Paperback ISBN: 9780128206560
Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.
Undergraduate programs: Software Engineering; Computer Science; Electrical Engineering; Computer Engineering; Information Technology; Applied Mathematics; Practicing engineers and computer scientists, and technical supervisors in the high-tech industry
Paperback ISBN: 9780323992800
Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations. Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations.
Advanced students in undergraduate and graduate programs taking courses on Advanced Ordinary Differential Equations in Math, Science, and Engineering
Part of Cambridge Mathematical Library
Not yet published - available from June 2022
FORMAT: Paperback ISBN: 9781009230056
Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Korner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Korner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.
Accessible to undergraduate students
Written in a fresh, humorous and engaging style
New foreword from Professor Terence Tao
Foreword Terence Tao
Preface
1. Fourier series
2. Some differential equations
3. Orthogonal series
4. Fourier transforms
5. Further developments
6. Other directions
Appendices
Index.
Part of Lecture Notes in Logic
Not yet published - available from August 2022
FORMAT: Hardback ISBN: 9781009229692
This is the first of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. In this volume, Cherlin develops a complete classification of homogeneous ordered graphs and provides a full proof. He then proposes a new family of metrically homogeneous graphs, a weakening of the usual homogeneity condition. A general classification conjecture is presented, together with general structure theory and applications to a general classification conjecture for such graphs. It also includes introductory chapters giving an overview of the results and methods of both volumes, and an appendix surveying recent developments in the area. An extensive accompanying bibliography of related literature, organized by topic, is available online.
Presents the state of the art in an area in which model theory, combinatorics, and topological dynamics interact richly
A rich source of new ideas and open problems for researchers and graduate students in the area
Contains an extensive appendix surveying recent developments in the field
Part of Lecture Notes in Logic
Not yet published - available from August 2022
FORMAT: Hardback ISBN: 9781009229487
This is the second of two volumes by Professor Cherlin presenting the state of the art in the classification of homogeneous structures in binary languages and related problems in the intersection of model theory and combinatorics. Researchers and graduate students in the area will find in these volumes many far-reaching results and interesting new research directions to pursue. This volume continues the analysis of the first volume to 3-multi-graphs and 3-multi-tournaments, expansions of graphs and tournaments by the addition of a further binary relation. The opening chapter provides an overview of the volume, outlining the relevant results and conjectures. The author applies and extends the results of Volume I to obtain a detailed catalogue of such structures and a second classification conjecture. The book ends with an appendix exploring recent advances and open problems in the theory of homogeneous structures and related subjects.
Presents the state of the art in an area in which model theory, combinatorics, and topological dynamics interact richly
A rich source of new ideas and open problems for researchers and graduate students in the area
Contains an extensive appendix surveying recent developments in the field
18. Classification problems for small binary languages
19. Homogeneous 3-multi-graphs
20. Imprimitive homogeneous 2-multi-tournaments
21. 3-constrained homogeneous 2-multi-tournaments
22. Homogeneous 2-multi-tournaments: forbidden triangles
Conclusion
Appendix B. Open problems and some recent results
References for Volume II
Index.
Not yet published - available from October 2022
FORMAT: Paperback ISBN: 9781009201445
Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.
Comprehensive coverage following the UGC's CBCS syllabus as well as those of most major universities across India
Simplified presentation of topics using definitions, theorems, and examples
Theoretic justifications of all major methods for deeper conceptual understanding
Sufficient practice exercises at the end of each chapter
1. Relevant Pre-requisites and Terminologies
2. Solution, Classification, and Formation of Partial Differential Equations
3. Easily Solvable Partial Differential Equations
4. First-Order Partial Differential Equations
5. Second-Order Partial Differential Equations
6. Higher Order Linear Partial Differential Equations.