Paperback ISBN: 9780128167984
Published Date: 1st January 2019
Page Count: 328
series: Mathematics in Science and Engineering
Expected Release date: January 1, 2019
1. Reduced-Order Extrapolation Finite Difference Schemes Based on Proper Orthogonal Decomposition
2. Reduced-Order Extrapolation Finite Element Methods Based on Proper Orthogonal Decomposition
3. Reduced-Order Extrapolation Finite Volume Element Methods Based on Proper Orthogonal Decomposition
4. Epilogue and Outlook
Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems.
Key Features
Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns
Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics
Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types
Readership
Graduate students and researchers in mathematically intensive environments who perform large scale computations
Hardcover ISBN: 9780128143469
Imprint: Academic Press
Published Date: 1st March 2019
Page Count: 700
Introduction to Probability Models, Twelfth Edition is the latest version of Sheldon Ross's classic bestseller. This trusted book introduces the reader to elementary probability modelling and stochastic processes and shows how probability theory can be applied in fields such as engineering, computer science, management science, the physical and social sciences and operations research. The hallmark features of this text have been retained in this edition, including a superior writing style and excellent exercises and examples covering the wide breadth of coverage of probability topics. In addition, many real-world applications in engineering, science, business and economics are included.
Retains the valuable organization and trusted coverage that students and professors have relied on since 1972
Includes new coverage on Coupling methods, Martingales, continuous time Markov chains, and a new derivation of Poisson Process
Offers updated examples and exercises throughout, along with required material for Exam 3 of the Society of Actuaries
UG/Grad Students in the Probability Modelling course
Introduction to Probability Theory
2. Random Variables
3. Conditional Probability and Conditional Expectation
4. Markov Chains
5. The Exponential Distribution and the Poisson Process
6. Continuous-Time Markov Chains
7. Renewal Theory and Its Applications
8. Queueing Theory
9. Reliability Theory
10. Brownian Motion and Stationary Processes
11. Simulation
Solutions to Starred Exercises
Part of Institute of Mathematical Statistics Textbooks
Product details
Publication planned for: March 2019
format: Hardback
isbn: 9781316510087
format: Paperback
isbn: 9781316649466
Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Ito calculus, the central theorems in the field, and such approximation schemes as stochastic Runge?Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods.
1. Introduction
2. Some background on ordinary differential equations
3. Pragmatic introduction to stochastic differential equations
4. Ito calculus and stochastic differential equations
5. Probability distributions and statistics of SDEs
6. Statistics of linear stochastic differential equations
7. Useful theorems and formulas for SDEs
8. Numerical simulation of SDEs
9. Approximation of nonlinear SDEs
10. Filtering and smoothing theory
11. Parameter estimation in SDE models
12. Stochastic differential equations in machine learning
13. Epilogue.
Part of Cambridge Monographs on Mathematical Physics
Publication planned for: April 2019
availability: Not yet published - available from April 2019
format: Hardback
isbn: 9781108429856
Many areas of continuum physics pose a challenge to physicists. What are the most general, admissible statistically homogeneous and isotropic tensor-valued random fields (TRFs)? Previously, only the TRFs of rank 0 were completely described. This book assembles a complete description of such fields in terms of one- and two-point correlation functions for tensors of ranks 1 through 4. Working from the standpoint of invariance of physical laws with respect to the choice of a coordinate system, spatial domain representations, as well as their wavenumber domain counterparts are rigorously given in full detail. The book also discusses, an introduction to a range of continuum theories requiring TRFs, an introduction to mathematical theories necessary for the description of homogeneous and isotropic TRFs, and a range of applications including a strategy for simulation of TRFs, ergodic TRFs, scaling laws of stochastic constitutive responses, and applications to stochastic partial differential equations. It is invaluable for mathematicians looking to solve problems of continuum physics, and for physicists aiming to enrich their knowledge of the relevant mathematical tools.
Introduction
1. Introduction to continuum theories
2. Mathematical preliminaries
3. Mathematical results
4. Tensor random fields in continuum theories
References
Index.
Hardback
October 23, 2018 Forthcoming
Reference - 406 Pages - 32 B/W Illustrations
ISBN 9781138345430
Series: Chapman & Hall/CRC Research Notes in Mathematics Series
Can serve as a text for a capstone course in applied mathematics for advanced undergraduate and beginning graduate students
Both regular and singular problems are treated with a high level of rigor and an emphasis on the types of problems that actually arise in mathematical modelling
Develops and uses shooting methods to calculate eigenvalues and eigenfunctions of both regular and singular Sturm-Liouville problems
Sturm-Liouville problems arise naturally in solving technical problems in engineering, physics, and more recently in biology and the social sciences. These problems lead to eigenvalue problems for ordinary and partial differential equations. Sturm-Liouville Problems: Theory and Numerical Implementation addresses, in a unified way, the key issues that must be faced in science and engineering applications when separation of variables, variational methods, or other considerations lead to Sturm-Liouville eigenvalue problems and boundary value problems.
Preface
1 Setting the Stage
2 Preliminaries
3 Integral Equations
4 Regular Sturm-Liouville Problems
5 Singular Sturm-Liouville Problems - I
6 Singular Sturm-Liouville Problems ? II
7 Approximation of Eigenvalues and Eigenfunctions
8 Concluding Examples and Observations
A Mildly Singular Compound Kernels
B Iteration of Mildly Singular Kernels
C The Kellogg Conditions