Book Image

Mastering Julia - Second Edition

By : Malcolm Sherrington
Book Image

Mastering Julia - Second Edition

By: Malcolm Sherrington

Overview of this book

Julia is a well-constructed programming language which was designed for fast execution speed by using just-in-time LLVM compilation techniques, thus eliminating the classic problem of performing analysis in one language and translating it for performance in a second. This book is a primer on Julia’s approach to a wide variety of topics such as scientific computing, statistics, machine learning, simulation, graphics, and distributed computing. Starting off with a refresher on installing and running Julia on different platforms, you’ll quickly get to grips with the core concepts and delve into a discussion on how to use Julia with various code editors and interactive development environments (IDEs). As you progress, you’ll see how data works through simple statistics and analytics and discover Julia's speed, its real strength, which makes it particularly useful in highly intensive computing tasks. You’ll also and observe how Julia can cooperate with external processes to enhance graphics and data visualization. Finally, you will explore metaprogramming and learn how it adds great power to the language and establish networking and distributed computing with Julia. By the end of this book, you’ll be confident in using Julia as part of your existing skill set.
Table of Contents (14 chapters)

Calculus

The Calculus package provides tools for working with the basic calculus operations of differentiation and integration. It can be used to produce approximate derivatives by several forms of finite differencing or to produce exact derivatives using symbolic differentiation (SD).

Differentiation

There are a few basic approaches to using the package, some of which we will examine in this section.

We use finite differencing to evaluate a derivative at a specific point and higher-order functions to create new functions that evaluate derivatives’ SD to produce exact derivatives for simple functions:

julia> using Calculus
julia> f(x)=sin(x)*cos(x);
julia> derivative(f,1.0) -0.4161468365471423
# Check since d(f) => cos*cos - sin*sin
julia> cos(1.0)^2 - sin(1.0)^2 -0.4161468365471423
# Possible to curry the function
julia> df = derivative(f)
julia> df(1.0)
-0.4161468365471423
# Also defined is the 2nd derivative
julia> d2f = second_derivative...