A Course in Homogenization-Based Techniques focuses on providing practical insights into select mathematical techniques for multiscale problems, with a close eye on real-world applications. Supported by examples and exercises chosen for their ability to serve as tools illustrating underlying theories — much like appetizers designed to spark further curiosity — this textbook explores the 'why' just as much as it explains the 'how' of multiscale modeling. It encourages readers to pose their ...

This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes. The focus of this presentation lies on many practical examples covering aspects such as coupled flow, diffusion and reaction in porous media or microwave heating of a pizza, as well as traffic issues in bacterial colonies and energy harves...

This book is the offspring of a summer school school “Macroscopic and large scalephenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins.Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions.Francois Golse ...

Ordinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology. This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of or...

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...

This book is an account of my first encounter with Einstein's Special Relativity. It is inevitable that in trying to unravel the theory's logical inconsistencies I did not at first attempt succeed in correcting it. The logic does not stand the test of a detailed follow through. Our fundamental understanding of relativity in the universe is thus still waiting to be put right. Patience. (Feb. 2019)

A concise but rigorous treatment of variational techniques, focussing primarily on Lagrangian and Hamiltonian systems, this book is ideal for physics, engineering and mathematics students. The book begins by applying Lagrange's equations to a number of mechanical systems. It introduces the concepts of generalized coordinates and generalized momentum. Following this the book turns to the calculus of variations to derive the Euler–Lagrange equations. It introduces Hamilton's principle and us...

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...

This text is an introduction to some of the mathematical wonders of Maxwell's equations. These equations led to the prediction of radio waves, the realization that light is a type of electromagnetic wave, and the discovery of the special theory of relativity. In fact, almost all current descriptions of the fundamental laws of the universe can be viewed as deep generalizations of Maxwell's equations. Even more surprising is that these equations and their generalizations have led to some of ...

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...

Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, a...

Philosophy would not be worth a penny if it would be contradicting natural sciences, and the same holds true for the sciences if they would be in conflict with nature. The claim of natural sciences is it to map nature. For consistency, hence, the author, here, is outlining the last frontiers fundamental physics, actually, is disposing of.This interface of physics towards philosophy is based on cognition gained by Quantum Gravity, the consistent unification of Einstein's General Rel...