn.m (the differential equation for a mildly stiff problem)

**Chapter 10 (Eigenvalues and Singular Values):**

- prob_10_1.m (a "gallery" of special matrices)

- prob_10_2.m (the largest and smallest eigenvalue of the magic squares)

- prob_10_3.m (the eigenvalues of the n-by-n Fourier matrix))

- prob_10_4.m (the eigenvalues of a differentiation matrix)

- prob_10_5.m (eigenvalue trajectories)

- prob_10_6.m (eigenvalue condition numbers)

- prob_10_7.m (the Rosser matrix)

- prob_10_8.m (matrices with lambda and 1/lambda as eigenvalues)

- prob_10_9.m (a timing comparison of three methods for computing the SVD)

- prob_10_11.m (a graphical comparison of three variants of the QR algorithm)

- prob_10_13.m (Nikolaus Troje's walker model)

- prob_10_14.m (diagraphs of various text sources)

- prob_10_15.m (experiments with the stepsize h in the circle generation solver)

- ret_mat_A.m (for prob_10_15.m constructs the discrete iteration matrix A)

- prob_10_16_a.m (Euler's method at generating circles)

- prob_10_16_b.m (implicit Euler's method at generating circles)

- prob_10_17.m (compare the numerical predicted aspect ratio to the eigenvector condition number)

John Weatherwax
Last modified: Mon Jul 31 20:43:01 EDT 2006