Book:
Calculus and Linear Algebra. Volume 1: Vectors in the Plane and One-Variable CalculusAuthor:
Wilfred Kaplan, Donald J. LewisPages:
712Format:
djvuLanguage:
EnglishISBN10:
1425589138This book is the first of a two-volume text on calculus and linear algebra that is intended to provide enough material for a freshman-sophomore course. The principal objective is the integration of linear algebra and calculus.
Chapter 0, an introductory chapter, is intended for reference and review. Part of it (or all of it) can be studied in depth in accordance with the background of the students.
Chapter 1 introduces vectors in the plane; the presentation relies heavily on plane geometry.
Chapter 2 reviews and develops the idea of a function and presents the concept of limit as the first stage in developing the calculus. The least upperbound axiom is introduced at the end and it is used to prove the main theorems.
Chapter 3 is a systematic development of differential calculus, with some applications to geometry and to the sciences. The derivatives of sin x, cos x, ln x, and exp x are given with intuitive justification and are used often; rigorous proofs are deferred until Chapter 5. Accordingly, they are available for early use by students in engineering and physics. A student who has completed this chapter has a solid grounding in differential calculus. Vectors appear at several points, especially for curves in parametric form.
Chapter 4 is a similarly complete treatment of integral calculus. The introductory sections explain the ideas of definite and indefinite integrals. Then the main techniques for finding indefinite integrals are developed. Finally, the third and longest part is devoted to the definite integral, with some applications, especially to area and arc length. The definition of the integral is based on upper and lower estimates and leads to a simple proof of the main theorems for integrals of continuous functions. The Riemann integral is also defined and is shown for continuous functions to be equivalent to the definite integral. Throughout there is emphasis on computational procedures and computers.
Chapter 5 is a brief, rigorous treatment of the trigonometric, logarithmic, exponential, and related functions. This chapter can be omitted without affecting continuity, since all the main results are given elsewhere in the text.
Chapter 6 provides further applications of differential calculus—tests for maxima and minima, graphs of plane curves in rectangular and polar coordinates, Newton's method, Taylor's formula, and indeterminate forms. Much of this chapter can be studied immediately following Chapter 3 , if so desired, since integration appears only occasionally.
Chapter 7 presents applications of the definite integral to area in rectangular and polar coordinates, volumes and surface area of solids of revolution, moments of mass distributions, and centroids. Line integrals are introduced at several points. The role of integration in the physical sciences is well illustrated. There are discussions of improper integrals and the trapezoidal and Simpson's rules. Six sections are devoted to differential equations; they are included here: (1) because their development is a natural extension of
earlier theory and (2) to make them available at an early stage for students of engineering and physics.
Chapter 8 is concerned with infinite sequences and series, convergence tests, rearrangement and product theorems, power series, Taylor's formula and series, and Fourier series. Some reference is made to complex series. To a considerable extent, this chapter is independent of the others and can be studied earlier or later.
Numerous problems sets are provided throughout. Answers to selected problems appear at the end of this volume. 
Book:
Space-Time CodingAuthor:
Branka Vucetic, Jinhong YuanPages:
331Format:
PDFLanguage:
EnglishISBN10:
0470847573This book is intended to provide an introductory coverage of the subject of space-time coding. It has arisen from our research, short continuing education courses, lecture series and consulting for industry. Its purpose is to provide a working knowledge of space-time coding and its application to wireless communication systems. With the integration of Internet and multimedia applications in next generation wireless communications, the demand for wide-band high data rate communication services is growing. As the available radio spectrum is limited, higher data rates can be achieved only by designing more efficient signaling techniques.
Book:
Comparative Statistical Inference, 3 EditionAuthor:
Vic BarnettPages:
410Format:
DjvuLanguage:
EnglishISBN10:
0471976431This fully updated and revised third edition, presents a wide ranging, balanced account of the fundamental issues across the full spectrum of inference and decision-making. Much has happened in this field since the second edition was published: for example, Bayesian inferential procedures have not only gained acceptance but are often the preferred methodology. This book will be welcomed by both the student and practising statistician wishing to study at a fairly elementary level, the basic conceptual and interpretative distinctions between the different approaches, how they interrelate, what assumptions they are based on, and the practical implications of such distinctions.As in earlier editions, the material is set in a historical context to more powerfully illustrate the ideas and concepts.* Includes fully updated and revised material from the successful second edition* Recent changes in emphasis, principle and methodology are carefully explained and evaluated* Discusses all recent major developments* Particular attention is given to the nature and importance of basic concepts (probability, utility, likelihood etc)* Includes extensive references and bibliographyWritten by a well-known and respected author, the essence of this successful book remains unchanged providing the reader with a thorough explanation of the many approaches to inference and decision making.
Book:
Discrete Distributions: Applications in the Health SciencesAuthor:
Daniel ZeltermanPages:
306Format:
PDFLanguage:
EnglishISBN10:
0470868880There have been many advances in the theory and applications of discrete distributions in recent years. They can be applied to a wide range of problems, particularly in the health sciences, although a good understanding of their properties is very important. Discrete Distributions: Applications in the Health Sciences describes a number of new discrete distributions that arise in the statistical examination of real examples. For each example, an understanding of the issues surrounding the data provides the motivation for the subsequent development of the statistical models.
Provides an overview of discrete distributions and their applications in the health sciences.
Focuses on real examples, giving readers an insight into the utility of the models.
Describes the properties of each distribution, and the methods that led to their development.
Presents a range of examples from the health sciences, including cancer, epidemiology, and demography.
Features discussion of software implementation – in SAS, Fortran and R – enabling readers to apply the methods to their own problems.
Written in an accessible style, suitable for applied statisticians and numerate health scientists.
Software and data sets are made available on the Web.Discrete Distributions: Applications in the Health Sciences provides a practical introduction to these powerful statistical tools and their applications, suitable for researchers and graduate students from statistics and biostatistics. The focus on applications, and the accessible style of the book, make it an excellent practical reference source for practitioners from the health sciences.Review
"…should appeal to those in statistical research and biostatistical practice who have similar applications." (Technometrics, August 2005)
Book:
Differential Geometry of Varieties with Degenerate Gauss MapsAuthor:
Maks A. Akivis and Vladislav V. GoldbergPages:
278Format:
PDFLanguage:
EnglishISBN10:
0387404635In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.
Book:
Management of Data in Clinical Trials, 2 EditionAuthor:
Eleanor McFaddenPages:
208Format:
PDFLanguage:
EnglishISBN10:
0470046082A valuable new edition of the trusted, practical guide to managing data in clinical trialsRegardless of size, type, or complexity, accurate results for any clinical trial are ultimately determined by the quality of the collected data. Management of Data in Clinical Trials, Second Edition explores data management and trial organization as the keys to developing an accurate and reliable clinical trial. With a focus on the traditional aspects of data collection as well as recent advances in technology, this new edition provides a complete and accessible guide to the management structure of a clinical trial, from planning and development to design and analysis. Practical approaches that result in the collection of complete and timely data are also provided.While maintaining a comprehensive overview of the knowledge and tools that are essential for the organization of a modern clinical trial, the author has expanded the topical coverage in the Second Edition to reflect the possible uses of recent advances in technology in the data collection process. In addition, the Second Edition discusses the impact of international regulations governing the conduct of clinical trials and provides guidelines on ensuring compliance with national requirements.Newly featured topics include:
The growing availability of "off-the-shelf" solutions for clinical trials
Potential models for collaboration in the conduct of clinical trials between academia and the pharmaceutical industry
The increasing use of the Internet in the collection of data and management of trials
Regulatory requirements worldwide and compliance with the ICH Good Clinical Practice (GCP) Guidelines
Development of Standard Operating Procedures for the conduct of clinical trialsComplete with chapter summaries that reinforce key points as well as over one hundred examples, Management of Data in Clinical Trials, Second Edition is an ideal resource for practitioners in the clinical research community who are involved in the development of clinical trials, including data managers, research associates, data coordinators, physicians, and statisticians. This book also serves as an excellent supplemental text for courses in clinical trials at both the undergraduate and graduate levels.
Book:
Lectures on Elliptic and Parabolic Equations in Sobolev SpacesAuthor:
N. V. KrylovPages:
357Format:
DJVULanguage:
EnglishISBN10:
0821846841This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequisites are basics of measure theory, the theory of $L_p$ spaces, and the Fourier transform.
Book:
H-Infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game ApproachAuthor:
Tamer Basar and Pierre BernhardPages:
412Format:
PDFLanguage:
EnglishISBN10:
0817647562This book is devoted to one of the fastest developing fields in modern control theory - the so-called H-infinity optimal control theory. The book can be used for a second or third year graduate level course in the subject, and researchers working in the area will find the book useful as a standard reference. Based mostly on recent work of the authors, the book is written on a good mathematical level. Many results in it are original, interesting, and inspirational. The topic is central to modern control and hence this definitive book is highly recommended to anyone who wishes to catch up with important theoretical developments in applied mathematics and control.
Book:
Modern Differential Geometry for Physicists, Second EditionAuthor:
C. J. IshamPages:
289Format:
pdfLanguage:
EnglishISBN10:
9810235623I have found Isham's treatment of differential geometry very clear, while maintaining quite an abstract nature. Isham takes care to motivate his definitions and include comments where comments are due. No problems are included but the book sometimes omits the simpler results and lets you work them out by yourself. A very readable introduction indeed.
Book:
Growth Theory of Subharmonic FunctionsAuthor:
V. S. AzarinPages:
259Format:
PDFLanguage:
EnglishISBN10:
3764388854In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables.The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function.All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.
Book:
Berkeley Problems in Mathematics,1998Author:
Paulo Ney De SouzaPages:
443Format:
PDFLanguage:
EnglishISBN10:
0387949348This book is a compilation of approximately nine hundred problems, which have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph.D. program. Students who work through this book will develop problem solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. The problems are organized by subject and ordered in an increasing level of difficulty. This new edition contains approximately 120 new problems and 200 new solutions. It is an ideal means for students to strengthen their foundation in basic mathematics and to prepare for graduate studies.
ReviewFrom the reviews of the third edition:"This new edition has been updated with the most recent exams … . There are numerous new problems and solutions which were not included in previous editions. It is an invaluable source of problems and solutions for every mathematics student who plans to enter a Ph. D program. … this book will develop problem-solving skills in areas such as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra. … Tags with the exact exam year provide the opportunity to rehearse complete examinations. … This new edition has been updated with the most recent exams … ." (Zentralblatt fur Didaktik der Mathematik, November 2004)"The Mathematics department of the University of California, Berkeley, has set a written preliminary examination to determine whether first year Ph.D. students have mastered enough basic mathematics to succeed in the doctoral program. Berkeley Problems in Mathematics is a compilation of all the … questions, together with worked solutions … . All the solutions I looked at are complete … . Some of the solutions are very elegant. … This is an impressive piece of work and a welcome addition to any mathematician’s bookshelf." (Chris Good, The Mathematical Gazette, 90:518, 2006)"During the last twenty-five years problems from written preliminary examinations that are required for the Ph.D. degree at the Mathematics Department of the University of California, Berkeley, have been assembled. … The book is suited for students in mathematics, physics or engineering. Solutions are well explained, making the book valuable for self-study. The problems have a satisfactory high level, so the book is a rich resource of examples for lecturers as well, who need exercises … . This book certainly is to be recommended." (Paula Bruggen, Bulletin of the Belgian Mathematical Society, 12:4, 2005)
Book:
Neural Codes and Distributed Representations: Foundations of Neural ComputationAuthor:
Laurence Abbott, Terrence J. SejnowskiPages:
351Format:
PDFLanguage:
EnglishISBN10:
0262511002Since its founding in 1989 by Terrence Sejnowski, Neural Computation has become the leading journal in the field. Foundations of Neural Computations collects, by topic, the most significant papers that have appeared in the journal over the past nine years.
The present volume focuses on neural codes and representations, topics of broad interest to neuroscientists and modelers. The topics addressed are: how neurons encode information through action potential firing patterns, how populations of neurons represent information, and how individual neurons use dendritic processing and biophysical properties of synapses to decode spike trains. The papers encompass a wide range of levels of investigation, from dendrites and neurons to networks and systems.
Book:
Principles and Practice of Structural Equation Modeling, Third EditionAuthor:
Rex B. Kline PhDPages:
427Format:
PDFLanguage:
EnglishISBN10:
1606238760This bestselling text provides a balance between the technical and practical aspects of structural equation modeling (SEM). Using clear and accessible language, Rex B. Kline covers core techniques, potential pitfalls, and applications across the behavioral and social sciences. Some more advanced topics are also covered, including estimation of interactive effects of latent variables and multilevel SEM. The companion Web page offers downloadable syntax, data, and output files for each detailed example for EQS, LISREL, and Mplus, allowing readers to view the results of the same analysis generated by three different computer tools.New to This Edition
*Thoroughly revised and restructured to follow the phases of most SEM analyses.
*Syntax, data, and output files for all detailed research examples are now provided online.
*Exercises with answers, which support self-study.
*Topic boxes on specialized issues, such as dealing with problems in the analysis; the assessment of construct measurement reliability; and more.
*Updated coverage of a more rigorous approach to hypothesis and model testing; the evaluation of measurement invariance; and more.
Book:
Algorithms in Combinatorial Design TheoryAuthor:
C.J. Colbourn and M.J. ColbournPages:
342Format:
PDFLanguage:
EnglishISBN10:
0444878025The scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs.
Book:
Introduction to the Theory of Numbers 4th editionAuthor:
OXFORD UNIVERSITY PRESSPages:
438Format:
PDFLanguage:
EnglishISBN10:
0000000000THIS book has developed gradually from lectures delivered in a number of universities during the last ten years, and, like many books which have grown out of lectures, it has no very definite plan. It is not in any sense (as an expert cari see by reading the table of contents) a systematic treatise on the theory of numbers. It does not even contain a fully reasoned account of any one side of that manysided theory, but is an introduction, or a series of introductions, to almost all of these sides in turn.
Book:
Riemann, Topology, and PhysicsAuthor:
Michael I. MonastyrskyPages:
216Format:
DjvuLanguage:
EnglishISBN10:
0817647783This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics, The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Gottingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prominently throughout the literature. "The book is highly recommendable—for students and scientific workers—not only for the valuable information in it, but also for its spirit: history and higher mathematics are not dry here; they become alive and motivate further studies."—ZAA "This is a new translation of a book first published in English in 1987... Translated from Russian...it consists of two separate but related works. The first is an account of the life and work of Riemann, the second an account of several different topics in physics which are illuminated by the introduction of topological ideas. The discussion of Riemann is even better in the new edition. The mathematical account is richer and various errors have been corrected... The second half has been revised in a similar fashion... It has also been enriched by a new chapter which starts with von Neumann algebras and the work of Vaughn Jones... The book does three things very well: it reminds us of the range and depth of Riemann’s interests, which are emblematic of what the author values in mathematical physics; describes some of the many successes of Russian mathematicians and physicists; and it provides a lucid account of some modern work in which topology is genuinely applied. Books like this are vital for the health of mathematics and it is to be hoped that more will be written."---Mathematical Reviews
Book:
Differential Algebraic TopologyAuthor:
Matthias KreckPages:
208Format:
PDFLanguage:
EnglishISBN10:
0821848984This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinary singular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincare duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres. This book is based on courses the author taught in Mainz and Heidelberg. Readers should be familiar with the basic notions of point-set topology and differential topology. The book can be used for a combined introduction to differential and algebraic topology, as well as for a quick presentation of (co)homology in a course about differential geometry.
Book:
Theory of Stein Spaces (Classics in Mathematics)Author:
Hans GrauertPages:
254Format:
pdfLanguage:
EnglishISBN10:
3540903887Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician.' J. Eells in Bulletin of the London Mathematical Society (1980)'Written by two mathematicians who played a crucial role in the development of the modern theory of several complex variables, this is an important book.' J.B. Cooper in Internationale Mathematische Nachrichten (1979)
Book:
Computer Algebra Methods for Equivariant Dynamical SystemsAuthor:
Karin GatermannPages:
153Format:
DjvuLanguage:
EnglishISBN10:
3540671617This book starts with an overview of the research of Grbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
Book:
Robust Nonlinear Control Design: State-Space and Lyapunov TechniqesAuthor:
Randy A. Freeman and Petar V. KokotovicPages:
258Format:
PDFLanguage:
EnglishISBN10:
0817647589This softcover book summarizes Lyapunov design techniques for nonlinear systems and raises important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues, and they report their findings in this text. The researcher who wishes to enter the field of robust nonlinear control could use this book as a source of new research topics. For those already active in the field, the book may serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the techniques presented here.
