LINEAR ALGEBRA II: ADVANCED TOPICS FOR APPLICATIONS

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This is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course. The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory. The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Matrices and Graphs Contents: Preface Matrices and Graphs Nonnegative Matrices Systems of Linear Inequalities Integer Matrices Polynomial Matrices Generalized Inverses Group Representation Theory Bibliography Index Readership: Graduate students majoring in engineering and other mathematical sciences.

Advanced Topics in Quantum Mechanics (1版)

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Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematical tools, followed by a detailed description of the Wentzel–Kramers–Brillouin (WKB) method. Two alternative formulations of quantum mechanics are then presented: Wigner's phase space formulation and Feynman's path integral formulation. The text concludes with a chapter examining metastable states and resonances. Step-by-step derivations, worked examples and physical applications are included throughout. Covers many advanced mathematical techniques in quantum mechanics, each illustrated with detailed examples Presents two alternative formulations of quantum mechanics; the path integral and phase space formulations, which are useful in advanced applications Provides a pedagogical and thorough overview of the exact WKB method, which plays an increasingly important role in many areas of modern physics