Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. Julia code is provided to illustrate concepts and allow readers to explore methods on their own. Written in a friendly and approachable style, the book contains detailed descriptions of algorithms along with illustrations and graphics that emphasize core concepts and demonstrate the algorithms. Numerical Linear Algebra with Julia is a textbook for advanced undergraduate and graduate students in most STEM fields and is appropriate for courses in numerical linear algebra. It may also serve as a reference for researchers in various fields who depend on numerical solvers in linear algebra.

This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.

This book provides an introduction to modern topics in scientific computing and machine learning, 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 and Bayesian estimation). JULIA is a relatively new programming language which has been developed with scientific and technical computing in mind. 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. Aimed at students of applied mathematics, computer science, engineering and bioinformatics, the book assumes only a basic knowledge of linear algebra and programming.

Learn to use Julia as a tool for research, and solve problems of genuine interest—like modeling the course of a pandemic—in this practical, hands-on introduction to the language. The Julia programming language is acclaimed in scientific circles for its unparalleled ease, interactivity, and speed. Practical Julia is a comprehensive introduction to the language, making it accessible even if you’re new to programming. Dive in with a thorough guide to Julia’s syntax, data types, and best practices, then transition to craft solutions for challenges in physics, statistics, biology, mathematics, scientific machine learning, and more. Whether you’re solving computational problems, visualizing data, writing simulations, or developing specialized tools, Practical Julia will show you how. As you work through the book, you’ll: • Use comprehensions and generators, higher-level functions, array initialization and manipulation, and perform operations on Unicode text • Create new syntax and generate code with metaprogramming and macros, and control the error system to manipulate program execution • Visualize everything from mathematical constructs and experimental designs to algorithm flowcharts • Elevate performance using Julia’s unique type system with multiple dispatch • Delve into scientific packages tailored for diverse fields like fluid dynamics, agent-based modeling, and image processing Whether your interest is in scientific research, statistics, mathematics, or just the fun of programming with Julia, Practical Julia will have you writing high-performance code that can do real work in no time. Online Resources: Ready-to-run code samples, illustrations, and supplemental animations available at https://julia.lee-phillips.org.

This book, "Pharmacoinformatics: Real-World Applications in Pharmacy and Medicine" is designed to bridge the gap between medicine and computer science by providing a practical and accessible introduction to programming languages and techniques specifically tailored to the needs of healthcare professionals. Whether you are a student, a practicing pharmacist, a physician, or any other healthcare professional, this book aims to equip you with the fundamental programming skills and domain-specific knowledge required to tackle real-world challenges in healthcare

Master matrix methods via engaging data-driven applications, aided by classroom-tested quizzes, homework exercises and online Julia demos.

This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.

This user-oriented guide describes state-of-the-art methods for nonlinear equations and shows, via algorithms in pseudocode and Julia with several examples, how to choose an appropriate iterative method for a given problem and write an efficient solver or apply one written by others. A sequel to the author’s Solving Nonlinear Equations with Newton’s Methods (SIAM, 2003), this book contains new material on pseudo-transient continuation, mixed-precision solvers, and Anderson acceleration. It is supported by a Julia package and a suite of Jupyter notebooks and includes examples of nonlinear problems from many disciplines. This book is will be useful to researchers who solve nonlinear equations, students in numerical analysis, and the Julia community.

This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice. The text addresses numerical analysis as a middle ground between practice and theory, addressing both the abstract mathematical analysis and applied computation and programming models instrumental to the field. While the text uses pseudocode, Matlab and Julia codes are available online for students to use, and to demonstrate implementation techniques. The textbook also emphasizes multivariate problems alongside single-variable problems and deals with topics in randomness, including stochastic differential equations and randomized algorithms, and topics in optimization and approximation relevant to machine learning. Ultimately, it seeks to clarify issues in numerical analysis in the context of applications, and presenting accessible methods to students in mathematics and data science.

A comprehensive guide to the theory, intuition, and application of numerical methods in linear algebra, analysis, and differential equations. With extensive commentary and code for three essential scientific computing languages: Julia, Python, and Matlab.