Hardback
ISBN: 9780980232745
Publication date: November 2010
600 pages
Dimensions: 253 x 196 mm
Weight: 1.73 kg
Gilbert Strang's clear, direct style and detailed, intensive explanations make this textbook ideal as both a course companion and for self-study. Single variable and multivariable calculus are covered in depth. Key examples of the application of calculus to areas such as physics, engineering and economics are included in order to enhance students' understanding. New to the second edition is a chapter on the 'Highlights of calculus', which accompanies the popular video lectures by the author on MIT's OpenCourseWare. (These can be accessed from math.mit.edu/~gs).
Summary Email a friend Features Table of contents Features
* Useful as both a reference and a self-study manual
* Contains ample diagrams, practice questions and examples, assisting the reader's grasp of the material
* A classic text, used by generations of students since the first edition was published in 1991
Highlights of calculus
1. Introduction to calculus
2. Derivatives
3. Applications of the derivative
4. The chain rule
5. Integrals
6. Exponentials and logarithms
7. Techniques of integration
8. Applications of the integral
9. Polar coordinates and complex numbers
10. Infinite series
11. Vectors and matrices
12. Motion along a curve
13. Partial derivatives
14. Multiple integrals
15. Vector calculus
16. Mathematics after calculus.
Paperback
ISBN: 9780521187961
Publication date: March 2011
713 pages
Dimensions: 244 x 170 mm
Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This 2006 textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.
* Complex ideas or computations are divided into a sequence of simple and clear statements which can then be easily grasped
* Much of the theory is illustrated through simple exercises (over 1000 altogether), with detailed hints
* End-of-chapter summaries give important concepts, results and formulas
* Uses both standard mathematical and physical terminology, building a bridge between the jargons involved
Hardback
ISBN: 9780521895446
150 b/w illus. 19 tables
Dimensions: 247 x 174 mm
available from August 2011
Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of complex-valued Gaussian variables and processes, time series and spectral representation, the Chernoff bound and large deviation approximation, martingales, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, semi-Markov and renewal processes, geometric Brownian motion and Ito process. Applications such as Wiener and Kalman filters, queueing and loss networks, hidden Markov models (HMM), the Black*Scholes differential equation for option pricing and the Viterbi, BCJR and Baum*Welch algorithms are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.
* Includes key advanced topics not covered in other textbooks, such as the EM algorithm, hidden Markov models, and queueing and loss systems
* Presents many illustrative examples from areas such as communications, signal processing, network theory and financial engineering
* Supplementary materials are provided online, including a solutions manual, lecture slides and MATLAB exercises
Series: Encyclopedia of Mathematics and its Applications (No. 141)
ISBN: 9781107002586 Hardback
70 b/w illus. 30 tables
Dimensions: 234 x 156 mm
available from April 2011
The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics.
* Presents a brand new method useful for high-precision evaluation
* Includes a detailed account of the classical method with examples and cases of breakdown due to coalescence problems
* Illustrated with many numerical examples
Preface
1. Asymptotics of Laplace-type integrals
2. Hadamard expansion of Laplace integrals
3. Hadamard expansion of Laplace-type integrals
4. Applications
Appendix A
Appendix B
Appendix C
References
Index.
Hardback
ISBN: 9780521196819
53 b/w illus. 347 exercises
Dimensions: 247 x 174 mm
available from March 2011
Csiszar and Korner's book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics. The presentations of all core subjects are self contained, even the advanced topics, which helps readers to understand the important connections between seemingly different problems. Finally, 320 end-of-chapter problems, together with helpful solving hints, allow readers to develop a full command of the mathematical techniques. It is an ideal resource for graduate students and researchers in electrical and electronic engineering, computer science and applied mathematics.
* Fully updated and revised edition of a classic book in the field
* Presents deep insights and expert treatment of the key theoretical issues, from two of the field's pioneering researchers
* Includes new, unique coverage of information theoretic secrecy and zero-error information, and provides 320 end-of-chapter problems, and helpful solving hints
Table of Contents
Part I. Information Measures in Simple Coding Problems:
1. Source coding and hypothesis testing: information measures
2. Types and typical sequences
3. Some formal properties of Shannon's information measures
4. Non-block source coding
5. Blowing up lemma: a combinatorial digression
Part II. Two-Terminal Systems: 6. The noisy channel problem
7. Rate-distortion trade-off in source coding and the source-channel transmission problem
8. Computation of channel capacity and *-distortion rates
9. A covering lemma: error exponent in source coding
10. A packing lemma: on the error exponent in channel coding
11. The compound channel revisited: zero-error information theory and extremal combinatorics
12. Arbitrary varying channels
Part III. Multi-Terminal Systems: 13. Separate coding of correlated source
14. Multiple-access channels
15. Entropy and image size characteristics
16. Source and channel networks
17. Information-theoretic security.
Series: New Mathematical Monographs (No. 19)
ISBN: 9780521516952 Hardback
35 b/w illus.
Dimensions: 228 x 152 mm
available from August 2011
The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
* Proposes a working theory of higher categories
* Focuses on one specific approach based closely on the work of Graeme Segal
* Useful reference to the different approaches adopted by researchers
Prologue
Acknowledgements
Part I. Higher Categories: 1. History and motivation
2. Strict n-categories
3. Fundamental elements of n-categories
4. The need for weak composition
5. Simplicial approaches
6. Operadic approaches
7. Weak enrichment over a Cartesian model category: an introduction
Part II. Categorical Preliminaries: 8. Some category theory
9. Model categories
10. Cartesian model categories
11. Direct left Bousfield localization
Part III. Generators and Relations: 12. Precategories
13. Algebraic theories in model categories
14. Weak equivalences
15. Cofibrations
16. Calculus of generators and relations
17. Generators and relations for Segal categories
Part IV. The Model Structure: 18. Sequentially free precategories
19. Products
20. Intervals
21. The model category of M-enriched precategories
22. Iterated higher categories
Part V. Higher Category Theory: 23. Higher categorical techniques
24. Limits of weak enriched categories
25. Stabilization
Epilogue
References
Index.