Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
This book studies the engagement of various Muslim communities with Bihar politics from colonial times to present-day India. It debunks several myths in highlighting Muslim resistance to the Two-Nation theory, and counters the ‘Isolation Syndrome’ faced by Muslim communities after Independence. Using rare archival sources and hitherto unexamined Urdu texts, this book offers a nuanced exploration of complex themes such as the struggle against Bengali hegemony, communalism, regionalism and alienation before Independence, recent language politics, the political assertion of low-caste Muslims in current Bihar, as well as their quest for social and gender justice. An important contribution to the study of South Asian Islam, this book will interest students and scholars of modern Indian history, politics, sociology, religion, gender, and minority studies.
At a time when ordinary courage has become rare, one has to look up to the lives of those who stood for dissent in the colonial era. Back in the 19th century, Justice Syed Mahmood, son of the great social reformer Sir Syed Ahmad Khan, became the first judge to resist colonial power by espousing the cause of judicial independence. At the age of just 32, he not only remains the youngest, but also the first Indian Muslim and first north Indian to be appointed as a High Court judge in India. Endowed with a judicial acuity ahead of his times, a number of his dissents were later accepted by the courts, and continue to be the law. This book chronicles the triumphs and tragedies of Syed Mahmood's life, and his contribution in shaping the consciousness of post 1857 India. With an impressive array of research, perception and analysis, the book succeeds in exhuming a seminal figure from the dust of history, and showcases the past speaking to the present.
This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.
‘Alī, son of Abī Ṭālib, Muhammad’s son-in-law and cousin, is the only Companion of the Prophet who has remained to this day the object of fervent devotion of hundreds of millions of followers in the lands of Islam, especially in the East. Based on a detailed analysis of several categories of sources, this book demonstrates that Shi‘ism is the religion of the Imam, of the Master of Wisdom, just like Christianity is that of Christ, and that ‘Alī is the first Master and Imam par excellence. Shi‘ism can therefore be defined, in its most specific religious aspects, as the absolute faith in ‘Alī: the divine Man, the most perfect manifestation of God’s attributes, simultaneously spiritual refuge, model and horizon. With contributions by Orkhan Mir-Kasimov & Mathieu Terrier Translated from French by Francisco José Luis & Anthony Gledhill
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
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