Group theory: Birdtracks, Lie’s, and exceptional groups

This monograph offers a derivation of all classical and exceptional semisimple Lie algebras through a classification of “primitive invariants.” Using somewhat unconventional notation inspired by the Feynman diagrams of quantumfield theory, the invariant tensors are represented by diagrams; severe limits on what simple groups could possibly exist are deduced by requiring that irreducible rep…

Non-linear finite element analysis of solids and structures: Volume 1: Essent…

This book was originally intended as a sequal to my book Finite Elements and Solution Proc.t.dures,fhr Structural Anufysis, Vol 1 -Linear Analysis, Pineridge Press, Swansea, 1986. However, as the writing progressed, it became clear that the range of contents was becoming much wider and that it would be more appropriate to start a totally new book. Indeed, in the later stages of writing, it …

Numerical Treatment of Partial Differential Equations

Many well-known models in the natural sciences and engineering, and today even in economics, depend on partial differential equations. Thus the efficient numerical solution of such equations plays an ever-increasing role in state-ofthe- art technology. This demand and the computational power available from current computer hardware have together stimulated the rapid development of numerica…

Numerical methods for engineers

It has been over twenty years since we published the first edition of this book. Over that period, our original contention that numerical methods and computers would figure more prominently in the engineering curriculum—particularly in the early parts—has been dramatically borne out. Many universities now offer freshman, sophomore, and junior courses in both introductory computing and numer…

An atlas of the global water cycle: Based on the IPCC AR4 Climate Models

Output data for the climate model simulations were available from the World Climate Research Programme’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multi-model dataset. The same database was used to prepare the 2007 IPCC 4th Assessment Report. Hence, the maps and tables presented here can be considered as the “detail” that underpins the water balance summaries presen…

Consistent Quantum Theory

Quantum theory is one of the most difficult subjects in the physics curriculum. In part this is because of unfamiliar mathematics: partial differential equations, Fourier transforms, complex vector spaces with inner products. But there is also the problem of relating mathematical objects, such as wave functions, to the physical reality they are supposed to represent. In some sense this second p…

Chaos: Classical and Quantum. I: Deterministic Chaos

Amotion on a strange attractor can be approximated by shadowing long orbits by sequences of nearby shorter periodic orbits. This notion has here been made precise by approximating orbits by prime cycles, and evaluating associated curvatures. A curvature measures the deviation of a long cycle from its approximation by shorter cycles; the smoothness of the dynamical system implies exponential fa…

Bisociative Knowledge Discovery: An Introduction to Concept, Algorithms, Tool…

We have all heard of the success story of the discovery of a link between the mental problems of children and the chemical pollutants in their drinking water. Similarly, we have heard of the 1854 Broad Street cholera outbreak in London, and the linking of it to a contaminated public water pump. These are two highprofile examples of bisociation, the combination of information from two differ…

Basic propability theory

This book has been written for a first course in probability and was developed from lectures given at the University of Illinois during the last five years. Most of the students have been juniors, seniors, and beginning graduates, from the fields of mathematics, engineering and physics. The only formal prerequisite is calculus, but an additional degree of mathematical maturity ma…

Average Case Analysis of Algorithms on Sequences

A timely book on a topic that has witnessed a surge of interest over the last decade, owing in part to several novel applications, most notably in data compression and computational molecular biology. It describes methods employed in average case analysis of algorithms, combining both analytical and probabilistic tools in a single volume.

Applied Analysis

Introduces applied analysis at the graduate level, particularly those parts of analysis useful in graduate applications. Only a background in basic calculus, linear algebra and ordinary differential equations, and functions and sets is required in order to fully understand the material presented.

Calculus in Context

Our point of view We believe that calculus can be for our students what it was for Euler and the Bernoullis: A language and a tool for exploring the whole fabric of science. We also believe that much of the mathematical depth and vitality of calculus lies in these connections to the other sciences. The mathematical questions that arise are compelling in part because the answers matter to other…

Calculus III

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book.

Calculus II

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book. Calculus students should not be tr…

Calculus I

The goal of this text is to help students learn to use calculus intelligently for solving a wide variety of mathematical and physical problems. This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book.

Algorithms

These notes assume the reader has mastered the material covered in the first two years of a strong undergraduate computer science curriculum, and that they have the intellectual maturity to recognize and repair any remaining gaps in their mastery. In particular, for most students, these notes are not suitable for a first course in data structures and algorithms. Specific prerequisites inclu…

Generic Polynomials Constructive Aspects of the Inverse Galois Problem

This book describes a constructive approach to the inverse Galois problem: Given a finite group G and a field K, determine whether there exists a Galois extension of K whose Galois group is isomorphic to G. Further, if there is such a Galois extension, find an explicit polynomial over K whose Galois group is the prescribed group G. The main theme of the book is an exposition of a family of �…

Fundamental methods of mathematical economics

This book is written for those students of economics intent on learning the basic mathe­ matical methods that have become indispensable for a proper understanding of the current economic literature. Unfortunately, studying tnathematics is. for many, something akin to taking bitter-tasting medicine- absolutely necessary, but extremely unpleasant. Such an at­ titude, referred to as "math anxie…

Algorithms and Data Structures

The book treats practically important algorithms and data structures. It starts with a chapter on data structure, then it treats sorting algorithms, concentrates on several examples of recursion, and deals with dynamic data structures.

Linear functional analysis

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Introduction to real analysis

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in…

Algorithms and Complexity

This is an introductory textbook, suitable for classroom use, on the design and analysis of algorithms, complexity, methods for solving problems on computers and the costs (usually in running time) of using those methods

Algorithms and Data Structures: The Basic Toolbox

This book is a concise introduction addressed to students and professionals familiar with programming and basic mathematical language. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, and optimization.

Algorithms and Data Structures: With Applications to Graphics and Geometry

Programming environments for motion, graphics, and geometry; Programming concepts - beyond notation; Objects, algorithms, programs; Complexity of problems and algorithms; Data structures; Interaction between algorithms and data structures - case studies in geometric computation.

Algorithms

This book evolved over the past ten years from a set of lecture notes developed by the authors while teaching the undergraduate Algorithms course at Berkeley and U.C. San Diego. Instead of dwelling on formal proofs, this book distills in each case the crisp mathematical idea that makes the algorithm work. In other words, this book emphasizes rigor over formalism. Undergraduate students in Compu…

Algebra: A Computational Introduction

This text is an introduction to algebra for undergraduates who are interested in careers which require a strong background in mathematics. It will benefit students studying computer science and physical sciences, who plan to teach mathematics in schools, or to work in industry or finance. The book assumes that the reader has a solid background in linear algebra. For the first 12 chapters el…

A Course on Mathematical Logic

This book is written on the occassion of the birth centenary year of Kurt G¨odel (1906–1978), the most exciting logician of all times, whose discoveries shook the foundations of mathematics. His beautiful technique to examine the whole edifice of mathematics within mathematics itself has been likened, not only figuratively but also in precise technical terms, to the music of Bach and dr…

A Dressing Method in Mathematical Physics

Generally, the term “dressing” implies a construction that contains a transformation from a simpler (bare, seed) state of a system to a more advanced, dressed state. In particular cases, dressing transformations, as the purely algebraic construction, are realized in terms of the B¨acklund transformations which act in the space of solutions of the nonlinear equation, or the Darboux transfor…

Finite Volume Methods for Hyperbolic Problems

This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wavepropagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are desc…

Examples in structural analysis

Prior to the development of quantitative structural theories in the mid-18th century and since, builders relied on an intuitive and highly developed sense of structural behaviour. The advent of modern mathematical modelling and numerical methods has to a large extent replaced this skill with a reliance on computer generated solutions to structural problems. Professor Hardy Cross1 aptly expr…

Exact Solutions for Buckling of Structural Members

In his book “Structural Design via Optimality Criteria”, George Rozvany articulates William Prager’s personal preferences in research on structural mechanics which may be summarized as: • Research should reveal some fundamental and unexpected features of the structural problem studied. • Closed form analytical solutions are preferable to numerical ones because the latter often obscu…

Engineering Analysis With ANSYS Software

This book is very much the result of a collaboration between the three co-authors: Professors Nakasone and Yoshimoto of Tokyo University of Science, Japan and Professor Stolarski of Brunel University, United Kingdom. This collaboration started some 10 years ago and initially covered only research topics of interest to the authors. Exchange of academic staff and research students have taken …

A Course in Financial Calculus

Financial mathematics provides a striking example of successful collaboration between academia and industry. Advanced mathematical techniques, developed in both universities and banks, have transformed the derivatives business into a multi-trillion-dollar market. This has led to demand for highly trained students and with that demand comes a need for textbooks. This volume provides a fir…

Computational methods for plasticity : theory and applications

THE purpose of this text is to describe in detail numerical techniques used in small and large strain finite element analysis of elastic and inelastic solids. Attention is focused on the derivation and description of various constitutive models – based on phenomenological hyperelasticity, elastoplasticity and elasto-viscoplasticity – together with the relevant numerical procedures and t…

Complex Variables and Applications

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9th ed.

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9780073383170

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QA331.7.C524 – 515’.9-dc23

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Calculus: Single Variable

Calculus is one of the greatest achievements of the human intellect. Inspired by problems in astronomy, Newton and Leibniz developed the ideas of calculus 300 years ago. Since then, each century has demonstrated the power of calculus to illuminate questions in mathematics, the physical sciences, engineering, and the social and biological sciences. Calculus has been so successful because o…

Calculus

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9th ed.

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9780547167022

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xxiii, 1142 Hlm.

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Calculus: A New Horizon

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6th ed.

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xxix, 1130 Hlm.

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Single Variable Calculus: Student’s Solutions Manual to accompany Jon Rogaw…

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978-0-7167-9866-8

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v, 741 Hlm.

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Calculus

The calculus course is a critical course for science, technology, engineering, and math majors. This course sets the stage for many majors and is where students see the beauty of mathematics, encouraging them to take upper-level math courses. In a calculus market-research study conducted in 2008, calculus faculty pointed out three critical components to student success in the calculus. …

Single Variable CALCULUS

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2nd ed.

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978-1-4292-4290-5

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iv, 810 Hlm.

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Calculus: Early Transcendentals

The art of teaching, Mark Van Doren said, is the art of assisting discovery. I have tried to write a book that assists students in discovering calculus—both for its practical power and its surprising beauty. In this edition, as in the first seven editions, I aim to convey to the student a sense of the utility of calculus and develop technical competence, but I also strive to give some app…

A Gr¨obner-Bases Algorithm for the Computation of the Cohomology of Lie (Sup…

Abstract We present an effective algorithm for computing the standard cohomology spaces of finitely generated Lie (super) algebras over a field K of characteristic zero. In order to reach explicit representatives of some generators of the quotient space Z k Bk of cocycles Z k modulo coboundaries Bk, we apply Gr¨obner bases techniques (in the appropriate linear setting) and take advantage of …

Student Solutions Manual for Mathematical Methods for Physics and Engineering

The second edition of Mathematical Methods for Physics and Engineering carried more than twice as many exercises, based on its various chapters, as did the first. In the Preface we discussed the general question of how such exercises should be treated but, in the end, decided to provide hints and outline answers to all problems, as in the first edition. This decision was an uneasy one as, o…

Spon’s First Stage Estimating Handbook

Assessing the total cost of a construction project is a continuous process that commences when the client asks his professional advisors what it will cost. It ends when the cheque for the release of the last portion of the retention is paid and the final account is settled. Whether a project is profitable or not can often depend on decisions taken at the first stages of its life. The people…

The Proceedings of the 12th International Congress on Mathematical Education …

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9783319126883

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Mathematical Methods: For Students of Physics and Related Fields

This book is intended to help bridge the wide gap separating the level of mathematical sophistication expected of students of introductory physics from that expected of students of advanced courses of undergraduate physics and engineering. While nothing beyond simple calculus is required for introductory physics courses taken by physics, engineering, and chemistry majors, the next level of…

Mathematical Methods for Physics and Engineering

Since the publication of the first edition of this book, both through teaching the material it covers and as a result of receiving helpful comments from colleagues, we have become aware of the desirability of changes in a number of areas. The most important of these is that the mathematical preparation of current senior college and university entrants is now less thorough than it used to be…

Mathematical Methods for Physicists

Through six editions now, Mathematical Methods for Physicists has provided all the mathematical methods that aspirings scientists and engineers are likely to encounter as students and beginning researchers. More than enough material is included for a two-semester undergraduate or graduate course. The book is advanced in the sense that mathematical relations are almost always proven, in a…

Mathematical Methods for Physicists: A Comprehensive Guide

This, the seventh edition of Mathematical Methods for Physicists, maintains the tradition set by the six previous editions and continues to have as its objective the presentation of all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. While the organization of this edition differs in some respects from that of its…