General Relativity Without Calculus

“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physi

“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physi

This is the first modern calculus book to be organized axiomatically and to survey the subject's applicability to science and engineering. A challenging exposition of calculus in the European style, i

The prediction of the special theory of relativity differ significantly from those of Newtonian physics only for bodies whose speeds are comparable with the speed of light. For this reason, special relativity is often considered as irrelevant to the macroscopic physics of ordinary material systems under terrestrial conditions. The aim of this book is to show that by uniting dynamics, thermodynamics and electromagnetism into a coherent whole, special relativity illuminated each of these subjects in a manner which cannot be obtained by studying them in isolation. The speed of the systems concerned is irrelevant. This deep and careful analysis of special relativity is suitable for second- and subsequent- year university students studying physics or applied mathematics. Its distinctive approach will also appeal to research workers in general relativity, in continuum thermodynamics and in the electrodynamics of continuous media.

This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.

This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mat

General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminat

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Part I of this classic work offers a rigorous presentation of tensor calculus as a development of vector analysis. Part II discusses the most important applications of tensor calculus, including the use of tensors in classical analytical dynamics and the role of tensors in special relativity. A concluding section examines field equations of general relativity theory.

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This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and impor

This compact guide presents the key features of general relativity, to support and supplement the presentation in mainstream, more comprehensive undergraduate textbooks, or as a re-cap of essentials for graduate students pursuing more advanced studies. It helps students plot a careful path to understanding the core ideas and basics of differential geometry, as applied to general relativity, without overwhelming them. While the guide doesn't shy away from necessary technicalities, it emphasises the essential simplicity of the main physical arguments. Presuming a familiarity with special relativity (with a brief account in an appendix), it describes how general covariance and the equivalence principle motivate Einstein's theory of gravitation. It then introduces differential geometry and the covariant derivative as the mathematical technology which allows us to understand Einstein's equations of general relativity. The book is supported by numerous worked exampled and problems, and impor

This book presents Special Relativity (SR) in a language deemed accessible to students without any topical preparation - avoiding the burden of geometry, tensor calculus, and space-time symmetries – a

This book provides a completely revised and expanded version of the previous classic edition ‘General Relativity and Relativistic Astrophysics’. In Part I the foundations of general relativity are tho

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DescriptionWelcome to the International Metric Version of Essential Calculus: Early Transcendental Functions. For this metric version, the units of measurement used in most of the examples and exercises have been changed from U.S. Customary units to metric units. We did not convert problems that are specific to the U.S. Customary units, such as dimensions of a baseball field or U.S. postal rates. We are excited to offer you a new edition with more resources then ever that will help you understand and master calculus. This text includes features and resources that continue to make Essential Calculus: Early Transcendental Functions a valuable learning tool for students and a trustworthy teaching tool for instructors.Essential Calculus: Early Transcendental Functions provides the clear instruction, precise mathematics, and thorough coverage that you expect for your course.FeaturesNEW Big Ideas of CalculusWe have added a new feature to help you discover and understand the Big Ideas of Calc

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Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.

Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.

A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein's equations - the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. S

This book explains the theory of special and general relativity in detail, without digressions such as information on Einstein's life or the historical background. However, complicated calculations ar