The expanded edition delves into advanced topics such as boundary layers, multiple scales, and homogenisation, alongside slender body theory and symbolic computing. It also covers discrete equations, providing a comprehensive exploration of these complex subjects. The book features exercises based on current research, making it a valuable resource for applications across various fields.
Focusing on the construction and analysis of mathematical models, this textbook aims to enhance understanding of contemporary scientific and engineering challenges. It emphasizes fundamental mathematical and physical concepts rather than relying on case studies. As science evolves, the text adapts to address the changing landscape of current problems, providing a dynamic framework for students to engage with real-world applications.
Focusing on numerical computing, this textbook serves as a comprehensive introduction for applications in science and engineering. It covers foundational topics alongside advanced data analysis methods, including optimization and regression techniques using singular value decomposition. Emphasizing problem-solving, the text features numerous exercises relevant to engineering and science, while also exploring the mathematical theories behind the methods and their computational errors. The latest edition incorporates essential material for upper division courses in computational linear algebra, with accompanying code available on GitHub.