ISBN: 978-1-84265-371-5
Publication Year: 2007
Pages: 310
Binding: Hard Back
Dimension: 185mm x 240mm
Weight: 840
About the book
Differential Geometry of Manifolds discusses the theory of differentiable and Riemannian manifolds to help students understand the basic structures and consequent developments. Since the tangent vector plays a crucial role in the study of differentiable manifolds, this idea has been thoroughly discussed. In the theory of Riemannian geometry some new proofs have been included to enable the reader understand the subject in a comprehensive and systematic manner. This book will also benefit the postgraduate students as well as researchers working in the field of differential geometry and its applications to general relativity and cosmology.
Key Features
Basic concepts Motivation of concepts Coordinate free approach is followed by local expressions Grasp the theory clearly and deeply Illuminating illustrations Numerous solved exercises
Table of content
Preface / Some Preliminaries / Differentiable Manifolds / Exterior Algebra and Exterior Derivative / Lie Group and Lie Algebras / Fibre Bundles / Linear Connections / Riemannian Manifolds / Submanifolds / Complex Manifolds / Bibliography / Index.
ISBN: 978-1-84265-366-1
Publication Year: December 2007
Pages: 400
Binding: Hard Back
Dimension: 185mm x 240mm
Textbook
About the book
Differential Equations for Scientists and Engineers mainly deals with linear equations, with non-linear equations very briefly discussed in the chapter on ordinary differential equations and towards the end of a chapter on some theoretical considerations. The book concentrates on the so called analytical or exact solutions of the equations. However, a chapter on semi-analytical treatment, for example, using variational and other methods is also included. Throughout the book the emphasis is on applications and development of the solution techniques. Therefore, the theory aspects regarding the existence and uniqueness of solutions and the conditions under which these are satisfied are not covered in the book. However, at some places brief mention is made of these and short proofs are offered whenever possible, without disturbing the flow of the text.
Key Features
Large Number of Solved Examples to Illustrate Solution Methods Number of Problems in the Exercises at the End of Each Chapter
Table of content
Ordinary Differential Equations / Partial Differential Equations of First Order / Partial Differential Equations of Second Order and Classification of Equations / Concepts in the Series Solutions to Boundary Value Problems using Basis Functions / Fourier Series, Brief Theory and Applications / Hyperbolic Equation (Wave Equation) / Elliptic Equation (Laplace’s Equation) / Parabolic Equation (Heat Equation) / Fourier and Other Transforms, Applications to Infinite Medium / Variational Method and Methods of Weighted Residuals for the Approximate Solution of Partial Differential Equations / Applications of Semi-Analytical Methods to the Approximate Solution of Partial Differential Equations / Non-linear Equations, Some Theoretical Considerations.
ISBN: 978-1-84265-374-6
Publication Year: 2007
Pages: 268
Binding: Hard Back
Dimension: 185mm x 240mm
Weight: 720
About the book
Survey Sampling reviews aspects of statistical inference in finite population sampling. After reviewing important results in fixed population models, the book considers in detail the model-dependent optimal strategies of Royall and Herson (1973) and the robustification of these strategies under model breakdown. It then reviews model assist strategies of Cassel, Sarndal and Wretman (1976) and Wright (1983). Asymptotic properties of these strategies are also reviewed. Another approach is design-based calibration of Deville and Sarndal (1992). Design-based conditional inference is an alternative approach which has drawn considerable attention to survey statisticians. Lastly the book reviews two important tools of making inference,-Model Calibration approach and Empirical Likelihood based approach. Post-stratification is another aspect which requires considerable attention.
Table of content
Preface / The Preliminaries / Some Inferential Problems under Fixed Population Set-up / Model-Dependent Optimal Strategies / Robustness of Model-Dependent Optimal Strategies / Model-Assisted Sampling Strategies / Asymptotically Optimum Sampling Strategies / Robust Strategies / Design-Based Conditional Approach / The Design-Based Calibration Approach / Model Based Calibration Approach / Empirical Likelihood Approach / Referenced / Author Index / Subject Index.
ISBN: 978-1-84265-361-6
Publication Year: 2007
Pages: 290
Binding: Hard Back
Dimension: 160mm x 240mm
Weight: 625
Textbook
About the book
Theory of Numbers: A Textbook is aimed at students of Mathematics who are graduates or even undergraduates. Very little prerequisites are needed. The reader is expected to know the theory of functions of a real variable and in some chapters complex integration and some simple principles of complex function theory are assumed. The entire book is self contained except theorems 7 and 9 of chapter 11 which are assumed. The most ambitious chapter is chapter 11 where the most attractive result on difference between consecutive primes is proved. References to the latest developments like Heath-Brown’s work and the work of R.C. Baker, G. Harman and J. Pintz alongwith readable accounts of Brun’s sieve and also of Apery’s Theorem on irrationality of zeta (3) are given. Finally the reader is acquainted with Montgomery-Vaughan Theorem in the last chapter. It is hoped that the reader will enjoy the leisurely style of presentation of many important results.
Table of content
Preface / Introduction and Reference Books and Articles / Elementary Estimates for p(x) and Allied Functions / Simple W Results Based on Simple Properties of z(s) / Landau’s Theorem on the Singularity of Dirichlet Series with Positive Coefficients / Roth’s Theorem on Square ? Free Integers / Landau-Ramanujan-Ingham-Wiener-Ikehara Approach to the Prime Number Theorem / Elementary Results of Chebyshev and the Advanced Prime Number Theorems of Hadamard and de la Vallee Poussin / A Theorem of Tijdeman (also Erdo2 s , Jutila, Ramachandra and Shorey) / Infinitely many zeros of z(s) in s 3 ? ? d / Infinity of zeros of z(s) in s 3 ? / Some Properties of G(s) and the order of z(s) in s ￡ 0 / Difference Between Consecutive Primes / Miscellaneous Results / Brun’s Sieve / Roth’s Theorem and Szemeredi’s Theorem / Erdo2 s Szemeredi Sieve / Irrationality of z(3) / A Remark on S. Srinivasan’s Theorem / Montgomery-Vaughan Theorem / Index.
ISBN: 978-1-84265-388-3
Publication Year: July 2007
Pages: 468
Binding: Hard Back
Dimension: 185mm x 240mm
Weight: 950
About the book
Bayesian Parametric Inference provides a systematic exposition and discusses in detail the conjugate and noninformative prior distributions, predictive distributions and their applications to problems of inventory control, finite populations, structural change in the model and control problems. Information theoretic approach to construct maximal data information prior and maximum entropy priors is also discussed. Bayesian decision theoretic approach is followed to obtain Bayes estimates under various loss functions. The concept of Bayes Factor for comparing hypotheses is explained with the help of some simple but illustrative examples.
Key Features
・ More than 300 Solved Examples ・ 250 Unsolved Exercises ・ 350 Remarks ・ Glossary of Bayesian Terms ・ Exhaustive List of References
Table of content
Foreword / Preface / Probability, Random Variables and their Probability Distributions / Some Special Distributions / Bayes Theorem / Conjugate Prior Distribution / Non-Informative Priors / Bayes Estimation / Hypothesis Testing / Predictive Inference / Bayesian Inference for the Linear Model / Large Sample Approximations / Other Topics / Question Bank / Glossary / Tables / Bibliography / Index.