Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory.

This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB (R) is presented. The codes are limited to 2D problems and can be easily translated in Python or Scilab, and used directly with Octave as well.

The burning of fossil fuels and emission of greenhouse gasses critically impacts the global environment. By utilizing better techniques and process, businesses can aid in the journey to an economic, sustainable, and environmentally-friendly future for generations to come. Business Models for Renewable Energy Initiatives: Emerging Research and Opportunities is an essential reference source for the latest scholarly perspectives on present and future business models in the renewable energy sector. Featuring coverage on a range of perspectives and topics such as techno-economics, decentralized power systems, and risk assessment, this book is designed for academicians, students, and researchers seeking current scholarly research on green business opportunities for renewable energy.

Few artworks have been the subject of more extensive modern interpretation than Melencolia I by renowned artist, mathematician, and scientist Albrecht Durer (1514). And yet, did each of these art experts and historians miss a secret manifesto that Durer included within the engraving? This is the first work to decrypt secrets within Melencolia I based not on guesswork, but Durer's own writings, other subliminal artists that inspired him (i.e., Leonardo da Vinci), the Jewish and Christian Bibles, and books that inspired Durer (De Occulta Philosophia and the Hieorglyphica). To read the covert message of Melencolia I is to understand that Durer was a humanist in his interests in mathematics, science, poetry, and antiquity. This book recognizes his unparalleled power with the burin, his mathematical skill in perspective, his dedication to precise language, and his acute observation of nature. Melencolia I may also be one of the most controversial (and at the time most criminal) pieces of art as it hid Durer's disdain for the hierarchy of the Catholic Church, the Kaiser, and the Holy Roman Empire from the general public for centuries. This book closely ties the origins of philosophy (science) and the work of a Renaissance master together, and will be of interest for anyone who loves scientific history, art interpretation, and secret manifestos.

The book contains a detailed account of numerical solutions of differential equations of elementary problems of Physics using Euler and 2nd order Runge-Kutta methods and Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.

This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.