Book Description

Designed for the three-semester course for math and science majors, the Larson/Hostetler/Edwards series continues its tradition of success by being the first to offer both an Early Transcendental version as well as a new Calculus with Precalculus text. This was also the first calculus text to use computer-generated graphics (Third Edition), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CD-ROM format (Fifth Edition), and to be offered as a complete, online calculus course (Sixth Edition). Every edition of the book has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. The Seventh Edition also expands its support package with an all-new set of text-specific videos.

• P.S. Problem-Solving Sections, an additional set of thought-provoking exercises added to the end of each chapter, require students to use a variety of problem-solving skills and provide a challenging arena for students to work with calculus concepts.
• Getting at the Concept Exercises added to each section exercise set check students' understanding of the basic concepts. Located midway through the exercise set, they are both boxed and titled for easy reference.
• Review Exercises at the end of each chapter have been reorganized to provide students with a more effective study tool. The exercises are now grouped and correlated by text section, enabling students to target concepts requiring review.
• The icon "IC" in the text identifies examples that appear in the Interactive Calculus 3.0 CD-ROM and Internet Calculus 2.0 web site with enhanced opportunities for exploration and visualization using the program itself and/or a Computer Algebra System.
• Think About It conceptual exercises require students to use their critical-thinking skills and help them develop an intuitive understanding of the underlying theory of the calculus.
• Modeling Data multi-part questions ask students to find and interpret mathematical models to fit real-life data, often through the use of a graphing utility.
• Section Projects, extended applications that appear at the end of selected exercise sets. may be used for individual, collaborative, or peer-assisted assignments.
• True or False? Exercises, included toward the end of many exercises sets, help students understand the logical structure of calculus and highlight concepts, common errors, and the correct statements of definitions and theorems.
• Motivating the Chapter sections opening each chapter present data-driven applications that explore the concepts to be covered in the context of a real-world setting.

Reviews (17)

Calculus With Analytic Geometry
This is an excellent book with lots of examples. First a concept is introduced, then an example given, and then the student can work problems relating to the section to reinforce the concepts presented.

Easy to read, and nice progression of topics.

Good book but NOT for a math major
I have to agree that larson's calculus is a very comprehensive calculus text. It includes a lot of material and applications.

If you are going to selfstudy calculus, i have some advices:
1 Not every section is necessary. Some sections are mainly about applications in mechanical engineerings(actually, most applications). If you are not interested in ME, just skip them.

2 Don't go too fast. If you don't have time, just skip some sections of the end of each chapters. Especially at the end of the book. Chapter 14 is quite confusing. Read them slowly, understand piece by piece.

If you are a math major, particularly pure math, this is not a book for you. You need a book that talks more about theory.

Refer to other editions 0618141804
Checkout the 7th edition without a CD. Slightly different listing. Copied below....
* Hardcover: 182 pages ; Dimensions (in inches): 11.25 x 1.75 x 9.00
* Publisher: Houghton Mifflin Company; 7th edition (July 1, 2001)
* ASIN: 0618141804
* In-Print Editions: Hardcover (7th Bk&Cdr) | Paperback (4th) | All Editions
* Average Customer Review: Based on 16 reviews. Write a review.
* Amazon.com Sales Rank: 857,204
(Publishers and authors: improve your sales)

Good but problems were too easy
Not bad at all! I found the book's explanations pretty easy to understand.

The CD I really did not use. Some of you probably got more use out of it. But the text and diagrams are well enough done that I found the CD unnecessary.

The only criticism is that perhaps some of the problems could have been harder/more challenging.

Calculus
I've worked with several calculus books over many years and this is the CLEAREST and most staightforward of all. It makes the concepts seem so obvious and simple, where many other books make them appear arcane and mysterious (even to me, and I love this stuff.) It's a joy to read and work with. ... Read more

Book Description

This the shortest mainstream calculus book available. The authors make effective use of computing technology, graphics, and applications, and provide at least two technology projects per chapter. This popular book is correct without being excessively rigorous, up-to-date without being faddish. Maintains a strong geometric and conceptual focus. Emphasizes explanation rather than detailed proofs. Presents definitions consistently throughout to maintain a clear conceptual framework. Provides hundreds of new problems, including problems on approximations, functions defined by tables, and conceptual questions. Ideal for readers preparing for the AP Calculus exam or who want to brush up on their calculus with a no-nonsense, concisely written book.

Reviews (12)

Buy Swokowski's Calculus instead.
It's hard to believe that this puzzling, error-filled book is in its 7th edition.

I've been using the book for two semesters in a distance learning program. In this setting, where the reader needs to learn from the book rather than from an instructor, the book is inadequate. It's single strength - brevity - doesn't make up for its weaknesses: mystifying explanations, worked examples that omit important steps, and errors. Many times, this book made me laugh out loud when, after literally hours of effort, I finally understood what the authors were trying to communicate. There is no way I could have completed my classes had I not had Swokowski to refer to.

Beyond these weaknesses, the book is loaded with throw-away Horatio Algerisms ("Skill at this, like most worthwhile activities, depends on practice.") and hokey humor ("We have no desire to let this text suffer from the standard ailment of older texts, called 'revisionitis.'") These give the book a dated, musty feel: it's as if you are looking back at how calculus used to be taught 40 years ago.

Finally, six weeks into the first semester, the binding failed, converting the book into an expensive, 900-page, loose-leaf folder. Overall, not a book I enjoyed spending time with.

good but solutions manual is a must have
This is a good book for calculus. I usually go to class and do not undestand the professor because he speaks a different language then come home and figure it out from the book. The solutions manual is a must have for this course unless you have an excellent teacher or tudor. I find it helpful to check my problems half-way through completing them to make sure I am on the right track. And when I do not understand the text book instructions, the solutions manual usually puts me on track.

Classic "Attachable" book
Requirements for all books should be;

(a). being able to feel attachment for.
(b). clearly understandable to readers in the assumed level.
(c). benefitial to buy and read.
(d).[equivalent to (a), (b), and (c)]. unique.

This book satisfies all the above conditions [and (d)]. The style is very accessible to everyone who knows algebra. Math lovers who want to go beyond algebra should buy this book. Now, its particular uniqueness are the followings: mine has been separated into many stapled pages, though I personally like to sort them whenever I touch the book; examples are enough to illustrate introduced theorems. Of course, it doesn't end up with down-to-earth proofs. Wherever that might happen, it says so, and theorems that can not be proven with attainable knowledge are "left for advanced Calculus courses." Consequently, all presented proofs are quite rigorous in understandability.

(c) will follow for appropriate readers.

Good to start with, and will be one of your old friends.

Calculus 8th Edition Varberg, Purcell, Rigdon
This book stinks. Most of the positive reviews came from mathematicians not from students that have to study from this book! My fear of calculus is worsen after using this book. For someone who try to make it though college and working her tails off this book isn't helping. I'm not saying that it have to be easy, but there are so many erros in this book that I wasted my time trying to figured it out how to solve some problem that isn't even correct! Many students told me that have they not been taking calcus before, they probably won't pass the class. This book doesn't give good method of how it goes from point A to point B. There were a number of times where I would stare at the pages, wondering how the book came up with the answers, (was it magic). Another very annoying thing about this book is giving the easiest example problems that it can. This can really screw me over when it gives an oversimplified example for a theorem, and then in the problem set, there isn't any guide of how I can solve it. There were alot of problems that I couldn't even start because this book didn't give me adequate explanations or examples! Bottom line is, I don't think I'm that stupid, but this book really hurt myself esteem.

Perhaps the best out there...but that's not saying much...
I am in something of a unique position to critique this book. You see, I have, due to the fact that I attended different schools and therefore had different teachers for Calculus I, II, and III, been forced to buy three different ... calculus textbooks.

I feel that this book in many ways is the best. Keep in mind, however, that this isn't saying much. For the most part, calculus (and math in general) textbooks are somewhat difficult to learn from. This stems from the fact that we students like to see lots of worked out example in order to "get" it (buy Schaum's outline or REA's Problem Solver for lots of worked examples). In many cases, a calculus book like this will give you, perhaps, one example for a given procedure and leave it to you to deduce the rest.

Still, I like the fact that this book contains the material for Calc. I, II, and III. If nothing else, it saves us some money.

One final comment: as another reviewer on amazon has already noted, the binding on this book is quite poor. I have seen many other students in my class with books in which the pages have started falling out. Perhaps Prentice Hall should provide us with a better binding for a hundred bucks. ... Read more

Book Description

This text is designed for a one-quarter or one-semester graduate couse in Riemannian geometry. It focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the Riemann curvature tensor, before moving on the submanifold theory, in order to give the curvature tensor a concrete quantitative interpretation. The remainder of the text is devoted to proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, and a special case of the Cartan-Ambrose- Hicks Theorem. This unique volume will especially appeal to students by presenting a selective introduction to the main ides of the subject in an easily accessible way. The material is ideal for a single course, but broad enough to provide students with a firm foundation from which to pursue research or develop applications in Riemannian geometry and other fields that use its tools. Of special interest are the "exercises" and "problems" dispersed throughout the text. The exercises are carefully chosen and timed so as to give the reader opportunities to review material that hasjust been introduced, to practice working with the definitions, and to develop skills that are used later in the book. The problems that conclude the chapters are generally more difficult. They not only introduce new mateiral not covered in the body of the text, but they also provide the students with indispensable practice in using the ... Read more

Reviews (2)

Calculus and Analytic Geometry:Student Solution Manual, Part
The examples worked in this manual are a great help when used along side of the text book.A must have for everyone purchasing the test book.

Well done solution manual
It was very helpful and useful.This solution manual is a great way for students to check their work and learn from their mistakes.I found some (minor) typo errors that needed to be fix. ... Read more

Book Description

This text has been adopted at:

University of Pennsylvania, Philadelphia University of Connecticut, Storrs Duke University, Durham, NC California Institute of Technology, Pasadena University of Washington, Seattle Swarthmore College, Swarthmore, PA University of Chicago, IL University of Michigan, Ann Arbor

"In the reviewer's opinion, this is a superb book which makes learning a real pleasure."

- Revue Romaine de Mathematiques Pures et Appliquees

"This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises."

- Monatshefte F. Mathematik

"This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry."

- Publicationes Mathematicae

Contents: Differential Manifolds * Riemannian Metrics * Affine Connections; Riemannian Connections * Geodesics; Convex Neighborhoods * Curvature * Jacobi Fields * Isometric Immersions * Complete Manifolds; Hopf-Rinow and Hadamard Theorems * Spaces of Constant Curvature * Variations of Energy * The Rauch Comparison Theorem * The Morse Index Theorem * The Fundamental Group of Manifolds of Negative Curvature * The Sphere Theorem * Index

Series: Mathematics: Theory and Applications ... Read more

Reviews (1)

Excellent start~!
I have gone through many books about riemannian geometry, only to find that most of them are playing magic in front of me. When it comes to curvature and variation of energy (arc length), most of the book are just playing around with the notations without drawing any geometric insight. When defining Levi-Civita connections, many books simply list out 4 meaningless formulae. I was so happy to read this book since it explains everything in riemannian geometry in a clear and concise way. Theoretical facts and geometrical interpretations are both having their place in this book.

Only one thing to notice: This book is a basic elementary introductory text in riemannian geometry. Those who want to know more should consult other book. Yet, as a first book in riemannian geometry, this book is undoubtedly the best. ... Read more

Reviews (27)

Not a real calculus book
"Thomas and Finney is remarkably easy to read." I agree. It's easy to read because there is not much of substance there. It's basically a recipe cookbook. The authors are not mathematicians and don't truly understand some of the more advanced concepts (in the last parts of the book.)

The problems are not challenging, and do not lead to any new insights. For a book with great problems and insightful discussions of the key concepts, I recommend Swokowski's Calculus.

Yet it is a decent text for what it is intended to do, which is to teach engineers. That's why the two stars.

A fine Calculus Textbook
This is perhaps one of the finest high-school Calculus textbooks in existance. The first eight chapters of Thomas-Finney deal with calculus of functions of a single variable, going through what is commonly known as BC calculus. In addition to covering the essential topics of differentiation and integration, Thomas-Finney pays ample attention to the applications of the two. What results is a lucid text full of examples that ground calculus in the real world.

The second half of Thomas-Finney is devoted mainly to three-dimensional analytic geometry, multivariate calculus, and finally vector calculus. Partial derivitives, conic sections, vector-valued functions, and multiple integrals are just some of the topics covered in the second half. Here too, the book devotes ample time to examples and applications. The presentation of advanced concepts is top-notch.

The text is also interspersed with mathematical biography and sidebars that explain how to use CAS to help understand concepts. These are well presented and do not take away from the core math taught in the book.

I taught myself calculus during a summer using this book and without teacher intervention. It was the only one of five calculus textbooks that presented material clearly and simply enough to understand without outside help. In my mind, that's the highest compliment a math textbook can be given.

A manditory read for Science Majors
Use this book along with CDs on intermediate algebra Calc I and Calc II from www.thinkwell.com. as an excellent way to start your college studies.

I especially liked the depth he went into with conic sections. I for one had not had that much prior use for conic sections. Newton did. He invented calculus in order to answer specific questions and that involved conics. I like that the writer goes beyond using some of Newtons conclusions and goes into more depth. If you dont like depth, then you can read the first first half of the book and stop there (as is done by most nonscience majors). I have seen other calculus books and specifically bought this once because I dont like just memorizing formulas. I wanted to know more about why this subject was invented in the first place.

The amaising thing is that if you get through this book, you will be able to understand some math and physics known a few generations ago only to Newton and Libenez. Dont you feel smarter already? Even if you have read other calculus books, read this one!

Hmmm..2.55 stars only!
This book, in my opinion, is not a very good book especially if you are the kind who enjoys an intellectual challenge. But it takes up a hell of a lot of time making you work through silly repetitive exercises and never ever giving you a challenging problem!! And doesnt give you any sort of "insight" into calculus... In short its like the "The Ultimate Calculus Cookbook!" But cookbooks
dont really increase your math ability and may even suppress it!

But theres another side to the story.. if you are kind who is interested in just knowing the recipies and how to apply them( engineering students)...then this must THE BEST BOOK you can find. And this can also be very helpful if you find calculus "hard"!!

BUT LEMME WARN YOU AGAIN IF YOU USE UR BRAINS A LOT DONT GO FOR THIS BOOK.. U'LL SOON STAR GETTING DAMN BORED!!

A classroom user from LA
I tried using this book's previous edition for a correspondence course, and with a math major, a doctor, and a college grad with 2 B's his entire 4 yrs we couldn't make it make sense. I'm not stupid. I have a 4.0 in my math classes (all the way to multivariable, differential equations, and a discrete dynamical systems course). I recommend Calculus: Early Transcendentals ed. 4th by James Stewart.

Unfortunately my previous review is not up, and I don't remember all the specific reason's why it didn't make since, but I could add and subtract negative numbers before I could read and I learned Calculus without a problem from the AP Calculus book by the Princeton Review (I used this instead of Finney's Calculus book). ... Read more

Book Description

Loop groups, the simplest class of infinite dimensional Lie groups, have recently been the subject of intense study. This book gives a complete and self-contained account of what is known about them from a geometrical and analytical point of view, drawing together the many branches of mathematics from which current theory developed--algebra, geometry, analysis, combinatorics, and the mathematics of quantum field theory.The authors discuss loop groups' applications to simple particle physics and explain how the mathematics used in connection with loop groups is itself interesting and valuable, thereby making this work accessible to mathematicians in many fields. ... Read more

Reviews (1)

Last of A Dying Breed
This is a classic textbook which introduces students to the fundamentals of analytic geometry. In order to understand calculus, one must have a thorough background in analytic geometry. Unfortunately, the current trend in math publishing is to forgo this great subject and present students with an motley mix of topics in a course called PreCalculus. Trigonometry and analytic geometry end up getting the short shrift, with greater emphasis being placed on algebraic manipulation. This is a tragic loss for students on a number of levels. They need analytic geometry in order to succeed in even first semester calculus, and yet for many analytic geometry is relegated to the second or third semester of a calculus class in college, or in one chapter (or less) in a precalculus book! Also, the analytic geometry allows the high school student a glimpse of mathematical beauty, of how things in mathematics work together: that mathematics holds up as a subject and is not just an assortment of tricks for various situations. Hopefully, the trend will turn around and this will not be the last of a dying breed: that others will continue to offer and write expository works on this subject for the benefit of students who wish to continue on to higher mathematics. ... Read more

Book Description

This book is meant for a one year course in Riemannian Geometry. The approach the author has taken deviates in some ways from the standard path. Instead of discussing variational calculus, the author introduces a more elementary approach which simply uses standard calculus together with some techniques from differential equations. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stoke's theorem. Scattered throughout the text is a variety of exercises which will help the readers to deepen their understanding of the subject. ... Read more

Book Description

Reviews (2)

Great book to work through
This book contains a facsimile of the original version which runs nearly page for page with the English version. This is a true mathematical masterpiece. This was the supposed beginning of analytical Geometry(although it is now known that this was not true). It's a great book to work through that should be accessable to a high school student with some Geometry background. A Fantastic Book!

Enter Modern Mathematics
Using the locii problems investigated by Apollonius, Descartes employs the rules of his "method" in this treatise on geometry. By approaching geometrical problems with algebraic processes and vice versa, he manages to create point coordinate geometry. This work drastically changed the way in which we view conic sections as well as the very process of analytic inquiry. The math is mostly straightforward and more familiar to the reader than the works of the ancient mathematicians. It is not neccesary to have studied much previous mathematical works to gain a basic comprehension of Descartes' solutions. Attempting at most times to maintain the simple and straighforward presentation advocated by his method, Descartes will give you most of the basics that you need to understand the rest of the work. However, close concentration must be paid for the math to mean anything. It is easy to skip a step in a proof and find yourself completely lost. Given the proper patience, this work is invaluable for anyone who wants to see the origins of our method of thought today. Fascinating both as a mathematical treatise and as a perfect trial run for anyone wanting to follow the cartesian method of learning. ... Read more

Book Description

The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject.

Line and surface integrals
Divergence and curl of vector fields ... Read more

Reviews (2)

great introductory text
My first course on manifolds was based on this book, and I believe that it is the best introduction to the subject (especially for beginners). I thoroughly enjoyed it! I should also recommend Conlon's 'Differentiable Manifolds' (2ed, Birkhauser), as it is the perfect follow-up to Boothby. --A

Very Nice Nontrivial Introduction
This book is a careful treatment of the subjects in the title. It is an introduction, but it manages to cover quite a bit of ground with lots of examples to illustrate. One of it's distinguishing points is the way in which the concrete, coordinate based calculations are emphasized even while usually presenting the more abstract, coordinate free approach as well.

The book does a good job at stimulating those studying it to develop intuition. I found the book helpful when I was first studying the subject. ... Read more

Book Description

This unique book explores the connections between the geometry of mappings and many important areas of modern mathematics such as Harmonic and non-linear Analysis, the theory of Partial Differential Equations, Conformal Geometry and Topology.Much of the book is new. It aims to provide students and researchers in many areas with a comprehensive and up to date account and an overview of the subject as a whole. ... Read more

Book Description

This proven textbook provides an introduction to and practical applications of the basic concepts of calculus.The book's usefulness extends far beyond the classroom, as many students find that it serves as an excellent reference tool for advanced courses and graduate work. This edition contains more exercises requiring written responses, and more numerical examples and exercises. Each of these features is a result of the present-day teaching techniques, in which students are asked to contemplate the concepts more, and use technology where applicable.Calculus, 6e is ideal for students majoring in physical sciences, engineering, computer science or mathematics. As with earlier editions, the text fits a three-semester (four or five quarter) introductory calculus of one and several variables.It can also be used for a one-year course in single-variable calculus. ... Read more

Reviews (13)

Thorough and Well-Written
This text book on calculus is well laid out and was instrumental in my son's math education.The Larson-Hostetler book that my son used in his high school calculus class is terrible: the binding falls apart, the examples don't relate to the problem sets, and the authors view rote memorization of techniques above developing them.An example: integral(1/sqrt(a^2-x^2) dx).Why give a formula for this when all the student has to do is get it into a 1-(x/a)^2 form and use arcsin?Within the first year of the textbook adoption, Larson-Hostetler was falling apart, and my son's math teacher had already realized what a mistake he had made choosing the book.I concede that the student study guide for Ellis-Gulick is not pretty (or correct) all the time, but the textbook itself is phenomenal.The approach of using theory to generate specific results works well.Variable examples are not too common, and if more examples are needed, the study guide is available.Thorough, well-written, and cheap, what else do you need?

Made Mechanical Engineering Undergrad Program enjoyable
From 1987-1993 this book was the Calculus I,II & III textbook at Washington State University (WSU-Go Cougs).If I was able to solve every problem in the book and tutor others in Multivariable Calculus than I'm sure it was more my being well taught and less my skill in Mathematics.Yes Math was and still is one of my strongest subjects but having the Thomas Finney Calculus Edition 7 book alongside this textbook I will not hesitate to choose Robert Ellis & Denny Gulick for a much more thorough explaination of Theory with a broad variety of application that reinforce the theorems until one can do this stuff so well one can see the answer nearly as quick as one can simplify it down to its final result.

Thomas/Finney is an excellent addition and combined one should never be concerned with Differential Equations and Vector Analysis.

Its been 10 years and having switched to Computer Science I am now just getting back to applying Mechanical Engineering with CS and I can say I'm glad I had this background.

I didn't give the book 5 stars because no book on Mathematical Theory is Flawless.

The worst book I have ever bought
This book is by far the worst book I have ever had to buy for any class I have ever taken.I am not sure who is to blame here, because this is the second book that I have had to buy from this publisher.Both books really stink, but "Calculus With Analytic Geometry" makes road kill smell like the perfume section at Macy's.First of all the book is not laid out in a way that it clearly explains the topics.Second of all, and this probably should be first, there are very few examples, and the examples that are given use arbitrary variables, so the examples are hardly different than the definitions...so why have examples at all!I would strongly recommend "Calculus" Seventh Edition Larson-Hostetler-Edwards.While it costs nearly twice as much, it is more than worth the extra money if you want to pass your classes.As for this book, I threw it away, because I did not want someone else to become a victim of this book.

The best calculus reference books out there!
I got this book for a calculus class in high school and subsequently used it as a reference throughout all of my college math classes. My husband (a math major) usually ended up with this books sitting open beside him as he did all of his work through college.
It provides great examples, is easy to read, and has numerous excellent integral and derivitive tables.
I recommend this book to anyone currently taking calculus or more advanced math classes, or anyone who wants to touch up on their calculus skills.

really good book!!
I am a senior undergrad in mathematics at Michigan State University and I recently finished reading Ellis and Gulicks Calculus text.I found it to be a wonderful book.Their discussion on the vector calculus was particularly instructive.I learned a great deal about line integrals, surface integrals, Greens theorem, Stokes theorem and the Divergence theorem from this text. This was, of course, after I had read that particular chapter about four times.But, I am very convinced of the worthiness of this book. ... Read more

Book Description

In Riemannian geometry, measurements are made with both yardsticks and protractors. These tools are represented by a family of inner-products. In Riemann-Finsler geometry (or Finsler geometry for short), one is in principle equipped with only a family of Minkowski norms. So ardsticks are assigned but protractors are not. With such a limited tool kit, it is natural to wonder just how much geometry one can uncover and describe?It now appears that there is a reasonable answer. Finsler geometry encompasses a solid repertoire of rigidity and comparison theorems, most of them founded upon a fruitful analogue of the sectional curvature. There is also a bewildering array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. This book focuses on the elementary but essential items among these results. Much thought has gone into making the account a teachable one. ... Read more

Reviews (1)

Mainly for experts in Finsler geometry
The authors claim to turn the subject of Finsler geometry with this book
into a more teachable one and to have a candid style of writing.
This is definitly true for the first 50 pages, where the concepts of
Finsler geometry are very well explained and the exercises
are manageable and perfectly interrelated with the text.

Then the Chern connection and the curvature tensor of Finsler geometry
drop out of the heaven without any explanation of the ideas leading to these
constructions. So one has to derive them alone. In doing so older
texts on Finsler geometry like the Grundlehren text of Rund are more
helpful than this volume.

But the book was apparently prepared with great care. The layout must be called
beautyful and it really facilitates reading this book. Many references
to the literature and classical papers of the subject are included. So beginners,
which want to get a first aquaintance in Finsler geometry, find at least some help.

... Read more

Book Description

In this book, the authors take the viewpoint that number theory and fractal geometry can be fruitfully combined. They study, in particular, the vibrations of fractal strings (one-dimensional drums with fractal boundary) and zeros of zeta-functions.

In earlier publications on fractal and spectral geometry, the Riemann Hypothesis was studied and this hinted at the notion of complex dimension as a means to describe certain geometric properties of a fractal, such as its fractal (Minkowski) dimension or the oscillations in the volume of its tubular neighborhoods. This notion of complex dimension is now precisely defined in this book.

A central problem in contemporary mathematics-often expressed as "Can one hear the shape of a drum?" -- consists in describing the relationship between the shape (geometry) of a drum and its sound (its spectrum). In the case of fractal strings, the complex dimensions provide a unified description of the oscillations in the geometry and the spectrum. This description is provided by an explicit formula -- an analytical tool, originally developed for the proof of the Prime Number Theorem, which is extended here to apply to the zeta-functions associated with fractals.

The context of vibrating fractal strings enables the authors to put the Riemann Hypothesis in a geometric setting. This famous conjecture states that the zeros r in the critical strip 0 {\leq} Re {\rho} {\leq} 1 of the Riemann zeta-function all lie on the critical line Re {\rho} = . Here, this conjecture becomes an inverse spectral problem, and its interpretation in the language of fractal strings, which have complex dimensions with real part between 0 and 1, is "One can hear if a fractal string is Minkowski measurable provided that its fractal dimension is not ".

In the more restricted context of fractal Cantor strings, the complex dimensions of which form an infinite vertical arithmetic progression, the inverse spectral problem gets an affirmative answer. The number-theoretical interpretation of this insight is that the Riemann zeta-function does not have an infinite vertical arithmetic progression of zeros. This result is generalized to apply to many other zeta-functions.

This highly original, self-contained monograph will appeal to geometers, fractalists, mathematical physicists, and number theorists, as well as to graduate students in these fields. ... Read more

Book Description

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow.

The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgangers-that is, other objects that are extremely difficult to distinguish from it.

Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.

... Read more

Book Description

This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré–Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori. ... Read more

Reviews (1)

This book Rules!
This book is just so full of useful information and details. It has a lot of problems for which most of the solutions are supplied. Man, I love differential manifolds after spending some quality time with this book. ... Read more