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This book provides an introduction to modern topics in scientific computing and Machine Learning (ML), using JULIA to illustrate the efficient implementation of algorithms. In addition to covering fundamental topics, such as optimization and solving systems of equations, it adds to the usual canon of computational science by including more advanced topics of practical importance. In particular, there is a focus on partial differential equations and systems thereof, which form the basis of many engineering applications. Several chapters also include material on Machine Learning (artificial neural networks (ANN) and Bayesian estimation).
The programming language used in this book is Julia. Julia is a highlevel, high-performance, and dynamic programming language that has been developed with scientific and technical computing in mind. It offers features that make it very well suited for computing in science, engineering, and Machine Learning. Its syntax is similar to other languages in this area, but it has been designed to embrace modern programming concepts. It is open source, and it comes with a compiler and an easy-to-use package system.
The applied topics are carefully chosen, from the most relevant standard areas like ordinary and partial differential equations and optimization to more recent fields of interest like machine learning and neural networks. The chapters on ordinary and partial differential equations include examples of how to use existing packages included in the Julia software. In the chapter about optimization the methods for standard local optimization are nicely explained. However, this book also contains a very relevant chapter about global optimization, including methods such as simulated annealing and agent based optimization algorithms. All this is not something usually found in the same book. Again, the global optimization theory, as far as the general theory exists, is well presented and the application examples (and, most importantly, the benchmark problems) are well chosen. One chapter – concerned with the currently maybe most relevant area – introduces practical problem solving in the field of machine learning. The author covers the basic approach of learning via artificial neural networks as well as probabilistic methods based on Bayesian theory. Again, the topics and examples are well chosen, the underlying theory is well explained, and the solutions of the chosen application problems are immediately implementable in Julia.
Aimed at students of applied mathematics, Computer Science, engineering and bioinformatics, the book assumes only a basic knowledge of linear algebra and programming