Book Description
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. The second edition contains some additions to the text and references. Some parts are completely rewritten. ... Read more

Customer Reviews (1)

Asuperb harmony
Just about every time I open this book I either find the elucidation of a concept which either I have always wanted to learn; or see the connection between ideas which I have known for some time.
This valuable work unifies a number of topics which are of great importance to the mathematical practitioner. Each of these is treated not merely as noetic nicety but as tool for applying the theory.
The thorough and extensive treatment of continguity theory for point processes and convergence of stochastic integrals are especially well done and satisfying.
Although even atwo semester course does not suffice to cover the entire book I nevertheless feel that the dedicated educator should be able to delineate a number of threads for two one-semeter graduate courses. ... Read more

Book Description
A revision of McGraw-Hill's leading calculus text for the 3-semester sequence taken primarily by math, engineering, and science majors. The revision is substantial and has been influenced by students, instructors in physics, engineering, and mathematics, and participants in the national debate on the future of calculus. Revision focused on these key areas: Upgrading graphics and design, expanding range of problem sets, increasing motivation, strengthening multi-variable chapters, and building a stronger support package. ... Read more

Customer Reviews (12)

Excellent if it si still as good as the edition from 20 years ago
I can only review an edition of this book dated at least 20 years ago. I bought it when I was in high school (in 10th grade actually) and used it by myself to learn calculus.

When I got to the actual class, I knew basicaly everything and I mean everything that the teacher taught us in 12th grade. I didn't even need anything for my first 2 university level courses in calculus, just took the notes in the class and that was enought to get A+ in both, differential and integral calculus (course 1) and Vetor calculus.

The explanation of derivatives was great and my teache just enhanced my knowledge there. The book was specially great when teaching integration. There was a chapter devoted to that. I skept the section about using tables for integration and only learned a few basic formulas. The book taught the methods and still now, after 20 years, I can integrate pretty much anyhing without any difficulty at all.

If the current edition is as good as it was 20 years ago, then this book is definitely a winner.

A totally ineffective method of teaching Calculus
I am a student at CSUSB and I have had to use this book for 3 quarters of Calculus.At the school all the professors say the book is horrible and can't wait until the department changes. In 2005 they finally changed the book to Caculus by Larson, Hostetler, Edwards. It is ironic in desperation I asked a fellow student how he was handing the problems of this book. He said that he borrowed a book from his friend who said the book was excellent. It turned out that it was the book written by Larson, Hostetler, and Edwards. I then obtained a copy for myself and found the book to be excellent.

Stein's and Barcellos's book has very poor explanations in the chapters and very few examples to explain to you the concepts. Whereas Larson's book has excellent explanation of concepts and follows it up with good examples that make the concepts easy to understand.At the present we are studying the disk and washer methods of finding volume. Stein covers these topics in approximately 3-4 pages of very poor explantions.The Larson book had 2 chapters on the subject and 9 pages just on the 2 methods. I currently have an A in the last quarter of Calculus and I attribute that to using the book by Larson.

As you can see I can not say enough bad about the book by Stein and Barcellos. Good luck and I hope you make the right choice, but don't buy this book.

Brilliant method
This book is literally the best basic calculus text you can possibly get.Anyone wanting to start learning calculus NOW should get this.No real previous mathematical knowledge is necessary.There are several appendices on algebra and series etc.The book discusses trigonometry, so you can learn the book practically without knowing a thing.The "feeling" of the book is inexplicable.Reading this book really gave me an true understanding of basic calculus.Excellent for people like me who need proofs (especially visual ones) have a solid grasp on concepts. If your only goal in learning calculus is to do well on examinations, this book is definatelynot for you.You should get "Calculus for Dummies" or something like that.The great thing about the text is that it appeals to almost everyone.If there is a certain chapter you don't care for or doesn't matter to you, for example on methods of graphing, you can just skip it, and it will not do any harm.Highly intelligently organized.If you want some help in you physics class on basic vector algebra, just turn to chaper 18 and just read! This bookis full of applications, which is great.It also has several historical notes.The colors make the book very engaging to read.Unless your colorblind, this will help engage your interest.Very adequate spacings on the paper as to keep you clearheaded and focused.The drawings rival those of Picasso.They show calculus to be a LIVELY subject.The examples (inside the chapters) are very helpfull.Stein offers several suggestions on how to solve certain problems. Its a shame; this book does not attract the amount of attention it deserves.I did get stuck a couple times; but that is inevitable.Definately get this one: its a gem to have.I can understand how some people would hate this book; its not very concise.That should not be a hindrance.If you feel there is no need to read on about a subject, skip some pages.At the end of chapters it all comes together with a summary of the most important concepts.The book prepares you for study of calculus-based sciences such as physics, and for more advanced mathematical topics as well.I worship this book.

excellent for basic calculus ....
This book is the best place to start to learn calculus. It starts from very basic principles and also contains some more advanced stuff like Stokes Theorem etc. Some readers may find that the book contains too many basic trivial explanations, but I see this as a strength. When you start learning calculus, I think it is a good idea to explain even the trivial, to make sure that you have a good understanding of really everything. I am sure that most readers will benifit from this, even those already having some more advanced math knowledge. Yes : even this latter group will appreciate the benifits of this book, they can always skip some explanations but will benifit from the very clear exposition of more advanced concepts like Stokes Theorem etc ... Myself for instance, I like the more rigorous and abstract math like "real mathematical analysis", but when I need to refresh some calculus and geometry techniques, this book is really the best to sharpen my intuition and understanding of calculus.
Another excellent feature of the book : this book should serve as an example for the layout of math books : it contains a lot of spacing (handy to make personnal annotations), contains a lot of examples, and contains a lot of excellent pictures illustrating a concept... Also some nice anecdotes are added to keep the reader interested. I wish all math books were like this.
If math is not your strongest skill and you need to learn some higher calculus this book will be your excellent companion helping you to gain the insight and intuition you need. If you are busy with more advanded and abstract math, this book also has something to offer to you : this book serves as a fallback point for sharpening your mathematical intuition and refreshing some concepts that you might have forgotten.
Small drawbacks are : -Some more advanced concepts (like Stokes Theorem) are very well explained, but others are explained without proof (convergence of series...) or with simplified proofs (for instance limited to two dimensional cases, though excellent again to gain mathematical intuition). Maybe this is acceptable for a calculus course, but may disappoint the reader who is looking for rigour.

Conclusion : perfect book to gain insight in calculus, it suits well on the shelf of everybody busy who needs calculus...

The worst math book ever
If you have to buy it, buy it. Otherwise, avoid it like the plague.I was forced to buy it because this ass was a professor at UC Davis and made all Davis math students buy it.Even the other professors hated it, but we were stuck with it becuase of his tenure. ... Read more

Book Description

One of the most diverse branch of mathematics, complex variables proves enormously valuable for solving problems of heat flow, potential theory, fluid mechanics, electromagnetic theory, aerodynamics and moany others that arise in science and engineering. As taught in this exceptional study guide, which progresses from the algebra and geometry of complex numbers to conformal mapping and its diverse applications, students learn theories, applications and first-rate problem-solving skills.

Customer Reviews (12)

Even in mathematics, Intuition remains the source of truth
This book, although providing solutions and/or answers to all problems, still focuses on a very formal treatment of complex variables.The selection of problems is highly abstract.It remains up to the reader to develop their own sense of direction in the realm of complex numbers.Instead of problems that focus on the final validation of truth in complex numbers, more problems of an applied nature would have been helpful.Even if advanced physics would need to involved.

good reference book...
more of a handbook with the important theorems and formulas.
the examples and excercise are well conceived.

This bookno longer need a review
This book no longer need a review. It is so popular among the academics and the students for its lucid way of treating complex variablesI used this book as my reference for complex variables for the graduate mathematical methods course. This book helped me a lot with lots of examples and interesting exercise problems. It is also verygood for students who wants to have a fast glance at the concepts. Overall, I would strongly recommend this book to any student who wants to learn complex variables in the most simple way with all kinds of examles to solve problems and score high grades.

Great cheap text on complex variables for the mathematician
Complaints seem to abound in regard to how this Schaum's outline is too theoretical and has too few problems involving applications. You must remember that this particular outline was meant to complement an undergraduate mathematics course in complex variables, not an applied physics or engineering course using complex variables. Thus, the purpose of this book is to develop the calculus of functions of a complex variable.

This is one of those Schaum's outlines that has sufficient explanation, figures, and examples that it can double as a cheap textbook on the subject. However, remember that the emphasis is on theorems and proofs of theorems versus applications. However, there are some sections of the outline that are excellent at illustrating some applications of the subject matter. In particular, chapter 9, "Physical Applications of Conformal Mapping" contains applications from physics using those equations that are defined by a potential, including the electromagnetic field, the gravitational field, and, in fluid dynamics, potential flow, which is an approximation to fluid flow assuming constant density, zero viscosity, and irrotational flow. By choosing an appropriate mapping, the outline demonstrates clearly how one can transform the inconvenient geometry of one set of these equations into a much more convenient one. The equations are solved in this new "convenient" geometry, and then transformed back into the old one. One example of a fluid dynamic application of a conformal map that is detailed is the Joukowsky transform.

If you are not looking for a book to complement a mathematics course on complex variables and you are looking for something more applied, you might look at "Complex Variables: Introduction and Applications". That book has the first part dedicated to theory and the second part dedicated to applications at a reasonable price.

too theoretical
I bought this thinking it would help me understand complex variables, complex integration and differentiation. As another customer commented there are wayyyy to few solved concrete problems, all of the solved problems are proving some theorem. This is useless. I can look those proofs up elsewhere. What I expected was concrete solved problems, there are very very few of those. All in all I am rather dissapointed with this book. Not recommended unless you are looking for many proofs of just theorems. ... Read more

Book Description
This easy-to-understand calculus study aid is ideal for those who are new to the subject. It offers a well-illustrated, step-by-step introduction that moves along at an easy-to-keep-up-with pace. Use it with your textbook or for independent study to improve your comprehension and boost your grades. It features 226 solved and 513 skill-building supplementary problems--more than other study guides. Whether you simply want to feel confident at test time or build a solid foundation in calculus for more advanced math, science, and engineering course, Schaum's Outline of Beginning Calculus is students' first choice.level of Ayres/Mendelson, Calculus, 3/e. This will make up the calculus segments of one-semester liberal arts courses and the various one-semester Calculus courses for business or life sciences. This book will also address weaker students in general freshman calculus and high school advanced placement courses. Theory is restricted to fundamentals of differentiation and integration (single-variable) and the solved problems, with no steps ommitted, include reviews of algebra. This updated edition will continue the excellent sales record of the first edition and will include: problems suitable for graphing calculators and existing problems adapted to involve calculator use; emphasis on aogorithmic aspects of Calculus; Newton's method will be given a separate section, a section various approximation techniques for integration, Simpson's Rule the Midpoint rule; a section that presents the traditional treatment of exponential and logarithmic functions, which method some textbooks have gone back to. ... Read more

Customer Reviews (6)

okay
the pages were a little bent when i received it, but it was otherwise in good condition

Just the best book for self study and review
This book can help an alien to math understand a calculus concept.

Good as supplemental text book, NOT good as primary textbook
There are not enough examples to explain everything you would need to know.I've found I had to go to the web or other more basic Calculus books many times to try to solve some of the problems in there.There are better books out there for those of us looking for complete breakdown of the problems and better explanations.

An excellent introduction and review of Calculus ......
I trudge back to this book again and again, being embarassed at having forgotten some basic idea or technique.This is an excellent supplemental text to a formal Calculus textbook like "Calculus " by Stewart.The writing is lucid and ideas are explained with the novice in mind. I find that reading this book first BEFORE getting into a meatier textbook helps me understand the material.

My experience has been that if I do not "do calculus" at least twice a week I forget the techniques (not ideas) almost immediately.Therefore, if you want a review of Calculus this book is a great tool.If you are new to calculus this book will help you understand important concepts like differentiation vs integration.I also found that reading pertinent chapters in Selby's "Geometry and Trigonometry For Calculus" and then reading related material in this book is a tremendous help.

Another strong point is that for us over 50 the font size and book layout is easy on the eye.So whether you are a novice or someone who has not had the chance to use Calculus in a while; or someone "brand new" to Calculus,get this book.An excellent resource for learning and entertainment!!

Very good value for the budget-minded math student
Elliott Mendelson does an excellent job of presenting basic calculus concepts in an inexpensive book.His explanations are very clear, and the book is actually fun to use.Perhaps my only criticism is that this bookdoes not use color which often helps to clarify figures of graphs, butblack and white figures are to be expected in an outline.If you'reinterested in a supplement to your text or if you want a book forself-study, I strongly recommend "Beginning Calculus." ... Read more