Product Description
This book provides a self-contained and accessible introduction to linear and multilinear algebra. Besides the standard techniques for linear and multilinear algebra many advanced topics are included. Emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, computer graphics, fractals, quantum mechanics and quantum computing. All these fields are covered in detail. A key feature of the book is the many detailed worked-out examples. Computer algebra applications are also given. Each chapter includes useful exercises. The book is well suited for pure and applied mathematicians as well as theoretical physicists and engineers. New topics added to the second edition are: braid-like relations, Clebsch-Gordan expansion, nearest Kronecker product, Clifford and Pauli group, universal enveloping algebra, computer algebra and Kronecker product. ... Read more

Product Description
This comprehensive work in three volumes by a combined Swedish-US team of authors is a complete course in basic mathematics geared towards beginning students in applied mathematics, science and engineering. It arose from a course developed for chemical engineering students at the prestigious Chalmers Tekniska Högskolan in Göteborg, Sweden. The text has been used there for several years and plenty of feedback by students has been integrated into the text.

These books are an ideal tool for beginning students, containing plenty of excercises, motivational sections, concrete examples of applications - a masterpiece of mathematics teaching. ... Read more

Customer Reviews (1)

Calculus + Linear Algebra in One Series
I wish Amazon would put a text list of the "Table of Contents" for books.

Sorry about the length: Amazon does not allow postings for each volume in a series!

Volume 1: Derivatives and Geometry in R^3
1. What is Mathematics?
2. The Mathematics Library
3. Introduction to Modeling
4. A Very Short Calculus Course
5. Natural Numbers and Integers
6. Mathematical Induction
7. Rational Numbers
8. Pythagoras and Euclid
9. What is a Function?
10. Polynomial Functions
11. Combinations of Functions
12. Lipschitz Continuity
13. Sequences and Limits
14. The Square Root of Two
15. Real Numbers
16. The Bisection Algorithm for f(x) = 0
17. Do Mathematicians Quarrel?
18. The Function y = x^r
19. Fixed Points and Contraction Mappings
20. Analytic Geometry in R^2
21. Analytic Geometry in R^3
22. Complex Numbers
23. The Derivative
24. Differentiation Rules
25. Newton's Method
26. Galileo, Newton, Hooke, Malthus and Fourier

Volume 2: Integrals and Geometry in R^n
27: The Integral
28: Properties of the Integral
29. The Logarithm log(x)
30. Numerical Quadrature
31. The Exponential Function exp(x) = e^x
32. Trigonometric Functions
33. The Functions exp(z), log(z), sin(z) and cos(z) for z e C
34. Techniques of Integration
35. Solving Differential Equations Using the Exponential
36. Improper Integrals
37. Series
38. Scalar Autonomous Initial Value Problems
39. Separable Scalar Initial Value Problems
40. The General Initial Value Problem
41. Calculus Tool Bag I
42. Analytic Geometry in R^n
43. The Spectral Theorem
44. Solving Linear Algebraic Systems
45. Linear Algebra Tool Bag
46. The Matrix Exponential exp(xA)
47. Lagrange and the Principle of Least Action
48. N-Body Systems
49. The Crash Model
50. Electrical Circuits
51. String Theory
52. Piecewise Linear Approximation
53. FEM for Two-Point Boundary Value Problems

Volume 3: Calculus in Several Dimensions
54. Vector-Valued Functions of Several Real Variables
55. Level Curves/Surfaces and the Gradient
56. Linearization and Stability of Initial Value Problems
57. Adaptive Solvers for IVPs
58. Lorenz and the Essence of Chaos
59. The Solar System
60. Optimization
61. The Divergence, Rotation and Laplacian
62. Meteorology and Coriolis Forces
63. Curve Integrals
64. Double Integrals
65. Surface Integrals
66. Multiple Integrals
67. Gauss' Theorem and Green's Formula in R^2
68. Gauss' Theorem and Green's Formula in R^3
69. Stoke's Theorem
70. Potential Fields
71. Center of Mass and Archimedes' Principle
72. Newton's Nightmare
73. Laplacian Models
74. Chemical Reactions
75. Calculus Tool Bag II
76. Piecewise Linear Polynomials in R^2 and R^3
77. FEM for Boundary Value Problems in R^2 and R^3
78. Inverse Problems
79. Optimal Control
80. Differential Equations Tool Bag
81. Applications Tool Bag
82. Analytic Functions
83. Fourier Series
84. Fourier Transforms
85. Analytic Functions Tool Bag
86. Fourier Analysis Tool Bag
87. Incompressible Navier-Stokes: Quick and Easy

This book/series has some problems; however, the attempt to wed Mathematical Analysis, Numerical Computation, and Application AND to also talk about Calculus and Linear Algebra at the same time -- makes these three books worth a look.
... Read more

Product Description
This volume contains articles that document the advances in thesubject of Total Positivity during the last two decades. The materialis divided into ten chapters. While some of the articles are of asurvey nature, others present new results appearing here for the firsttime. Also, some papers contain introductory material and aretherefore accessible to non-experts interested in becoming familiarwith the important ideas and techniques of Total Positivity.
Audience: This book will be of value to mathematicians,engineers and computer scientists whose work involves applications ofTotal Positivity to problems in the theory of spline functions,numerical quadrature, nonlinear analysis, entire functions,probability, mathematical biology, statistics, approximation theory,combinatorics, geometric modelling, matrix theory and integralequations. ... Read more

Customer Reviews (1)

Good reference for deciding which method fits your problem
The book gives good insights about choosing particular methods. The author shows many tables comparing different strategies and matrices. The reader doesn't need to have background on sparse matrices.It is really a`cookbook' on sparse matrix solutions. ... Read more

Product Description

This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework.

The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition.

This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.

Product Description
Now in paperback, this remains one of the classic expositions of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases. Sparse matrix representations of these operators can be given in terms of wavelet bases that have important applications in image processing and numerical analysis. This method is now widely studied and can be used to tackle a wide variety of problems arising in science and engineering. Put simply, this is an essential purchase for anyone researching the theory of wavelets. ... Read more

Customer Reviews (1)

Ray M. Bowen
At first, I found this book to be difficult reading. However, after a very serious attempt to discover the Author's intent, I truely began to cheerish the information presented in this book. One day I plan to contact Mr.Bowen, and maybe study with him for a time. ... Read more

Product Description

The first edition (94301-3) was published in 1995 in TIMS and had 2264 regular US sales, 928 IC, and 679 bulk.

This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.

Product Description

This book presents the authors' personal selection of topics in multivariate statistical analysis with emphasis on tools and techniques. Topics included range from definitions of multivariate moments, multivariate distributions, asymptotic distributions of commonly used statistics and density approximations to a modern treatment of multivariate linear models. The theory used is based on matrix algebra and linear spaces and applies lattice theory in a systematic way. Many of the results are obtained by utilizing matrix derivatives which in turn are built up from the Kronecker product and vec-operator. The matrix normal, Wishart and elliptical distributions are studied in detail. In particular, several moment relations are given. Together with the derivatives of density functions, formulae are presented for density approximations, generalizing classical Edgeworth expansions. The asymptotic distributions of many commonly used statistics are also derived. In the final part of the book the Growth Curve model and its various extensions are studied.

The book will be of particular interest to researchers but could also be appropriate as a text-book for graduate courses on multivariate analysis or matrix algebra.

Product Description

Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

The authors are leading researchers in Computational Mathematics who have written various successful books.

Product Description
This volume presents a comprehensive compendium of classicaland new inequalities as well as some recent extensions to well-knownones.
Variations of inequalities ascribed to Abel, Jensen, Cauchy,Chebyshev, Hölder, Minkowski, Stefferson, Gram, Fejér,Jackson, Hardy, Littlewood, Po'lya, Schwarz, Hadamard and a host ofothers can be found in this volume. The more than 1200 citedreferences include many from the last ten years which appear in a bookfor the first time.
The 30 chapters are all devoted to inequalities associated with agiven classical inequality, or give methods for the derivation of newinequalities. Anyone interested in equalities, from student toprofessional, will find their favorite inequality and much more.
... Read more

Product Description
Matrix diagonal stability and the related diagonal type Liapunov functions possess properties that make them attractive and very useful for applications. This new book addresses the matrix-stability concept and its applications to the analysis and design of several types of dynamical systems, both discrete-time and continuous-time.

The comprehensive presentation begins with an introductory chapter surveying applied examples from diverse fields, i.e., robust stability analysis, asynchronous iterative computation, neural networks and variable structure dynamical systems. The next few chapters develop the theory and includes a unified presentation of results in the area of matrix-diagonal stability and D-stability. The remaining chapters examine the various applications in greater detail. Both classical and new results are discussed, and the overall treatment is self-contained, only requiring linear algebra, difference equations and differential equations.

Topics and Features:

Diverse applications presented with minimum of technical prerequisites
Unified presentation of results on discrete-time and continuous-time diagonal and D-stability
Extensive guide to current literature and discussion of open problems
Asynchronous iterative methods
Stability and stabilization
Neural networks, circuits and systems

"Matrix Diagonal Stability in Systems and Computation" provides an essential reference for new methods and analysis related to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations. Researchers, professionals and graduates in applied math, control engineering, stability of dynamical systems, scientific computation and computer science will find the book a successful guide to current results and developments. ... Read more

Product Description
Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control applications. If sampling is performed in order to control periodic processes, almost periodic systems are obtained. This is a strong motivation to investigate the discrete-time systems with time-varying coefficients. This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. All these tools aim to solve the problems of stabilization and attenuation of disturbances in the framework of H2- andH-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results. ... Read more

Product Description

This book teaches mathematical structures and how they can be applied in environmental science. Each chapter presents story problems with an emphasis on derivation. For each of these, the discussion follows the pattern of first presenting an example of a type of structure as applied to environmental science. The definition of the structure is presented, followed by additional examples using MATLAB, and analytic methods of solving and learning from the structure.

Product Description
Text heavily biased toward functional methods. Discusses the Hankel norm approximation for the case of scalar rational functions. Paper. DLC: Algebras, Linear. ... Read more

Product Description
This book offers a comprehensive treatment of linear programming as well as of the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. An introduction surveying fifty years of linear optimization is given. The book can serve both as a graduate textbook for linear programming and as a text for advanced topics classes or seminars. Exercises as well as several case studies are included. The book is based on the author's long term experience in teaching and research. For his research work he has received, among other honors, the 1983 Lanchester Prize of the Operations Research Society of America, the 1985 Dantzig Prize of the Mathematical Programming Society and the Society for Industrial Applied Mathematics and a 1989 Alexander-von-Humboldt Senior U.S. Scientist Research Award. ... Read more

Customer Reviews (2)

Computational and Mathematical Excellence
For nearly 30 years, Padberg has been a leader in computational integer programming and in combinatorial optimization theory.

In practice, Padberg has helped to design and implement "branch-and-cut" methods for finding exact optimal solutions to large traveling salesman problems, and this approach is a method of choice for finding approximately optimal solutions to tough industrial problems.The book provides the mathematical and computational background for understanding branch-and-cut; the established mathematical texts by Nemhauser and Wolsey and by Schrijver are less detailed and more condensed, and omit numerical issues.The treatment of modern simplex algorithms for linear programming---updating LU factorizations and using column- and constraint-generation and -purging---is excellent, and a large bibliography contains recent references.Besides industrial and Berlin-airlift scheduling problems, the book contains TSP examples of circuit-board wiring, U.S. state capitals, and Odysseus!

Three more highlights: The double description algorithm receives a complete description, and this is useful for combinatorial geometers.The discussion of integer-arithmetic and complexity theory is very readable, and these technical topics are slighted by interior-point books (besides Wright's quickie), despite their importance in integer programming and combinatorial optimization. The discussion of interior-point algorithms emphasizes projective geometry, a beautiful theory that has inspired so much of optimization theory---besides Karmarkar's interior-point algorithm,Dantzig's simplex algorithm, Fenchel duality, Davidon's conic algorithm for nonlinear optimization, etc.).

The book is not a comprehensive survey of linear programming,
and lacks a treatment of Nesterov's theory of self-concordant barrier-functions.Also, no treatment is given of pivoting algorithms besides Dantzig's (e.g., Terlaky's criss-cross method, Todd's oriented matroid algorithm).

A good reference for Linear Programming Theory
This book is certainly a very good reference for theoretical topics of linear programming. It covers the Simplex method and the Ellipsoid algorithms. It also covers the geometry of linear programming (polyhedraand polytopes, etc). It certainly covers more topics than most other linearprogramming texts.As expected, a book writen for theoretical topics iscertainly not easy to read, especially for people with no training in doingrigorous mathematical proofs. Also, not many examples or illustrations aregiven in this book, and this might be a problem for some readers. ... Read more

Product Description
Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical applications such software is often essential. However, using this tool when learning about matrices, without first gaining a proper understanding of the underlying theory, limits the ability to use matrices and to apply them to new problems. This book explains matrices in the detail required by engineering or science students, and it discusses linear systems of ordinary differential equations. These students require a straightforward introduction to linear algebra illustrated by applications to which they can relate. It caters of the needs of undergraduate engineers in all disciplines, and provides considerable detail where it is likely to be helpful.According to the author the best way to understand the theory of matrices is by working simple exercises designed to emphasize the theory, that at the same time avoid distractions caused by unnecessary numerical calculations. Hence, examples and exercises in this book have been constructed in such a way that wherever calculations are necessary they are straightforward. For example, when a characteristic equation occurs, its roots (the eigenvalues of a matrix) can be found by inspection.The author of this book is Alan Jeffrey, Emeritus Professor of mathematics at the University of Newcastle upon Tyne. He has given courses on engineering mathematics at UK and US Universities. ... Read more

Product Description

This book is intended as an alternative to the standard differential equations text, which typically includes a large collection of methods and applications, packaged with state-of-the-art color graphics, student solution manuals, the latest fonts, marginal notes, and web-based supplements. These texts adds up to several hundred pages of text and can be very expensive for students to buy. Many students do not have the time or desire to read voluminous texts and explore internet supplements. Here, however, the author writes concisely, to the point, and in plain language. Many examples and exercises are included. In addition, this text also encourages students to use a computer algebra system to solve problems numerically, and as such, templates of MATLAB programs that solve differential equations are given in an appendix, as well as basic Maple and Mathematica commands.

Product Description
Descriptor linear systems theory is an important part in the general field of control systems theory, and has attracted much attention in the last two decades. In spite of the fact that descriptor linear systems theory has been a topic very rich in content, there have been only a few books on this topic. This book provides a systematic introduction to the theory of continuous-time descriptor linear systems and aims to provide a relatively systematic introduction to the basic results in descriptor linear systems theory.The clear representation of materials and a large number of examples make this book easy to understand by a large audience. General readers will find in this book a comprehensive introduction to the theory of descriptive linear systems. Researchers will find a comprehensive description of the most recent results in this theory and students will find a good introduction to some important problems in linear systems theory. ... Read more