Copyright Year 2023
ISBN 9781032302461
March 14, 2023 Forthcoming
288 Pages 31 B/W Illustrations
Courses on linear algebra and numerical analysis need each other. Often NA courses have some linear algebra topics, and LA courses mention some topics from numerical analysis/scientific computing. This text merges these two areas into one introductory undergraduate course. It assumes students have had multivariable calculus. A second goal of this text is to demonstrate the intimate relationship of linear algebra to applications/computations.
A rigorous presentation has been maintained. A third reason for writing this text is to present, in the first half of the course, the very important topic on singular value decomposition, SVD. This is done by first restricting consideration to real matrices and vector spaces. The general inner product vector spaces are considered starting in the middle of the text.
The text has a number of applications. These are to motivate the student to study the linear algebra topics. Also, the text has a number of computations. MATLAB, is used, but one could modify these codes to other programming languages. These are either to simplify some linear algebra computation, or to model a particular application.
Preface
Introduction
1. Solution of AX = d
2. Matrix Factorizations
3. Least Squares and Normal Equations
4. Ax = d with m<n
5. Orthogonal Subspaces and Bases
6. Eigenvectors and Orthonormal Basis
7. Singular Value Decomposition
8. Three Applications of SVD
9. Pseudoinverse of A
10. General Inner Product Vector Spaces
11. Iterative Methods
12. Nonlinear Problems and Least Squares
Bibliography
Index
Robert E. White is Professor Emeritus, North Carolina State University. He is also the author of Computational Mathematics: Models, Methods, Analysis with MATLABR and MPI, second edition and Elements of Matrix Modeling and Computing with MATLABR, both published by CRC Press.
Copyright Year 2023
ISBN 9781032356860
April 28, 2023 Forthcoming by CRC Press
400 Pages 172 B/W Illustrations
The art of applying mathematics to real world dynamical problems such as structural dynamics, fluid dynamics, wave dynamics, robot dynamics, etc., can be extremely challenging. Various aspects of mathematical modelling that may include deterministic or uncertain (fuzzy, interval, or stochastic) scenarios, along with integer or fractional order, are vital to understanding these dynamical systems. Mathematical Methods in Dynamical Systems offers problem solving techniques and includes different analytical, semi-analytical, numerical and machine intelligence methods for finding exact and/or approximate solutions of governing equations arising in dynamical systems. It provides a singular source of computationally efficient methods to investigate these systems, and includes coverage of various industrial applications in a simple yet comprehensive way.
1. Dynamical Problems for Generally Anisotropic Shells With the GDQ Method. Francesco Tornabene, Matteo Viscoti, Rossana Dimitri 2. Dynamical Problems of Functionally Graded Non-Uniform Nanoplates under Thermal Field. Rahul Saini 3. Effect of External Resistances on Energy Harvesting Behaviour of Porous Functionally Graded Magneto-Electro-Elastic Beam. Arjun Siddharth, Vinyas Mahesh, Vishwas Mahesh, Sriram Mukunda, Sathiskumar A Ponnusami, Dineshkumar Harursampath 4. Mass Resonator Sensor and Its Inverse Problems. Yin Zhang 5. Axial Wave Propagation of Carbon Nanorod Conveying Fluid with Elastic Support using Nonlocal Continuum Elasticity. V. Senthilkumar 6. Differential Transformation and Adomian Decomposition Methods for the Radiation Effect on Marangoni Boundary Layer Flow of Carbon Nanotubes. P.K. Ratha, R.S. Tripathy, S.R. Mishra 7. Min-Max Game Theory for Coupled Partial Differential Equation Systems in Fluid Structure. S. M. Chithra 8. Numerical Simulation for Time Fractional Integro Partial Differential Equations Arising in Viscoelastic Dynamical System. J. Mohapatra, S. Santra 9. From Continuous Time Random Walk Models to Human Decision-Making Modeling: A Fractional Perspective. Amir Hosein Hadian Rasanan, Mohammad Mahdi Moayeri, Jamal Amani Rad, Kourosh Parand 10. Dynamics of Slender Single-Link Flexible Robotic Manipulator Based on Timoshenko Beam Theory. Priya Rao, S. Chakraverty, Debanik Roy 11. Non-Probabilistic Solution of Imprecisely Defined Structural Problem with Beams and Trusses using Interval Finite Element Methods. Sukanta Nayak, Shravani V Shetgaonkar 12. Linear Eigenvalue Problems in Dynamic Structure With Uncertainty: An Expectation Based Approach. Mrutyunjaya Sahoo, S. Chakraverty 13. Dynamical Approach to Forecast Decentralized Currency Exchange Value with Respect to Indian National Rupees. Bhubaneswari Mishra, S. Chakraverty, Rohtas Kumar 14. Curriculum Learning-Based Approach to Design an Unsupervised Neural Model for Solving Emden?Fowler Type Equations of the Third-Order. Arup Kumar Sahoo, S. Chakraverty
Hardcover
728 pp., 8 x 9 in, 150 figures
9780262047296
Published: December 6, 2022
An introduction to game theory that offers not only theoretical tools but also the intuition and behavioral insights to apply these tools to real-world situations.
This introductory text on game theory provides students with both the theoretical tools to analyze situations through the logic of game theory and the intuition and behavioral insights to apply these tools to real-world situations. It is unique among game theory texts in offering a clear, formal introduction to standard game theory while incorporating evidence from experimental data and introducing recent behavioral models. Students will not only learn about incentives, how to represent situations as games, and what agents gshouldh do in these situations, but they will also be presented with evidence that either confirms the theoretical assumptions or suggests a way in which the theory might be updated.
Each chapter begins with a motivating example that can be run as an experiment and ends with a discussion of the behavior in the example. Parts I?IV cover the fundamental gnuts and boltsh of any introductory game theory course, including the theory of games, simple games with simultaneous decision making by players, sequential move games, and incomplete information in simultaneous and sequential move games. Parts V?VII apply the tools developed in previous sections to bargaining, cooperative game theory, market design, social dilemmas, and social choice and voting, while part VIII offers a more in-depth discussion of behavioral game theory models including evolutionary and psychological game theory. A website offers solutions to end-of-chapter exercises, a manual for running each chapter's experimental games using pencil and paper, and the oTree codes for running the games online.
Oxford Logic Guides
Hardback
Published: 21 March 2023 (Estimated)
528 Pages
234x156mm
ISBN: 9780192867964
A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are algorithmically solvable for restricted subsets?-or, as we say, fragments?-of first-order logic, a fact which is today of considerable interest in Computer Science. This book provides an up-to-date survey of the principal axes of research, charting the limits of decision in first-order logic and exploring the trade-off between expressive power and complexity of reasoning.
Preface
Acknowledgements
1:Introduction
Part I: Syntactic Restrictions
2:Roots
3:Variables
4:Guards
5:Prefixes
6:Fluting
Part II: Counting Quantifiers
7:Counting with one variable
8:Counting with two variables
9:Guarded counting
10:Omitting graphs
Part III: Semantic Constraints
11:Modalities
12:Equivalence
13:Equivalence and counting
14:Transitivity
15:Trees
Oxford Graduate Texts in Mathematics
Hardback
Published: 30 January 2023 (Estimated)
528 Pages
234x156mm
ISBN: 9780192863867
Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.
The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.
1:Hilbert Spaces
2:Diagonal Operators
3:Infinite Matrices
4:Two Multiplication Operators
5:The Unilateral Shift
6:The Cesaro Operator
7:The Volterra Operator
8:Multiplication Operators
9:The Dirichlet Shift
10:The Bergman Shift
11:The Fourier Transform
12:The Hilbert Transform
13:Bishop Operators
14:Operator Matrices
15:Constructions with the Shift Operator
16:Toeplitz Operators
17:Hankel Operators
18:Composition Operators
19:Subnormal Operators
20:The Compressed Shift