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In recent years cosmologists have advanced from largely qualitative models of the Universe to precision modelling using Bayesian methods, in order to determine the properties of the Universe to high accuracy. This timely book is the only comprehensive introduction to the use of Bayesian methods in cosmological studies, and is an essential reference for graduate students and researchers in cosmology, astrophysics and applied statistics. The first part of the book focuses on methodology, setting the basic foundations and giving a detailed description of techniques. It covers topics including the estimation of parameters, Bayesian model comparison, and separation of signals. The second part explores a diverse range of applications, from the detection of astronomical sources (including through gravitational waves), to cosmic microwave background analysis and the quantification and classification of galaxy properties. Contributions from 24 highly regarded cosmologists and statisticians make this an authoritative guide to the subject.
Cosmology --- Bayesian statistical decision theory. --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Astronomy --- Deism --- Metaphysics --- Statistical methods.
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This Student Solution Manual provides complete solutions to all the odd-numbered problems in Essential Mathematical Methods for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to select an appropriate method, improving their problem-solving skills.
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This Student Solution Manual provides complete solutions to all the odd-numbered problems in Foundation Mathematics for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to arrive at the correct answer and improve their problem-solving skills.
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Mathematical analysis. --- Wiskunde --- Wiskunde. --- Mathematical analysis --- #KVIV:BB --- 51-74 --- 517.1 Mathematical analysis --- 51-74 Mathematics--?-74 --- Mathematics--?-74 --- 517.1. --- Analyse mathématique --- Physics. --- Methodology. --- Mathematics. --- Engineering. --- Construction --- Industrial arts --- Technology --- Math --- Science --- Philosophy --- Research --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Advanced calculus --- Analysis (Mathematics) --- Algebra --- Methodology --- Monograph --- 517.1 --- Mathématiques --- Mathematics --- Analyse mathématique
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After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is 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.
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Mathematical analysis. --- 517 --- 51-74 --- 517 Analysis --- Analysis --- 51-74 Mathematics--?-74 --- Mathematics--?-74 --- Mathematical analysis --- 517.1 Mathematical analysis --- 517.1. --- 517.1 --- Mathématiques --- Mathematics --- Analyse mathématique --- Engineering. --- Mathematics. --- Analyse mathématique --- Mathématiques --- Methodes mathematiques de la physique
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The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.
Mathematical physics --- Engineering mathematics --- Mathematical analysis --- wiskunde --- 51-74 --- Physical mathematics --- Physics --- 517.1 Mathematical analysis --- Engineering --- Engineering analysis --- 51-74 Mathematics--?-74 --- Mathematics--?-74 --- Mathematics --- 517.1. --- Engineering mathematics. --- Mathematical analysis. --- Mathematical physics. --- Analyse mathématique --- Physique mathématique --- Mathématiques de l'ingénieur --- Analyse mathématique --- Mathématiques de l'ingénieur --- Physique mathématique --- Problems, exercises, etc. --- Problems, exercices, etc --- Problèmes et exercices --- Analyse mathématique. --- Mathématiques de l'ingénieur. --- Physique mathématique. --- 517.1 --- Problems, exercices, etc.
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The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers). To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions. Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail. The presentation of probability has been reorganised and greatly extended, and includes all physically important distributions. New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F-tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting. In other chapters the following topics have been added: linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods.
Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis
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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 illuminate and extend the discussion in the text.
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