Part of Cambridge Texts in Applied Mathematics
Publication planned for: October 2015
availability: Not yet published - available from October 2015
format: Hardback
isbn: 9781107098411
format: Paperback
isbn: 9781107485495
dimensions: 228 x 152 mm
contains: 125 b/w illus. 8 colour illus. 180 exercises
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
Preface
Part I. Setting the Scene:
1. What are singularities all about?
2. Blow-up
3. Similarity profile
4. Continuum equations
5. Local singular expansions
6. Asymptotic expansions of PDEs
Part II. Formation of Singularities:
7. Drop break-up
8. A numerical example: drop pinch-off
9. Slow convergence
10. Continuation
Part III. Persistent Singularities ? Propagation:
11. Shock waves
12. The dynamical system
13. Vortices
14. Cusps and caustics
15. Contact lines and cracks
Appendix A. Vector calculus
Appendix B. Index notation and the summation convention
Appendix C. Dimensional analysis
References
Index.
Part of New Mathematical Monographs
Publication planned for: November 2015
format: Hardback
isbn: 9781107030251
dimensions: 228 x 152 mm
contains: 20 b/w illus.
Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams. The book contains 300 examples and provides detailed explanations of many fundamental results. Part I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy pullbacks and pushouts, and the Blakers?Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an accessible account of homotopy limits and colimits of diagrams of spaces, and a treatment of cosimplicial spaces. The book finishes with applications to some exciting new topics that use cubical diagrams: an overview of two versions of calculus of functors and an account of recent developments in the study of the topology of spaces of knots.
Preface
Part I. Cubical Diagrams:
1. Preliminaries
2. 1-cubes: homotopy fibers and cofibers
3. 2-cubes: homotopy pullbacks and pushouts
4. 2-cubes: the Blakers-Massey Theorems
5. n-cubes: generalized homotopy pullbacks and pushouts
6. The Blakers?Massey Theorems for n-cubes
Part II. Generalizations, Related Topics, and Applications:
7. Some category theory
8. Homotopy limits and colimits of diagrams of spaces
9. Cosimplicial spaces
10. Applications
Appendix
References
Index.
Part of New Mathematical Monographs
Publication planned for: November 2015
format: Hardback
isbn: 9781107027787
dimensions: 228 x 152 mm
contains: 1 b/w illus. 100 exercises
availability: Not yet published - available from November 2015
An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
Preface
16. The spaces M(A) and H(A)
17. Hilbert spaces inside H2
18. The structure of H(b) and H(b? )
19. Geometric representation of H(b) spaces
20. Representation theorems for H(b) and H(b?)
21. Angular derivatives of H(b) functions
22. Bernstein-type inequalities
23. H(b) spaces generated by a nonextreme symbol b
24. Operators on H(b) spaces with b nonextreme
25. H(b) spaces generated by an extreme symbol b
26. Operators on H(b) spaces with b extreme
27. Inclusion between two H(b) spaces
28. Topics regarding inclusions M(a) ⊂ H(b?) ⊂ H(b)
29. Rigid functions and strongly exposed points of H1
30. Nearly invariant subspaces and kernels of Toeplitz operators
31. Geometric properties of sequences of reproducing kernels
References
Symbols index
Index.
ISBN: 978-1-119-05099-5
272 pages
December 2014
An enlightening introduction to the study of logic: its history, philosophical foundations, and formal structures
Logic: Inquiry, Argument, and Order is the first book of its kind to frame the study of introductory logic in terms of problems connected to wider issues of knowledge and judgment that arise in the context of racial, cultural, and religious diversity. With its accessible style and integration of philosophical inquiry and real-life concerns, this book offers a novel approach to the theory of logic and its relevance to questions of meaning and value that arise in the world around us.
The book poses four problems for logic: Is logic separate from experience? Does logic require dualisms? Can logic reconcile opposed ways of understanding the world? And when things are divided, does the boundary have a logic? The author begins the exploration of these questions with a discussion of the process of analyzing and constructing arguments. Using the logical theories of C. S. Peirce, John Dewey, and Josiah Royce to frame the investigation, subsequent chapters outline the process of inquiry, the concept of communicative action, the nature of validity, categorical reasoning through the theory of the syllogism, and inductive reasoning and probability. The book concludes with a presentation of modal logic, propositional logic, and quantification.
Logic is presented as emerging from the activities of inquiry and communication, allowing readers to understand even the most difficult aspects of formal logic as straightforward developments of the process of anticipating and taking action. Numerous practice problems use arguments related to issues of diversity and social theory, and the book introduces methods of proving validity that include Venn diagrams, natural deduction, and the method of tableaux.
Logic: Inquiry, Argument, and Order is an ideal book for courses on philosophical methods and critical reasoning at the upper-undergraduate and graduate levels. It is also an insightful reference for anyone who would like to explore a cross-cultural approach to the topic of logic.
ACKNOWLEDGMENTS ix
CHAPTER ONE: THE SIGNIFICANCE OF LOGIC 1
1.1 The Problem of Abstraction 2
1.2 The Problem of Dualism 5
1.3 The Problem of Incommensurability 8
1.4 The Problem of Boundaries 11
1.5 Examples for Discussion 15
1.6 Premises and Conclusions 19
1.7 Exercises 23
CHAPTER TWO: WHAT IS LOGIC? 31
2.1 The Study of Logic 31
2.2 The Concepts of Truth and Inference 35
2.3 The Process of Inquiry 40
2.4 Exercises 48
2.5 Argument as Inquiry 52
2.6 Exercises 57
CHAPTER THREE: COMMUNICATIVE ACTION 61
3.1 Strategic and Communicative Action 61
3.2 Exercises 64
3.3 Lifeworlds 68
3.4 Exercises 71
3.5 Validity 72
3.6 Fallacies 75
3.7 Exercises 85
CHAPTER FOUR: THEORY OF THE SYLLOGISM 91
4.1 Nominalism, Realism, and Abduction 91
4.2 The Theory of the Syllogism 97
4.3 Standard Form Propositions 98
4.4 Exercises 105
4.5 Direct Inference 106
4.6 Exercises 111
4.7 The Validity of Syllogisms 112
4.8 Exercises 120
CHAPTER FIVE: INDUCTION AND THE LIMITS OF REASON 123
5.1 Limits of the Syllogism 123
5.2 The Principles of Induction 129
5.3 Analogical Arguments 139
5.4 Exercises 143
5.5 Causal Arguments 145
5.6 Exercises 148
5.7 Probability 151
5.8 Exercises 160
CHAPTER SIX: PRINCIPLES OF ORDER AND DEDUCTION 165
6.1 Introduction 165
6.2 Modes of Action 167
6.3 Principles of Order 171
6.4 Logic and the Act of Judgment 174
6.5 Deduction: The Logic of Assertions 178
6.6 Graphical Proofs of Validity 190
6.7 Exercises 194
CHAPTER SEVEN: AN OVERVIEW OF QUANTIFIED LOGIC 197
7.1 Introduction 197
7.2 Representing Relations 202
7.3 The Meaning of Quantifi ers 205
7.4 Exercises 207
7.5 Rules of Quantifi cational Logic 208
7.6 Exercises 210
7.7 The Validity of Syllogisms 211
7.8 Graphical Proofs of Validity 214
7.9 Exercises 217
7.10 Border Agents and the Problems of Logic 218
SOLUTIONS 223
BIBLIOGRAPHY 249
INDEX 255
ISBN: 978-1-118-67502-1
652 pages
May 2015
Since publication of the first edition in 1970, Time Series Analysis has served as one of the most influential and prominent works on the subject. This new edition maintains its balanced presentation of the tools for modeling and analyzing time series and also introduces the latest developments that have occurred in the field over the past decade through applications from areas such as business, finance, and engineering. Along with the addition of a new co-author, Greta Ljung, a student of George Box, the Fifth Edition provides a clearly written exploration of the key methods for building, classifying, testing, and analyzing stochastic models for time series as well as their use in five important areas of application: forecasting; determining the transfer function of a system; modeling the effects of intervention events; developing multivariate dynamic models; and designing simple control schemes. New to this edition are more exercises; streamlined chapter introductions; updated examples and references; increased coverage of multivariate time series and their use in financial applications; SV models, MCMC based inference, and Bayesian Network modeling; and the incorporation of the ‘R’ freeware language.
Hardcover | ISBN: 9780262028967 | 584 pp. | 6 x 9 in | February 2015
We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated.
This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.
About the Authors
Gerald Jay Sussman is Panasonic Professor of Electrical Engineering at MIT. He is the coauthor (with Hal Abelson and Julie Sussman) of Structure and Interpretation of Computer Programs (MIT Press). Sussman and Wisdom are also coauthors of Functional Differential Geometry (MIT Press).
Jack Wisdom is Professor of Planetary Science at MIT. Sussman and Wisdom are also coauthors of Functional Differential Geometry (MIT Press).
“Sussman and Wisdom make a bold experiment in communicating mathematical physics: they say exactly what they mean. Even a computer can follow their equations. By using this textbook, students painlessly master Scheme, a minimalist programming language, at the same time. This empowers them to go beyond the simplistic integrable systems that dominate the traditional course, to the richness of nonlinear resonance and chaotic dynamics. The hard core of rigor is softened by a personal and enthusiastic writing style.”
?David Ritz Finkelstein, School of Physics, Georgia Institute of Technology
“With many new additions, from quaternions to Lie transforms, the core virtue of the book remains the same as in the first edition: by making the physics precise enough to run on a computer, the authors open the door to a deeper understanding of classical reality, with the promise of a deeper understanding of all reality.”
?Piet Hut, Professor of Astrophysics, Institute for Advanced Study, Princeton, New Jersey
“How can one write a new book on classical mechanics? Hasn’t everything already been said? No! Things have changed. Now that there are computers, you can actually solve the equations of motion for interesting problems. Mathematical niceties are not the obsession of the authors, but rather to find out what happens, by a natural combination of mathematical argument and computer use. This new and effective approach should attract students to a subject which, since Newton, has constantly managed to rejuvenate itself. This second edition has kept the principles that made the value of the first, with a number of improvements concerning in particular computer-implemented methods.”
?David Ruelle, Honorary Professor, Institut des Hautes Etudes Scientifique, France