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An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and theSecond Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB® An appendix that contains proofs of various theorems and other material

The author can awaken for you a faculty which is surprisingly dormant in accountants, engineers, scientists, businesspeople, and others who work with figures. This is "number sense" — or the ability to recognize relations between numbers considered as whole quantities. Lack of this number sense makes it entirely possible for a scientist to be proficient in higher mathematics, but to bog down in the arithmetic of everyday life.

This book teaches the necessary mathematical techniques that schools neglect to teach: Horizontal addition, left to right multiplication and division, etc. You will learn a method of multiplication so rapid that you'll be able to do products in not much more time than it would take to write the problem down on paper.

This is not a collection of tricks that work in only a very few special cases, but a serious, capably planned course of basic mathematics for self-instruction. It contains over 9,000 short problems and their solutions for you to work during spare moments. Five or ten minutes spent daily on this book will, within ten weeks, give you a number sense that will double or triple your calculation speed.

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.

By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

Amy Langville and Carl Meyer provide the first comprehensive overview of the mathematical algorithms and methods used to rate and rank sports teams, political candidates, products, Web pages, and more. In a series of interesting asides, Langville and Meyer provide fascinating insights into the ingenious contributions of many of the field's pioneers. They survey and compare the different methods employed today, showing why their strengths and weaknesses depend on the underlying goal, and explaining why and when a given method should be considered. Langville and Meyer also describe what can and can't be expected from the most widely used systems.

The science of rating and ranking touches virtually every facet of our lives, and now you don't need to be an expert to understand how it really works. Who's #1? is the definitive introduction to the subject. It features easy-to-understand examples and interesting trivia and historical facts, and much of the required mathematics is included.

The book covers the results of a variety of major projects in industrial mathematics following an initiative of the German Federal Ministry of Education and Research. All projects are collaborations of industrial companies and university-based researchers, and range from automotive industry to computer technology and medical visualisation. In general, the projects presented in this volume prove that new mathematical ideas and methods can be decisive for the solution of industrial and economic problems.

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2011. The reports cover all fields of computational science and engineering, ranging from CFD to computational physics and chemistry, to computer science, with a special emphasis on industrially relevant applications. Presenting results for both vector systems and microprocessor-based systems, the book allows readers to compare the performance levels and usability of various architectures. As HLRS operates not only a large cluster system but also one of the largest NEC vector systems in the world, this book also offers excellent insights into the potential of vector systems. The book covers the main methods used in high-performance computing. Its outstanding results in achieving highest performance for production codes are of particular interest for scientists and engineers alike. The book comes with a wealth of color illustrations and tables of results.

Most problems in science and engineering require the solution of mathematical problems, most of which can only be done on a computer. Accurately approximating those problems requires solving differential equations and linear systems with millions of unknowns, and smart algorithms can be used on computers to reduce calculation times from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations?

Scientific Computing for Scientists and Engineers covers:

An introduction to a wide range of numerical methods for linear systems, eigenvalue problems, differential equations, numerical integration, and nonlinear problems; Scientific computing fundamentals like floating point representation of numbers and convergence; Analysis of accuracy and efficiency; Simple programming examples in MATLAB to illustrate the algorithms and to solve real life problems; Exercises to reinforce all topics.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.

This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourier Series and the Fourier Integral, Bessel Functions and Fourier-Bessel Series, and the Eigenfunction Method and its Applications to Mathematical Physics. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text. Richard Silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering. He has also added a bibliography, containing suggestions for collateral and supplementary reading. 1962 edition.

The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.

The Economist Numbers Guide is invaluable for everyone who has to work with numbers, which in today's commercially focused world means most managers. In addition to general advice on basic numeracy, the guide points out common errors and explains the recognized techniques for solving financial problems, analyzing information of any kind, forecasting and effective decision making. Over 100 charts, graphs, tables and feature boxes highlight key points, and great emphasis is put on the all-important aspect of how you present and communicate numerical information effectively and honestly. At the back of the book is an extensive A-Z dictionary of terms covering everything from amortization to zero-sum game. Whatever your business, whatever your management role, for anyone who needs a good head for figures The Economist Numbers Guide will help you achieve your goals.

The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.

The papers published here are grouped into three broad categories that cover mathematical and computational methods, research developments in information systems, and a detailed portrayal of ongoing work on documenting, restoring and presenting cultural monuments including the temples in Pompeii and the Banteay Chhmar temples of the Angkorian period in present-day Cambodia. Originally presented at a research workshop in Heidelberg, Germany, they reflect the rapidly developing identity of computational humanities as an interdisciplinary field in its own right, as well as demonstrating the breadth of perspectives in this young and vibrant research area.

Chapters 0–3 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material.

Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization ― the minimal spanning tree problem and the shortest distance problem ― are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix.

It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.

Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.

The book covers key foundation topics:

o Taylor series methods

o Runge--Kutta methods

o Linear multistep methods

o Convergence

o Stability

and a range of modern themes:

o Adaptive stepsize selection

o Long term dynamics

o Modified equations

o Geometric integration

o Stochastic differential equations

The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding, and it includes three chapters on analytical methods?explicit solutions, regular pertubation expansions, and singular perturbation series (including hyperasymptotics)?unlike other books that give only numerical algorithms for solving algebraic and transcendental equations. This book is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes, and as a reference for engineers and others working with difficult equations.

Algorithms exert an extraordinary level of influence on our everyday lives - from dating websites and financial trading floors, through to online retailing and internet searches - Google's search algorithm is now a more closely guarded commercial secret than the recipe for Coca-Cola. Algorithms follow a series of instructions to solve a problem and will include a strategy to produce the best outcome possible from the options and permutations available. Used by scientists for many years and applied in a very specialized way they are now increasingly employed to process the vast amounts of data being generated, in investment banks, in the movie industry where they are used to predict success or failure at the box office and by social scientists and policy makers.

What if everything in life could be reduced to a simple formula? What if numbers were able to tell us which partners we were best matched with – not just in terms of attractiveness, but for a long-term committed marriage? Or if they could say which films would be the biggest hits at the box office, and what changes could be made to those films to make them even more successful? Or even who is likely to commit certain crimes, and when? This may sound like the world of science fiction, but in fact it is just the tip of the iceberg in a world that is increasingly ruled by complex algorithms and neural networks.

In The Formula, Luke Dormehl takes readers inside the world of numbers, asking how we came to believe in the all-conquering power of algorithms; introducing the mathematicians, artificial intelligence experts and Silicon Valley entrepreneurs who are shaping this brave new world, and ultimately asking how we survive in an era where numbers can sometimes seem to create as many problems as they solve.

Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.

Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.

Optional sections designated as "excursion" and "exploration" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols.

Every number in this book is identified by its "field marks," "similar species," "personality," and "associations." For example, one field mark of the number 6 is that it is the first perfect number-- the sum of its divisors (1, 2, and 3) is equal to the number itself. Thus 28, the next perfect number, is a similar species. And the fact that 6 can easily be broken into 2 and 3 is part of its personality, a trait that is helpful when large numbers are being either multiplied or divided by 6. Associations with 6 include its relationship to the radius of a circle. In addition to such classifications, special attention is paid to dozens of other fascinating numbers, including zero, pi, 10 to the 76th power (the number of particles in the universe), transfinite and other exceptionally larger numbers, and the concept of infinity.

Ideal for beginners but organized to appeal to the mathematically literate, The Kingdom of Infinite Number will not only add to readers' enjoyment of mathematics, but to their problem-solving abilities as well.

Exploring the growing relevance of wavelets in the field of mathematics, Wavelet Theory: An Elementary Approach with Applications provides an introduction to the topic, detailing the fundamental concepts and presenting its major impacts in the world beyond academia. Drawing on concepts from calculus and linear algebra, this book helps readers sharpen their mathematical proof writing and reading skills through interesting, real-world applications.

The book begins with a brief introduction to the fundamentals of complex numbers and the space of square-integrable functions. Next, Fourier series and the Fourier transform are presented as tools for understanding wavelet analysis and the study of wavelets in the transform domain. Subsequent chapters provide a comprehensive treatment of various types of wavelets and their related concepts, such as Haar spaces, multiresolution analysis, Daubechies wavelets, and biorthogonal wavelets. In addition, the authors include two chapters that carefully detail the transition from wavelet theory to the discrete wavelet transformations. To illustrate the relevance of wavelet theory in the digital age, the book includes two in-depth sections on current applications: the FBI Wavelet Scalar Quantization Standard and image segmentation.

In order to facilitate mastery of the content, the book features more than 400 exercises that range from theoretical to computational in nature and are structured in a multi-part format in order to assist readers with the correct proof or solution. These problems provide an opportunity for readers to further investigate various applications of wavelets. All problems are compatible with software packages and computer labs that are available on the book's related Web site, allowing readers to perform various imaging/audio tasks, explore computer wavelet transformations and their inverses, and visualize the applications discussed throughout the book.

Requiring only a prerequisite knowledge of linear algebra and calculus, Wavelet Theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level.

High-performance computing plays an increasingly important role for numerical simulation and modelling in academic and industrial research. At the same time, using large-scale parallel systems efficiently is becoming more difficult. A number of tools addressing parallel program development and analysis have emerged from the high-performance computing community over the last decade, and what may have started as collection of small helper script has now matured to production-grade frameworks. Powerful user interfaces and an extensive body of documentation allow easy usage by non-specialists. Some of these tools have been commercialized, but others are operated as open source by a growing research community.