Algorithms with JULIA: Optimization, Machine Learning, and Differential Equations Using the JULIA Language

This book provides an introduction to modern topics in scientific computing and machine learning,using the JULIA programming language to illustrate efficient algorithm implementation. It covers fundamental topics like optimization and equation solving,and emphasizes partial differential equations and systems,with a focus on practical applications in engineering. JULIA is a versatile programming language designed for scientific and technical computing,with an open-source compiler and easy-to-use package system. It is aimed at students with a basic knowledge of linear algebra and programming.

Format: Hardback
Length: 439 pages
Publication date: 13 December 2022
Publisher: Springer International Publishing AG

This comprehensive book offers an insightful introduction to modern topics in scientific computing and machine learning, leveraging the powerful JULIA programming language to demonstrate efficient algorithm implementation. In addition to covering fundamental concepts like optimization and solving systems of equations, it delves into more advanced topics of practical significance, such as partial differential equations and their applications in various engineering fields. Furthermore, the book includes chapters dedicated to machine learning, encompassing artificial neural networks and Bayesian estimation, providing valuable insights into this rapidly evolving field.

Developed with scientific and technical computing in mind, JULIA is a relatively new programming language that boasts a syntax similar to other languages in this domain while incorporating modern programming concepts. It is open source and comes with a compiler and an intuitive package system, making it accessible to students of applied mathematics, computer science, engineering, and bioinformatics with a basic understanding of linear algebra and programming.

The book is organized into five chapters, each focusing on a specific aspect of scientific computing and machine learning. The first chapter provides an overview of JULIA and its features, highlighting its strengths for scientific computing and its suitability for various applications. The second chapter introduces the basics of linear algebra and programming, which are essential prerequisites for understanding the subsequent chapters.

Chapter three explores optimization techniques, including gradient descent, Newton's method, and quasi-Newton methods, and demonstrates their application in solving linear and non-linear optimization problems. Chapter four discusses the solution of systems of equations, including matrix methods, finite difference methods, and iterative methods, and showcases their effectiveness in solving a wide range of engineering problems.

Chapter five focuses on partial differential equations (PDEs), which are fundamental equations that describe the behavior of many physical systems. The chapter introduces the basic concepts of PDEs, including their definition, solution methods, and applications in fields such as fluid dynamics, heat transfer, and solid mechanics. Several chapters also include material on machine learning (artificial neural networks and Bayesian estimation), providing students with a comprehensive understanding of these powerful tools for data analysis and prediction.

Throughout the book, JULIA is used as a vehicle to illustrate the implementation of algorithms and techniques. The programming language is praised for its simplicity, readability, and efficiency, making it an ideal choice for scientific computing and machine learning applications. The book also includes numerous examples and exercises to reinforce the concepts presented, allowing students to apply their knowledge and gain hands-on experience with the topics covered.

In conclusion, this comprehensive book provides an excellent introduction to modern topics in scientific computing and machine learning, leveraging the power of JULIA to demonstrate efficient algorithm implementation. With its focus on practical applications, advanced topics, and hands-on exercises, the book is suitable for students of applied mathematics, computer science, engineering, and bioinformatics with a basic understanding of linear algebra and programming. By embracing JULIA as a programming language, students can develop the skills and knowledge necessary to tackle complex scientific computing and machine learning problems and contribute to the advancement of these fields.

Weight: 942g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031165597
Edition number: 1st ed. 2022