Language: English
Paperback ISBN: 9780443134760
- August 1, 2025
Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who havenft taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation.
Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.
1. Matrices
2. Linear equations
3. Subspaces
4. Determinants
5. Eigenvalues and eigenvectors
6. Orthogonal vectors and matrices
7. Vector and matrix norms
8. Floating point arithmetic
9. Algorithms
10. Conditioning of problems and stability of algorithms
11. Gaussian elimination and the LU decomposition
12. Linear system applications
13. Important special systems
14. Gram-Schmidt decomposition
15. The singular value decomposition
16. Least-squares problems
17. Implementing the QR factorization
18. The algebraic eigenvalue problem
19. The symmetric eigenvalue problem
20. Basic iterative methods
21. Krylov subspace methods
22. Large sparse eigenvalue problems
23. Computing the singular value decomposition
Part of New Mathematical Monographs
Not yet published - available from April 2025
format: Hardbackisbn: 9781009554220
Hardback
This text examines Markov chains whose drift tends to zero at infinity, a topic sometimes labelled as 'Lamperti's problem'. It can be considered a subcategory of random walks, which are helpful in studying stochastic models like branching processes and queueing systems. Drawing on Doob's h-transform and other tools, the authors present novel results and techniques, including a change-of-measure technique for near-critical Markov chains. The final chapter presents a range of applications where these special types of Markov chains occur naturally, featuring a new risk process with surplus-dependent premium rate. This will be a valuable resource for researchers and graduate students working in probability theory and stochastic processes.
Includes many novel elements and much of the material presents original research
Builds on the classical topic of asymptotic analysis and classification of Markov chains
Offers a high-precision alternative to classical Lyapunov functions
1. Introduction
2. Lyapunov functions and classification of Markov chains
3. Down-crossing probabilities for transient Markov chain
4. Limit theorems for transient and null-recurrent Markov chains with drift proportional to 1/x
5. Limit theorems for transient Markov chains with drift decreasing slower than 1/x
6. Asymptotics for renewal measure for transient Markov chain via martingale approach
7. Doob's h-transform: transition from recurrent to transient chain and vice versa
8. Tail analysis for recurrent Markov chains with drift proportional to 1/x
9. Tail analysis for positive recurrent Markov chains with drift going to zero slower than 1/x
10. Markov chains with asymptotically non-zero drift in Cramer's case
11. Applications
Publication planned for: July 2025
Not yet published - available from July 2025
format: Paperback isbn: 9781009610025
Paperback
This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular Sturm?Liouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra and geometry in the study of differential equations. It provides sufficient theoretical material at the beginning of each chapter, which will enable students to better understand the concepts and begin solving problems straightaway.
Chapter-wise exercises with solutions
Includes problems from traditional topics as well as from control theory and kinematics
Includes the local version of potential theory and Widder's uniqueness result of positive solutions of the heat equation
Includes a coverage of multiple characteristics problems for hyperbolic equations and systems
Acknowledgements
Preface
List of illustrations
PART I. ORDINARY DIFFERENTIAL EQUATIONS:
1. First and Second Order ODE
2. Linear Systems
3. Series Solutions: Frobenius Theory
4. Regular Sturm-Liouville Theory and Boundary Value Problems
5. Qualitative Theory
PART II. PARTIAL DIFFERENTIAL EQUATIONS:
6. First Order Partial Differential Equations
7. Classification of Partial Differential Equations
8. Laplace and Poisson Equations
9. Heat Equation
10. One Dimensional Wave Equation
11. Wave Equation in Higher Dimensions
References
Index.
Part of London Mathematical Society Student Texts
Not yet published - available from July 2025
format: Paperback isbn: 9781009335980
John McKay's remarkable insights unveiled a connection between the 'double covers' of the groups of regular polyhedra, known since ancient Greek times, and the exceptional Lie algebras, recognized since the late nineteenth century. The correspondence involves certain diagrams, the ADE diagrams, which can be interpreted in different ways: as quivers associated with the groups, and Dynkin diagrams of root systems of Lie algebras. The ADE diagrams arise in many areas of mathematics, including topics in relativity and string theory, spectral theory of graphs and cluster algebras. Accessible to students, this book explains these connections with exercises and examples throughout. An excellent introduction for students and researchers wishing to learn more about this unifying principle of mathematics.
Enhances interdisciplinary understanding of ADE, an important unifying principle of mathematics
Motivates the study of foundational topics such as multilinear algebra and group theory and demonstrates their applications
Of interest to a wide range of mathematicians and application, from graph theory to general relativity
Nomenclature
1. An invitation
2. Algebraic preliminaries
3. ADE classifications
4. ADE correspondences
5. Advanced miscellany
References
Index.
Part of London Mathematical Society Lecture Note Series
- available from August 2025
format: Paperback isbn: 9781009576710
Paperback
Everywhere one looks, one finds dynamic interacting systems: entities expressing and receiving signals between each other and acting and evolving accordingly over time. In this book, the authors give a new syntax for modeling such systems, describing a mathematical theory of interfaces and the way they connect. The discussion is guided by a rich mathematical structure called the category of polynomial functors. The authors synthesize current knowledge to provide a grounded introduction to the material, starting with set theory and building up to specific cases of category-theoretic concepts like limits, adjunctions, monoidal products, closures, monoids, modules, and bimodules. The text interleaves rigorous mathematical theory with concrete applications, providing detailed examples illustrated with graphical notation as well as exercises with solutions. Graduate students and scholars from a diverse array of backgrounds will appreciate this common language by which to study interactive systems categorically.
Interspersed concrete applications show students and practitioners how to put theory into practice
Presents detailed, illustrated examples of each piece of polynomial functor theory introduced in action and formal graphical calculi to aid computation
Provides more than 220 exercises with comprehensive, concise solutions, giving the reader hands-on practice with the material
Part I. The Category of Polynomial Functors:
1. Representable functors from the category of sets
2. Polynomial functors
3. The category of polynomial functors
4. Dynamical systems as dependent lenses
5. More categorical properties of polynomials
Part II. A Different Category of Categories:
6. The composition product
7. Polynomial comonoids and retrofunctors
8. Categorical properties of polynomial comonoids
9. Future work in polynomial functors
References
Index.