The second edition of the book A First Course in Numerical Linear Algebra, authored by Dr. Masoud Hajarian, Professor at the Faculty of Mathematical Sciences, Shahid Beheshti University, has been published.
This book was first released in 2025 by Shahid Beheshti University Press in 535 pages (octavo size) and is offered at the price of 4,800,000 IRR.
Since the production of the first modern computer in 1946, numerical linear algebra—also known as matrix computations—has occupied a significant and unique position in applied sciences and engineering. The importance and practical applications of numerical linear algebra, especially in large-scale problems, are undeniable. Today, hardly any engineer or graduate of applied disciplines can be found who does not need to solve systems of linear equations, compute eigenvalues and eigenvectors of a matrix, or approximate functions using numerical methods to address challenges in their field. Considering the scarcity of comprehensive works in Persian on this subject, this book was written based on a review of diverse references, providing an up-to-date and comprehensive source to meet the needs of students in various disciplines.
In preparing the second edition, every effort has been made to cover nearly all topics required for teaching numerical linear algebra at undergraduate, master’s, and doctoral levels. With respect to updated curricula and practical applications, the book has been designed to serve a wide range of readers.
This edition contains six chapters, each suitable for teaching as a complete course at the master’s or doctoral level. For undergraduate teaching, certain sections of each chapter may be omitted (as specified in the book) without compromising the overall flow of the material.
Chapter 1 reviews the essential concepts of linear algebra, which form the foundation for the rest of the book and must be studied carefully.
Chapter 2, one of the most important, discusses direct methods for solving systems of linear equations.
Chapter 3 introduces iterative methods for solving such systems.
Chapter 4 addresses linear least-squares problems (constrained, unconstrained, multi-objective, and nonlinear) as well as nonlinear optimization.
Chapter 5 focuses on eigenvalues, eigenvectors, and their computation.
Chapter 6 is devoted to four advanced topics: Kronecker products and sums and their applications in solving matrix equations, preconditioning of linear systems, matrix functions, and matrix differentiation.
Each chapter concludes with a set of well-designed exercises, enabling students to deepen their understanding and mastery of the concepts. Additionally, important MATLAB commands are introduced where applicable to support the implementation of various methods.
Students and interested readers may purchase the book at the Sales Office of the University’s Center for Academic Publications, located on the ground floor of the IT Building at Shahid Beheshti University, or place an online order through the Center’s website. The electronic version of the book is also available via Fidibo and Taghche platforms.