Bücher veröffentlicht von Springer New York

One of the authors' stated goals for this publication is to "modernize" the course through the integration of Mathematica. Besides introducing students to the multivariable uses of Mathematica, and instructing them on how to use it as a tool in simplifying calculations, they also present intoductions to geometry, mathematical physics, and kinematics, topics of particular interest to engineering and physical science students. In using Mathematica as a tool, the authors take pains not to use it simply to define things as a whole bunch of new "gadgets" streamlined to the taste of the authors, but rather they exploit the tremendous resources built into the program. They also make it clear that Mathematica is not algorithms. At the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The problem sets give students an opportunity to practice their newly learned skills, covering simple calculations with Mathematica, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numberical integration. They also cover the practice of incorporating text and headings into a Mathematica notebook. A DOS-formatted diskette accompanies the printed work, containing both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students. This supplementary work can be used with any standard multivariable calculus textbook. It is assumed that in most cases students will also have access to an introductory primer for Mathematica.

When I encountered the idea of chaotic behavior in deterministic dynami- cal systems, it gave me both great pause and great relief. The origin of the great relief was work I had done earlier on renormalization group properties of homogeneous, isotropic fluid turbulence. At the time I worked on that, it was customary to ascribe the apparently stochastic nature of turbulent flows to some kind of stochastic driving of the fluid at large scales. It was simply not imagined that with purely deterministic driving the fluid could be turbulent from its own chaotic motion. I recall a colleague remarking that there was something fundamentally unsettling about requiring a fluid to be driven stochastically to have even the semblance of complex motion in the velocity and pressure fields. I certainly agreed with him, but neither of us were able to provide any other reasonable suggestion for the observed, apparently stochastic motions of the turbulent fluid. So it was with relief that chaos in nonlinear systems, namely, complex evolution, indistinguish- able from stochastic motions using standard tools such as Fourier analysis, appeared in my bag of physics notions. It enabled me to have a physi- cally reasonable conceptual framework in which to expect deterministic, yet stochastic looking, motions. The great pause came from not knowing what to make of chaos in non- linear systems.

For the last eighteen years, I have been teaching an introductory course in as- trophysics. The course is intended for nonscience majors satisfying a general education requirement in natural science. It is a physics course with applications in astronomy. The only prerequisite is the high school mathematics required for ad- mission to the university. For a number of years, I used an astronomy text, which I supplemented with lecture notes on physics. There are many good astronomy texts available, but this was not a satisfactory state of affairs, since the course is a physics course. The students needed a physics text that focused on astronomical applications. Over the last few years, I have developed a text which my students have been using in manuscript form in this course. This book is an outgrowth of that effort. The purpose of the book is to develop the physics that describes the behavior of matter here on the earth and use it to try to understand the things that are seen in the heavens. Following a brief discussion of the history of astronomy from the Greeks through the Copernican Revolution, we begin to develop the physics needed to understand three important problems at a level accessible to undergraduate nonscience majors: (1) the solar system, (2) the structure and evolution of stars, and (3) the early universe. All ofthese are related to the fundamental problem of how matter and energy behave in space and time.

Now available in paperback. This is a text comprising the major theorems of probability theory and the measure theoretical foundations of the subject. The main topics treated are independence, interchangeability,and martingales; particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familar with measure theory as indicated by the guidelines in the preface. Special features include: A comprehensive treatment of the law of the iterated logarithm; the Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof;  development and applications of the second moment analogue of Wald's equation; limit theorems for martingale arrays, the central limit theorem for the interchangeable and martingale cases, moment convergence in the central limit theorem; complete discussion, including central limit theorem, of the random casting of r balls into n cells; recent martingale inequalities; Cram r-L vy theore and factor-closed families of distributions. This edition includes a section dealing with U-statistic, adds additional theorems and examples, and includes simpler versions of some proofs.

Object technology is maturing rapidly. One sign of that is the formality of the discussions that occur all around the world: at conferences, in newsgroups, in industry developer groups and in academe. One face of formality is metamodelling: seeking the model of the model that gives the rules by which the model itself is constructed. In OT terms, it means seeking the underpinning rules in a methodology in which, for instance, it is suggested we depict an aggregate structure using one particular notation. The questions that need answering are the semantics of that relation- ship and the constraints; i. e. , when and how it is allowable and what values/constructs are not admissible. In the past, these rules and constraints have been merely written down in textbooks and methodology manuals. Unfortunately, despite the plethora of au- thoring and word processing programs available, this leads to in- consistencies when cross-checks are not assiduously undertaken. There are few explict signs of metamodels in the published OOAD texts. In this book, we describe how we found those metamodels implicitly written into the methods. We formalized each of these in exactly the same way, using the same metalevel concepts and metarelationships. This book describes the fruits of those metamodelling labours, which we undertook as objectively as possible in 1995. In 1996 we then worked with the individual methodologists to ensure that we had not misinterpreted any par- ticular metamodels.

Complex dynamics is today very much a focus of interest. Though several fine expository articles were available, by P. Blanchard and by M. Yu. Lyubich in particular, until recently there was no single source where students could find the material with proofs. For anyone in our position, gathering and organizing the material required a great deal of work going through preprints and papers and in some cases even finding a proof. We hope that the results of our efforts will be of help to others who plan to learn about complex dynamics and perhaps even lecture. Meanwhile books in the field a. re beginning to appear. The Stony Brook course notes of J. Milnor were particularly welcome and useful. Still we hope that our special emphasis on the analytic side will satisfy a need. This book is a revised and expanded version of notes based on lectures of the first author at UCLA over several \Vinter Quarters, particularly 1986 and 1990. We owe Chris Bishop a great deal of gratitude for supervising the production of course notes, adding new material, and making computer pictures. We have used his computer pictures, and we will also refer to the attractive color graphics in the popular treatment of H. -O. Peitgen and P. Richter. We have benefited from discussions with a number of colleagues, and from suggestions of students in both our courses.

This book was prepared to present an integrated review of selected topics in Human Embryology. It is designed specifically for students who completed stan- dard courses in the various anatomical disciplines and who wish to review the developmental history of the major organ systems. This book will provide medical students with a highly suitable review for Step 1 of the United States Medical Licensing Exam (USMLE, Step 1). R. E. Coalson J. J. Tomasek Acknowledgments We wish to acknowledge the invaluable assistance provided by our colleagues at the University of Oklahoma Health Sciences Center during preparation of this review. In particular, we would like to thank Ms. Nancy Halliday for proofread- ing, Mr. Shawn Schlinke for preparation of the illustrations, Mr. Melville Vaughan for assistance with mounting the illustrations, and Ms. Trenda Tanner for assis- tance with the typing. Contents Preface to the Oklahoma Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1. Gametogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Female Reproductive Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3. Fertilization and Pregnancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4. Implantation and Formation of the Deciduae . . . . . . . . . . . . . . . . . . . . 15 5. Formation of the Placenta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6. Fetal Membranes and Umbilical Cord . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 7. Early Development of the Conceptus 26 8. Development of General Body Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 9. Nervous System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 10. Musculoskeletal System . . . . . . . . . . . :. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 11. Integumentary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 12. Oral Cavity and Development of the Branchial Apparatus . . . . . . . . 62 13. Differentiation of the Branchial Apparatus . . . . . . . . . . . . . . . . . . . . . . . 66 14. Face and Palate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 15. Digestive System and Mesenteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 16. Diaphragm and Body Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 17. Respiratory System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Programming is a fascinating and challenging subject. Unfortunately, it is rarely presented as such. Most often it is taught by "e;induction"e;: features of some famous programming languages are given operational meaning (e.g. a loop "e;goes round and round"e;), a number of examples are shown, and by induction, we are asked to develop other programs, often radically different from the ones we've seen. Basically we are taught to guess our programs, and then to patch up our guesses. Our errors are given the cute name of "e;bugs"e;. Fixing them becomes puzzle-solving, as does finding tricks that exploit or avoid poorly designed features of the programming language. The entire process is time-consuming and expensive. And even so, we are never quite sure if our programs really work in all cases. When approached in this way, programming is indeed a dull activity. There is, however, another approach to programming, an approach in which programs can be developed reliably, with attention to the real issues. It is a practical approach based on methodically developing programs from their specifications. Besides being practical, it is exciting. Many programs can be developed with relative ease. Problems which once were difficult can now be solved by beginners. Elegant solutions bring great satisfaction. This is our subject. We are interested in making programming an exciting topic!

Phaser is a sophisticated program for IBM personal com-puters, developed atBrown University by the author and someof his students, which enables usersto experiment withdifferential and difference equations and dynamical systemsin an interactive environment using graphics. This bookbegins with a brief discussion of the geometric inter-pretation of differential equations and numerical methods,and proceeds to guide the student through the use of theprogram. To run Phaser, you need an IBM PC, XT, AT, or PS/2with an IBM Color GRaphics Board (CGB), Enhanced GraphicsAdapter (VGA). A math coprocessor is supported; however, oneis not required for Phaser to run on the above hardware.

All students and professionals in statistics should refer to this volume as it is a handy reference source for statistical formulas and information on basic probability distributions. It contains carefully designed and well laid out tables for standard statistical distributions (including Binomial, Poisson, Normal, and Chi-squared). In addition, there are several tables of Critical Values for various statistics tests.

This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

We, the authors of this book, are three ardent devotees of chance, or some- what more precisely, of discrete probability. When we were collecting the material, we felt that one special pleasure of the field lay in its evocation of an earlier age: many of our 'probabilistic forefathers' were dexterous solvers of discrete problems. We hope that this pleasure will be transmitted to the readers. The first problem-book of a similar kind as ours is perhaps Mosteller's well-known Fifty Challenging Problems in Probability (1965). Possibly, our book is the second. The book contains 125 problems and snapshots from the world of prob- ability. A 'problem' generally leads to a question with a definite answer. A 'snapshot' is either a picture or a bird's-eye view of some probabilistic field. The selection is, of course, highly subjective, and we have not even tried to cover all parts of the subject systematically. Limit theorems appear only seldom, for otherwise the book would have become unduly large. We want to state emphatically that we have not written a textbook in probability, but rather a book for browsing through when occupying an easy-chair. Therefore, ideas and results are often put forth without a machinery of formulas and derivations; the conscientious readers, who want to penetrate the whole clockwork, will soon have to move to their desks and utilize appropriate tools.

The design of this book is based on teaching the ]SP (Jackson Structured Pro- gramming) methodology to undergaduates and postgraduates over a period of a number of years. I am grateful for the comments and feedback that have been provided by students who have taken these courses. The aim of the book is to provide readers with an understanding of the concepts behind the ]SP methodology in order that they may apply it for themselves; simply using the notation is not sufficient, it must be used appropriately. The answer to the question "e;Why is this wrong?"e; can lead to a greater understanding than a sim- ple response to "e;Is this right?"e;. I have included illegal structures as "e;under- standable mistakes"e; in the early sections for this reason. It is not necessary for readers of this text to have experience with any par- ticular programming language; indeed, one of the virtues of ]SP is that it is lan- guage independent. Examples have been given in Pascal, C and COBOL as these are languages which students of ]SP are likely to have met in the course of their studies, or will be meeting while they are learning ]SP. The COBOL lan- guage is widely used in industry in a ]SP development environment.