This book introduces groupoids and n-fold groupoids as powerful mathematical tools that unify and generalize local and distant symmetries observed in physical systems. While these concepts are typically discussed in highly specialized literature, this volume makes them accessible to a broader audience by grounding them in concrete applications to solid mechanics, including composite materials and metamaterials. No prior knowledge of the theory or its applications is assumed. The c...

This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further ...

This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The ...

Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics.Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constit...

Although the setting of this play is modern, it involves a fictitious encounter between Machiavelli and Richard Pace, a Tudor diplomat. It also involves John Keats and explores the meaning of poetry, love and life. Richard Pace was an important English diplomat during the Tudor period, a younger contemporary of Machiavelli. The meeting described in the play never took place, or did it? At any rate, the aging and broken Machiavelli opens his heart to Pace. This is the beginning of the story...

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresse...

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view.This book, unlike other introductory t...

A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of se...

Students and research workers in mathematics, physics, engineering and other sciences will find this compilation of more than 4,000 mathematical formulas and tables invaluable. All the information included is practical, rarely used results are excluded. Topics range from elementary to advanced - from algebra, trigonometry and calculus to linear algebra and statistics. Great care has been taken to present all results concisely and clearly. Excellent to keep as a handy reference! If you don'...

The US economy today is confronted with the prospect of extended stagnation. This book explores why. Thomas I. Palley argues that the Great Recession and destruction of shared prosperity is due to flawed economic policy over the past thirty years. One flaw was the growth model adopted after 1980 that relied on debt and asset price inflation to fuel growth instead of wages. A second flaw was the model of globalization that created an economic gash. Third, financial deregulation and the hous...

Boost Your grades with this illustrated Study Guide. You will use it from college all the way to graduate school and beyond.FEATURES:- Clear and concise explanations - Difficult concepts are explained in simple terms - Illustrated with graphs and diagrams TABLE OF CONTENTS:I. Linear equations System of linear equations Determinant Minor Cauchy-Binet formula Cramer's rule Gaussian elimination Gauss-Jordan elimination Strassen algorithm II. Matrices Matrix addition Matrix multiplication Basi...

The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into its eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical signifi...