KEY SELLING POINTS
Excellent post-graduate textbook
Material drawn from 25 years teaching experience
BOOK INFORMATION
ISBN: 9781905740543
Pub Date: April 2007
Format: Hardback
Extent: 190 pages
This book is intended to suit mathematics courses for post-graduate students. It has been written by an author with 25 years experience of lectures on differential geometry, and is therefore designed to help the reader overcome the difficulties in understanding the underlying concepts of the subject. The book will also be useful for introducing the methodology of differential geometry to research students in associated disciplines; physics, engineering, biosciences and economics.
The book is divided into 5 chapters ? curvilinear co-ordinates, geometry of space curves, intrinsic geometry of a surface, fundamental formulae of a surface, curves on a surface ? and each chapter contains numerous examples which are either worked out or given as an exercise in order to facilitate understanding. Finally the book concludes with a brief history of differential geometry. This book is an excellent text for post-graduate maths courses, and will also be of interest to all mathematicians.
Contents:
1. CURVILINEAR COORDINATES
1.1 Curvilinear Coordinate System in E3 1.2 Elementary Arc Length 1.3 Length of a Vector 1.4 Angle between Two Non-null Vectors 1.5 Reciprocal Base System 1.6 On the Meaning of Covariant Derivatives 1.7 Intrinsic Differentiation 1.8 Parallel Vector Fields
2. GEOMETRY OF SPACE CURVES
2.1 Serret-Frenet Formulae 2.2 Equation of a Straight Line in Curvilinear Coordinate system 2.3 Some Results on Curvature and Torsion. How to Find out Curvature and Torsion of Space Curves 2.4 Helix
3. INTRINSIC GEOMETRY OF A SURFACE
3.1 Curvilinear Coordinates of a Surface 3.2 The Element of Length and the Metric Tensor 3.3 The First Fundamental Form 3.4 Directions on a Surface. Angle between Two Directions 3.5 Geodesic and its Equations 3.6 Parallelism with respect to a Surface 3.7 Intrinsic and Covariant Differentiation of Surface Tensors 3.8 The Riemann-Christoffel Tensor. The Gaussian Curvature of a Surface 3.9 The Geodesic Curvature of a Curve on a Surface
4. THE FUNDAMENTAL FORMULAE OF A SURFACE
4.1 The Tangent Vector to a Surface 4.2 The Normal Vector to a Surface 4.3 The Tensor Derivation of Tensors 4.4 Gauss’s Formulae: The second Fundamental Form of a Surface 4.5 Weingarten’s Formulae: The Third Fundamental Form of a Surface 4.5 The Equations of Gauss and Codazzi
5. CURVES ON A SURFACE
5.1 The Equations of a Curve on a Surface 5.2 Meusnier’s Theorem 5.3 The principal curvatures 5.4 The Lines of Curvature 5.5 The Asymptotic Lines. Enneper’s Formula 5.6 The Geodesic Torsion of a Curve on a Surface
KEY SELLING POINTS
Real world applications for mathematical theory
Prestigious international editors of proven pedigree
Relevant to all mathematicians ? academic or professional
BOOK INFORMATION
ISBN: 9781904798644
Pub Date: April 2007
Format: hardback
Extent: 480 pages
This is presentation of the diverse uses and applications of contemporary mathematics in real world systems. Distinguished international scholars have contributed a total of twenty chapters discussing practical applications of mathematical theory across a range of disciplines, from financial markets to DNA sequencing from meteorology to economics in agriculture.
This book will be a boon to advanced mathematicians, whether academic or professional, who are looking for real world applications for their theories. It is an outstanding collection of articles on mathematics for the new millennium.
Contents:
What Can We Learn from the Analysis of Scale Invariance and Long-range Correlation Properties of DNA Sequences Using Wavelet Techniques? * Optimal Input Signal Design in Data-Centric System Identification * Wavelet Approximation of Safing Sensor Model * Giga-Periodic Orbits for Weakly Coupled Tent and Logistic Discretized Maps * Usual Mathematical Tools Updated for a Variety of Complexities and Purposes: Development and Adaptation * Non-Linear Stability in the Perturbed Photogravitational Restricted Three Body Problem * Mathematical Modelling of Progressive Collapse of Thin Tubes and Frusta * Rotational Motion of a Satellite Under the Influence of Aerodynamic or Magnetic-Torque * Recent Developments in Frame Theory * The Wavelet, Directional Wavelet, and Ridgelet Transforms with Applications in Texture Identification * Wavelet Based Multifractal Analysis of Indian Rainfall Data * A Direct Method for Solving Variational Problems Using Walsh Wavelet Packets and Error Estimates * Generalized Implicit Vector Quasi-Variational Inequalities with Applications * Best Approximation Operator and Fixed Points of Multivalued Mappings * Characterization of Lebesgue Spaces Lp (R) Using Wavelet Packets * Wavelet-Based Multifractal Formalism in Exploration Geophysics * Optimizing Observations and Regions for Effective Rainfall Studies * The Explicit Solutions of BBGKY Chain of Quantum Kinetic Equations * Design Optimization of Structural Topology and Shape: State-of-the-art and Recent Advancements * Combining Direct and Iterative Methods for the solution of Large Systems in Different Application Areas * Block Krylov Space Methods for Linear Systems with Multiple Right-Hand Sides: An Introduction * Numerical Experiments with Toeplitz Matrix Approximation Methods * A New Iterative Scheme for Strongly Nonlinear Variational-Like Inclusions * Mathematical Model for Navier Stokes Equation in Stream Function-Vorticity Form Using Finite Difference Method.
KEY SELLING POINTS
Latest information on Key discipline.
Both theory and practical applications.
International contributors
BOOK INFORMATION
ISBN: 978190574000
Pub Date: April 2007
Format: Hardback
Extent: 508 pages
In the last two decades, Bayesian Statistics has acquired immense importance and has penetrated almost every area including those where the application of statistics appeared to be a remote possibility. This volume provides both theoretical and practical insights into the subject with detailed up-to-date material on various aspects. It serves two important objectives ? to offer a thorough background material for theoreticians and gives a variety of applications for applied statisticians and practitioners.
Consisting of 33 chapters it covers topics on biostatistics, econometrics, reliability, image analysis, Bayesian computation, neural networks, prior elicitation, objective Bayesian methodologies, role of randomisation in Bayesian analysis, spatial data analysis, nonparametrics and a lot more.
The book will serve as an excellent reference work for updating knowledge and for developing new methodologies in a wide variety of areas. It will become an invaluable tool for statisticians and the practitioners of Bayesian paradigm.
Contents: Two-fold Spatial Zero-inflated Models for Analysing Isopod Settlement Patterns * Prior Model for Reconstruction of Contingency Table * Bayesian Estimation for the Key Parameters of a Fish Population * Why Bayesianism? A Primer on a Probabilistic Philosophy of Science * Coregionalized Models for Spatially Replicated Experiments in Weed Proliferation Studies * Bayes Factors for One Sided Hypothesis Testing in Linear Calibration * Bayesian Hierarchical Spatio-Temporal Analysis of fMRI Data: A Case Study * Intrinsic Point Estimation of the Normal Variance * Analysing Financial Data Using Polya Trees * Shape Classification Procedures with Application to Schizophrenia Diagnosis * Checking for Pro-Data Conflict with Hierarchically Specified Priors * Bayesian Cross-Sectional Analysis of the Conditional Distribution of Earnings of Men in the USA (1967-1996) * Role of Randomization in Bayesian Analysis: An expository Overview * Bayesian Neural Nets for Survival Analysis * Semiparametric Accelerated Failure Time Models for Censored Data * Sequential Monte Carlo in Bayesian Inference for Dynamic Models: An Overview * Estimation of Threshold Time Series Models Using Efficient Jump MCMC * A Semiparametric Accelerated Failure Time Model for Survival Data with Time Dependent Covariates * Biological Monitoring: A Bayesian Model for Multivariate Compositional Data * Semiparametric Multivariate Survival Models with Random Effects * Modelling Rainfall Data Using a Bayesian Kriged-Kalman Model * A Line Finding Assignment Problem and Rock Fracture Modelling * On Bayesian Models Incorporating Covariates in Reliability Analysis of Repairable Systems * Semi-Parametric Bayesian Models for Population Pharmacokinetics and Pharmacodynamics * Bayesian Predictive Inference Under Informative Sampling via Surrogate Samples * Research in Elicitation * On a Characterization of Dirichlet Distribution * Simpler Calculation of Posterior Distributions of the Parameters in Structural Equation Model * Nonparametric Empirical Bayes Two-Tail Tests for Scale Exponential Family When Random Variables in the Sequence are Negatively Associated * Bayesian Methods in Educational Measurement * A Bayes Analysis of the Birnbaum-Saunders Distribution Using the Gibbs Sampler Approach * Bayesian Approaches to Content-based Image Retrieval * Theoretical and Applied Bayesian Information Processing
KEY SELLING POINTS
Will appeal to all pure mathematicians
Suitable for graduate and post graduate courses
BOOK INFORMATION
ISBN: 9781904798637
Pub Date: July 2007
Format: paperback
Extent: 176 pages
This book provides a gateway into the difficult two fields of algebraic geometry and commutative algebra. Algebraic geometry is in essence the study of the solution of equations. It is the backbone of the discipline of pure mathematics. Commutative algebra is a fundamental part of algebraic geometry, and is the study of commutative rings.
The authors have made a selection from the wealth of material in the discipline and have written concise, clear definitions and synopses.
The book will prove to be an ideal introductory text for graduate courses in pure mathematics involving algebraic geometry and algebraic number theory.
Contents:
Finitely generated algebras * The K-spectrum and the Zariski topology * Prime spectra and dimension * Schemes * Projective schemes * Regular, normal, smooth points * Reimann-Roch theorem