Denis Serre Books

The book offers a comprehensive introduction to matrix theory, enriched with a variety of applications across mathematics, science, and engineering. This second edition features 40% new material, including topics like Dunford decomposition, tensor calculus, and eigenvalue regularity for complex matrices. It integrates algebra, analysis, complexity theory, and numerical analysis, making it a valuable resource for both advanced undergraduate and graduate students pursuing applied or theoretical studies. Based on a course at the École Normale Supérieure de Lyon, it serves as a reliable reference for scientists and mathematicians alike.

Clear and concise introduction to matrices with elegant proofs; Of interest to scientists from many disciplines; Gives many interesting applications to different parts of mathematics, such as algebra, analysis and complexity theory; Contains 160 exercises, half of them on advanced material; Includes at least one advanced result per chapter

Focusing on the mathematical theory of conservation laws and partial differential equations, this graduate-level text delves into advanced concepts and methodologies. It presents rigorous mathematical frameworks and applications, catering to students and researchers seeking a deep understanding of these fundamental topics in applied mathematics. The book emphasizes theoretical foundations while also exploring practical implications, making it a valuable resource for those pursuing studies in mathematical physics and engineering.