Copyright Year 2023
ISBN 9781032185224
August 8, 2022 Forthcoming by Chapman and Hall/CRC
312 Pages 41 B/W Illustrations
This book is an invaluable resource for applied researchers to find the analytical solution of differential equations describing the dynamical system with less computational effort and time. It describes the basic concepts of the differential transform method and solution of various real-world problems described by simple to complicated differential equations. It provides a computational technique that is not only conceptually simple and easy to use but also readily adaptable for computer coding. Different chapters of the book deal with the basic differential equations involved in the physical phenomena as well as a complicated system of differential equations described by the mathematical model.
The book offers comprehensive coverage of the most essential topics, including
Basic concepts and fundamental properties of the proposed technique with proof
The solution of linear, nonlinear, homogeneous, and nonhomogeneous ordinary differential equations (ODEs) and partial differential equations (PDEs)
The initial and boundary value problems
Real-world ODE and PDE problems are also discussed
Applications of Differential Transform to Real World Problems is primarily aimed at undergraduates, graduates, and researchers studying differential equations. Scientists dealing with complicated differential equations or systems of differential equations will also find this book useful.
1. One Dimensional Differential Transformation Method. 2. Application of One Dimensional Differential Transform Method to Solve Real World Problems. 3. Solution of System of Differential Equation by Differential Transformation Method. 4. Coupled System of ODE based Real World Problems and their Solution by DTM. 5. Two Dimensional Differential Transformation Method. 6. Application of Differential Transformation Method to System of Partial Differential Equation. 7. Solution of Well known PDE Describing Transport Phenomena by Differential Transformation Method. 8. Compartment Model of Reaction Diffusion Mechanism InCell42 and their so- lution by DTM. 9. Application of DTM to solve PDE based real world problems. 10. Analytical Solution by DTM and their Convergence.
ISBN 9780367030377
August 5, 2022 Forthcoming by Chapman and Hall/CRC
296 Pages 53 B/W Illustrations
Survival analysis generally deals with analysis of data arising from clinical trials. Censoring, truncation, and missing data create analytical challenges and the statistical methods and inference require novel and different approaches for analysis. Statistical properties, essentially asymptotic ones, of the estimators and tests are aptly handled in the counting process framework which is drawn from the larger arm of stochastic calculus. With explosion of data generation during the past two decades, survival data has also enlarged assuming a gigantic size. Most statistical methods developed before the millennium were based on a linear approach even in the face of complex nature of survival data. Nonparametric nonlinear methods are best envisaged in the Machine Learning school. This book attempts to cover all these aspects in a concise way.
Survival Analysis offers an integrated blend of statistical methods and machine learning useful in analysis of survival data. The purpose of the offering is to give an exposure to the machine learning trends for lifetime data analysis.
Classical survival analysis techniques for estimating statistical functional and hypotheses testing
Regression methods covering the popular Cox relative risk regression model, Aalen’s additive hazards model, etc.
Information criteria to facilitate model selection including Akaike, Bayes, and Focused
Penalized methods consisting of , , and elastic net
Survival trees and ensemble techniques of bagging, boosting, and random survival forests
A brief exposure of neural networks for survival data
R program illustration throughout the book
I Classical Survival Analysis. 1. Lifetime Data and Concepts. 2 Core Concepts. 3. Inference - Estimation. 4. Inference - Statistical Tests. 5. Regression Models. 6. Further Topics in Regression Models. 7. Model Selection.
II Machine Learning Methods. Why Machine Learning? 8. Survival Trees. 9. Ensemble Survival Analysis. 10. Neural Network Survival Analysis. 11. Complementary Machine Learning Techniques. Bibliography. Index.
ISBN 9781032073163
August 19, 2022 Forthcoming by Chapman and Hall/CRC
208 Pages
Partial Differential Equations: Topics in Fourier Analysis, Second Edition explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models. It shows how this powerful approach is valuable in getting plausible answers that can then be justified by modern analysis.
Using Fourier analysis, the text constructs explicit formulas for solving PDEs governed by canonical operators related to the Laplacian on the Euclidean space. After presenting background material, it focuses on: Second-order equations governed by the Laplacian on Rn; the Hermite operator and corresponding equation; and the sub-Laplacian on the Heisenberg group
Designed for a one-semester course, this text provides a bridge between the standard PDE course for undergraduate students in science and engineering and the PDE course for graduate students in mathematics who are pursuing a research career in analysis. Through its coverage of fundamental examples of PDEs, the book prepares students for studying more advanced topics such as pseudo-differential operators. It also helps them appreciate PDEs as beautiful structures in analysis, rather than a bunch of isolated ad-hoc techniques.
Three brand new chapters covering several topics in analysis not explored in the first edition
Complete revision of the text to correct errors, remove redundancies, and update outdated material
Expanded references and bibliography
New and revised exercises.
1. The Multi-Index Notation. 2. The Gamma Function. 3. Convolutions. 4. Fourier Transforms. 5. Tempered Distributions. 6. The Heat Kernel. 7. The Free Propagator. 8. The Newtonian Potential. 9. The Bessel Potential. 10. Global Hypoellipticity in the Schwartz Space. 11. The Poisson Kernel. 12. The Bessel?Poisson Kernel. 13. Wave Kernels. 14. The Heat Kernel of the Hermite Operator. 15. The Green Function of the Hermite Operator. 16. Global Regularity of the Hermite Operator. 17. The Heisenberg Group. 18. The Sub-Laplacian and the Twisted Laplacians. 19. Convolutions on the Heisenberg Group. 20. Wigner Transforms and Weyl Transforms. 21. Spectral Analysis of Twisted Laplacians. 22. Heat Kernels Related to the Heisenberg Group. 23. Green Functions Related to the Heisenberg Group. 24. Theta Functions and the Riemann Zeta-Function. 25. The Twisted Bi-Laplacian. 26. Complex Powers of the Twisted Bi-Laplacian. Bibliography. Index.
ISBN: 978-1-119-80268-6 January 2022 640 Pages
Elementary Differential Equations and Boundary Value Problems, 12th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. In this revision, new author Douglas Meade focuses on developing students conceptual understanding with new concept questions and worksheets for each chapter. Meade builds upon Boyce and DiPrima’s work to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal two or three semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Concept Checks have been added to every end of chapter question sets. Concept Check were designed to reinforce key chapter learning objectives and prepare students for the end-of-chapter problems.
Worksheets were developed as a lecture aid to teach class in a synchronous in-person, online or hybrid environment. Worksheets were designed to help students follow the presentation and discussion of topics in each section. When completed the students should have a good set of notes with examples for that section.
An updated design provides an easy to navigate, student friendly reference.
Published: 15 August 2022 (Estimated)
576 Pages
234x156mm
Hardback ISBN: 9780192849540
Paperback ISBN: 9780192849557
Covers a wide range of topics, starting from undergraduate modern analysis and progressing gradually to advanced graduate-level topics
Includes numerous exercises, which cover some important results beyond what is provided in the main text
New to this Edition:
Devotes several new chapters to operator algebras, a central area in functional analysis
Includes several other advanced topics such as Von Neumann algebras, tensor products of C*-algebras, and group C*-algebras
Contains many new exercises
This textbook provides an introduction to modern analysis aimed at advanced undergraduate and graduate-level students of mathematics. Professional academics will also find this to be a useful reference work. It covers measure theory, basic functional analysis, single operator theory, spectral theory of bounded and unbounded operators, semigroups of operators, and Banach algebras. Further, this new edition of the textbook also delves deeper into C*-algebras and their standard constructions, von Neumann algebras, probability and mathematical statistics, and partial differential equations.
Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills.
1:Measures
2:Construction of measures
3:Measure and topology
4:Continuous linear functionals
5:Duality
6:Bounded operators
7:Banach algebras
8:Hilbert spaces
9:Integral representation
10:Unbounded operators
11:C*-algebras
12:Von Neumann algebras
13:Constructions of C*-algebras
Application I
Probability
Application II
Distributions