Material for a 2-day workshop on Julia, first given at the Université de Paris-Sud on June 16th and 17th, 2015
An introductory workshop on Julia at JuliaCon on June 24th, 2015
"This course is an exploration of the art and science of extracting numbers from mathematical expressions. The material we will cover may be broadly divided into two units.
Unit 1 is all about basic numerical calculus. We will discuss elementary methods for obtaining accurate numerical estimates of integrals, derivatives, and infinite sums. This unit will include discussions of extrapolation, interpolation, root-finding, optimization, and evaluation of special functions.
This will set the stage for Unit 2 of our course, Fourier analysis and spectral methods. The overarching theme here is that we can often revolutionize the speed and accuracy of a calculation by approximating a function as an expansion in some convenient set of expansion functions -- often a set of orthogonal functions. Our discussion of orthogonal-function expansions will begin, as must any, with the granddaddy of them all: the Fourier series and its immediate descendants (the Fourier transform, Parseval's and related theorems, the FFT, etc.). Then we will broaden the setting to consider more general classes of functions and more general spectral methods: Gaussian quadrature, Chebyshev polynomials, ... and more.
The examples are drawn from engineering and the sciences, including binding energies of solids, coding and modulation schemes for efficient use of the wireless communications spectrum, spherical Bessel functions for electromagnetic scattering and thermal engineering, and Ewald summation.
The course is intended to introduce students who are already somewhat familiar with scientific computing to what Julia has to offer.
A tentative schedule:
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