Paperback (ISBN-13: 9780521154154)
Page extent: 400 pages
Size: 216 x 140 mm
The purpose of this book, first published in 1939, updated in 1953, is to give a treatment of the so-called operational method and to illustrate its application to problems in various branches of technology. It is written primarily for technologists who use mathematics in solving technical problems in industrial and applied research work, and the treatment is sufficiently rigorous for their needs. The theory of the complex variable and of transform calculus occupy the first half of the book. A further third of the book describes the application of this theory to problems arising in electrical circuits; vibrational systems; aeroplane dynamics; the deflexion of beams; radio and television receivers; the solution of partial differential equations; electrical transmission limes; electrical wave filters; solenoids with metal cores; condenser microphones; loud speaker horns and the absorption of moisture. The final part contains over 100 problems - many with hints for their solution - appendices and references.
Preface to the second edition; Preface to the first edition; Part I. Theory of Complex Variable; 1. Functions of a complex variable; 2. Integration: Cauchy's theorem: Taylor's and Laurent's theorems; 3. Calculus of residues; 4. The Bromwich contour: equivalent contours: evaluation of integrals; 5. Gamma, error and Bessel functions; 6. Evaluation of 1/2*i∫Br1 ezto(z)dz/z when o(z) has branch points; 7. Differentiation and integration under the integral sign; Part II. Theory of Transform Calculus: 8. Mellin inversion theorem: transform theory; 9. Solution of ordinary linear differential equations; 10. Discontinuous functions: impulses: frequency spectra; Part III. Technical Applications of Parts I and II: 11. Electrical circuits: vibrational systems: aeroplane dynamics: deflexion of beams; 12. Radio and television receivers; 13. Partial linear differential equations: electrical transmission lines: electrical wave filters; 14. Solenoid with metal core: condenser microphone: loud speaker horn; 15. Diffusion of heat: absorption of moisture problems to be worked out by the reader; Part IV. Appendices and List of References; Index.
Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 7)
Paperback (ISBN-13: 9780521159418)
Page extent: 442 pages
Size: 254 x 178 mm
This 2001 book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods; for mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book provides a basic background in numerical analysis emphasizing issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats application of numerical tools: numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. The book concludes with an examination of sorting, FFT and the application of other ‘fast’ algorithms to statistics. Each chapter contains exercises that range from the simple to research problems, as well as examples of the methods at work.
* Lots of exercises, ranging from elementary to research-level problems * Accompanying computer code * Useful both as text or reference book
1. Algorithms and computers; 2. Computer arithmetic; 3. Matrices and linear equations; 4. More methods for solving linear equations; 5. Least squares; 6. Eigenproblems; 7. Functions: interpolation, smoothing and approximation; 8. Introduction to optimization and nonlinear equations; 9. Maximum likelihood and nonlinear regression; 10. Numerical integration and Monte Carlo methods; 11. Generating random variables from other distributions; 12. Statistical methods for integration and Monte Carlo; 13. Markov chain Monte Carlo methods; 14. Sorting and fast algorithms.
Availability: In Stock
Format: Book
ISBN: 0486477673
Page Count: 192
Dimensions: 5 3/8 x 8 1/2
This introduction to Boolean algebra begins with an intuitive approach to set theory and an axiomatic account of the fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. Answers to selected problems appear at the end. 1961 edition.
Reprint of the Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1961 edition.
THE ALGEBRA OF SETS
BOOLEAN ALGEBRA
SYMBOLIC LOGIC AND THE ALGEBRA OF PROPOSITIONS
SWITCHING ALGEBRA
RELAY CIRCUITS AND CONTROL PROBLEMS
CIRCUITS FOR ARITHMETIC COMPUTATION
INTRODUCTION TO PROBABILITY IN FINITE SAMPLE SPACES
ANSWERS TO SELECTED PROBLEMS
INDEX
Availability: In Stock
Format: Book
ISBN: 0486477665
Page Count: 448
Dimensions: 5 3/8 x 8 1/2
This definitive look at modern analysis includes applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. The self-contained treatment contains clear explanations and all the appropriate theorems and proofs. A selection of more than 750 exercises includes some hints and solutions. 1981 edition.
Reprint of the Marcel Dekker, Inc., New York, 1981 edition.
Preface
Preface to the Dover Edition
I Sets and Functions
II The Real Number System
III Set Equivalence
IV Sequences of Real Numbers
V Infinite Series
VI Limits of Real-Valued Functions and Continuous Functions on the Real Line
VII Metric Spaces
VIII Differential Calculus of the Real Line
IX The Riemann-Stieltjes Integral
X Sequences and Series of Functions
XI Transcendental Functions
XII Inner Product Spaces and Fourier Spaces
XIII Normed Linear Spaces and the Riesz Representation Theorem
XIV The Lebesgue Integral
Appendix: Vector Spaces
References
Hints to Selected Exercises
Index
Errata
EMS Series of Lectures in Mathematics
ISBN 978-3-03719-078-4
DOI 10.4171/078
April 2010, 234 pages, softcover, 17 x 24 cm.
Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks.
Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated web page that provides MATLAB codes for many of the examples.
The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering.
ISBN 978-3-03719-077-7
DOI 10.4171/077
April 2010, 488 pages, hardcover, 16.5 x 23.5 cm.
The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000) and Stockholm (2004), the Fifth European Congress of Mathematics (5ECM) took place in Amsterdam, The Netherlands, July 14*18, 2008, with about 1000 participants from 68 different countries.
Ten plenary and thirty-three invited lectures were delivered. Three science lectures outlined applications of mathematics in other sciences: climate change, quantum information theory and population dynamics. As in the four preceding EMS congresses, ten EMS prizes were granted to very promising young mathematicians. In addition, the Felix Klein Prize was awarded, for the second time, for an application of mathematics to a concrete and difficult industrial problem. There were twenty-two minisymposia, spread over the whole mathematical area. Two round table meetings were organized: one on industrial mathematics and one on mathematics and developing countries.
As part of the 44th Nederlands Mathematisch Congres, which was embedded in 5ECM, the so-called Brouwer lecture was presented. It is the Netherland's most prestigious award in mathematics, organized every three years by the Royal Dutch Mathematical Society. Information about Brouwer was given in an invited historical lecture during the congress.
These proceedings contain a selection of the contributions to the congress, providing a permanent record of the best what mathematics offers today.
This second edition is enlarged and considerably rewritten in comparison with the first edition. Among the new topics are: infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl´s theorems on equidistribution. Topics that have continued from the first edition include Minkowski´s theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem.
This second edition is enlarged and considerably rewritten in comparison with the first edition. Among the new topics are: infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl´s theorems on equidistribution. Topics that have continued from the first edition include Minkowski´s theorem，measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem.
...this volume can be an excellent way to get one´s feet wet and see whether it is worthwhile to take the plunge. The book has helpful and challenging exercises for the reader. It should be emphasized that the great strength of the book lies in the large number of interesting special results it contains. Many of the prettiest facts of harmonic analysis are on display here in a very attractive setting.
1. Fourier Series and Integrals 2. The Fourier Integral 3. Discrete and Compact Groups 4. Hardy Spaces 5. Conjugate Functions 6. Translation 7.Distribution
Texts and Readings in Mathematics 7
Paperback reprint-2010, 236 pages, Paperback, ISBN 978-93-80250-05-2,