Book Description
This text comprises Chapters 0-7 of Larson and Edwards' Calculus: An Applied Approach, 6/e. For a complete description of this text's features, refer to the entry for that text.
Customer Reviews:
Easy book.......2007-03-27
Easiest calculus book ever, wish it had thorough answers in the back of the book.
Not that helpful for trying to teach yourself.......2003-09-21
This book assumes a knowledge that not everyone will have. It has an algebra/pre-calc review section, but the review is very basic (ie what an exponent is). The problems require you to remember about negative exponents and cube roots and whatnot.
The explanation parts are very simple and the problems are much more complex.It's hard to make the connection, and the answers in the back don't explain anything. (Don't buy the solutions manual - it's not any more help.) The answers are also simplified in inconsistent ways, so it's sometimes hard to use even if you have the problem right. Calculus for Dummies was more helpful, and explains a little better. It's still not as in depth as the problems in Brief Calculus, though.
(Sidenote: I'm "trying to teach myself" because my professor is incomprensible and has illegible writing as well.)
Yeah, maybe on the cover.......2002-03-01
I used this book for my high school curiculum and will use the exact same book in my collge calc class. And I have enough experience to say that, although this book seems to be user-friendly, it is by far not. The layout is relatively simple, however is not very in depth. Additionally, this book smashes together several large topics together with very little explanation. This lack of explanation, in turn, makes some of the problems practically impossible due to the fact that you haven't seen any problems like them before. All in all forget this book, and pay attention to your instructor.
Student Friendly Text.......2000-09-07
This is a great book. It helped me pass my business calculus course.
Excellent for Business majors.......2000-04-18
This text is an excellent text for business majors of all disciplines. It features real world applications and examples to learn from, and comprehensive excersises to demonstrate mastery of the material. The text is jam packed with helpful and clear illustrations and pictures.
Book Description
Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.
The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.
Customer Reviews:
Average Elementary Numerical Analysis Text.......2007-07-10
Just so you know the source of this review and whether or not you should bother trusting me (hmm..maybe not?):
Ph.D. student in Statistics at Iowa State University.
B.S. Computer Science
B.A. Mathematics
Research areas: numerical analysis, analysis of large data sets, stochastic processes
Former research areas: truth maintenance systems, microarray analysis, parallel computing
Note: Not a plug. I like my job.
First off, the book's title is very appropriate. It requires extensive knowledge of calculus and linear algebra, but it uses a fairly non-rigorous "easy" approach to numerical analysis. It's not advanced enough for use in a graduate level class, even for non-majors, but it is very useful and appropriate for sophomore/junior undergraduates. Even though the approach is somewhat non-rigorous, the book doesn't avoid proofs, and though a more advanced mathematician or computer scientist would see holes, it's a book that surely feels complete to most undergraduate math/cs majors/minors.
The explanations and proofs are definitely not perfect. The proofs leave out steps that they assume readers should find obvious. Academic types like Atkinson who have spent years of research in this field often forget just how difficult these concepts are to undergraduates, so some of these "obvious" steps are not going to be obvious to all readers and should not have been omitted. Mixed in with the proofs are some straightforward explanations, but often they are not in layman's terms and I remember scratching my head at times. So I would give the explanations and proofs a C-/D+.
The author does a better job at the exercises. This is a difficult topic, so you don't want to have to work out problems that are too difficult, but some challenge is required to attain mastery of the subject. I think that this book accomplishes that goal. The problems are rarely overly difficult, and though most would be trivial to professors or professionals, they provide enough challenge to undergraduates who are new to the field. The author also does a good job at choosing problems which are relevant. This is nice since many (most, actually) mathematics books include many problems which look contrived and whose results seem meaningless. Anyways, I give the exercises an A.
The content is decent, but a LOT is left out. Traditionally, a two-semester sequence includes a class on numerical analysis as it relates to differential equations and a class on numerical analysis as it relates to linear algebra. Preceding discussion of either one of these topics is a necessary discussion of general iterative methods and analysis of computational error. This book covers all of those topics but none of them extensively. For a one-semester overview, the content is perfect and includes more than enough material. For a traditional two-semester sequence, this book is a bit skimpy. As stated before, the book is also not appropriate for graduate level classes. So if you haven't learned functional analysis, then don't worry--this book is for you. I give the content a B-/C+.
I was a bit disappointed with the computing examples. The examples were not poorly chosen, but there were not enough of them. Also, I think that they should have used a programming language which is easy to read even if you don't know the language. I give the computing examples a D+.
Even though I said that this book is inappropriate for graduate classes, it might serve as a nice reference for graduate students. I always skim through it as a review before certain classes. Though it can be nice as a refresher, a graduate student would probably be happier with something more rigorous like Peter Linz's "Theoretical Numerical Analysis: An Introduction to Advanced Techniques" (overview - very short) or Kendall Atkinson's (the author who wrote this book) "Theoretical Numerical Analysis: A Functional Analysis Framework".
Final note: To those who complain that it requires extensive knowledge of calculus, was that not a prerequisite at your school? The calculus required to understand this book and work the problems is not at a high school level, but it's nothing that a student who has passed college univariate and multivariate calculus shouldn't be able to handle.
2.5 stars
will need supplimentation.......2004-09-16
Of course this book assumes (advanced?) knowledge of Calc 1 & 2 as well as linear algebra and preferably Dif. EQ. These are all prerequisites for the course in which the book is used. That being said, it is quite annoying when the book *completely* skips over intermediate steps involving calculus leaving the student scratching his head. I find myself with my nose more in my Calc. books trying to figure out what the steps leading to the answer rather than learning Num. Analysis. Would have been nice if at least some intermediate steps were added to most problems, but hey, this is college and hand holding should not be assumed.
There are 3 main gripes which contribute to the low rating.
1. The Cost. For the price of the book, (considering the way the material is presented (see 2.) there should be a solution manual bundled with it. (see 3.)
2. The explanations of the material is cut and dry and not verbose at all, [which adds 2 stars to an original 0 rating] however, there is usually only one example for a topic, followed by 10-15 excercises associated with that topic. This often leads to pure frustration and having to "google" for supplimentary material to help me through the problems due to the fact that the example is far more elemantary than the excercises.
3. Lack of solutions. Coupled with the lack of GOOD examples is the lack of solutions for the excercises you just struggled to drudge through. Chapters that typically have 10-15 problems, some with sub-problems in them usually have 5 or so solutions in the back. (so if there is say question 1, parts a-h, question 2, question 3 a - k....there would be a solution for question 1 part c, question 3 part g...).
If you take this course and this is the required text, pray that your professor has great lectures and notes(neither of which my prof. has) or be prepared to spend many hours on google looking for other references.
Maybe i'm just biased..........2002-01-29
I'm biased because i had the good fortune to take Intro to Numeric Analysis from Ken Atkinson himself. I beta-tested this edition of the text, so my copy is in a loose-leaf binder.
Some reviewers have complained that the book is difficult because examples are in FORTRAN rather than C. I disagree. The real meat of the book is written in mathematical form; what source he provides is merely a convenience. When i took his class, most of the students (myself included) implemented in C rather than FORTRAN. No problem, because he was looking for correct results, not reviewing code.
And yes, this book assumes a solid knowledge of calculus, linear algebra, basic differential equations, and discrete logic. Did you think you'd be able to code mathematics without *understanding* it? If you understand the math in the first place, his implementations are very clear. If you don't understand the math, no amount of clarity will save you.
The real beauty, for me, was how he logically built a progression of topics, with each step providing the foundation for the next one. It was like seeing two years of college math in miniature.
it makes numeric sense.......2001-05-09
i had the pain to use this book for my undergrad. coursework for a 200 level class at Cal Poly. Contrary to the other reviewers, i believe the exercises are mediocre, and the material presented lack depth to provide a solid grounding to numerical analysis. Codes are inconveniently written in fortran-97? instead of the more readable pseudo-code. It may provide a good application supplementary for engineering students, but i strongly advise against it for mathematics undergrads. No fun. Lots of handwaving and smoking mirrors.
A strict NO for starters.......2001-04-22
The author presumes that the reader has an advanced knowledge of calculus even though the book is intended for use by undergrads.the content in the chapters of the book are not enough to solve the questions at the end of ech chapter.if you are looking for an introductory course in NA dont even think of using this book.
Book Description
This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.
Customer Reviews:
Progresses Well - Used for Self Study.......2007-07-18
I self studied this book to improve my applied math skills. The book progresses well, with examples clear and easy to follow, even for a non mathematician such as myself. My background is only through the Calculus level. The book begins with linear equations then moves to matrix algebra, a logical approach. The author balances nicely what he refers to as "scaffolding" and the inherent efficiency of the topic.
With the exercises, I focused on the steps required to reach an accurate result and how I may apply this to the business I'm in and used Mathematica for many of the interim computations. This approach worked well for me and allowed me to better understand the topic as a whole, though it's doubtful I could have gotten away with this approach had I been in a formal classroom.
Matrix Analysis and Applied Linear Algebra.......2006-11-11
The book is ok. But It has A lot oF math proof and Word problems
A Model of Authorship.......2006-11-10
This book contains a comprehensive treatment on the topic of matrix analysis and applied linear algebra. The concepts are clearly introduced and developed. It is rich with detailed proofs that are easy to follow. Results are summarized and clearly grouped and marked for reference. As a researcher and a practitioner, I found this book quite useful in explaining mathematical concepts without the need for a classroom instructor.
Besides, this book comes with a CD that contains a PDF version which makes it quite useful to port as a reference. It is very rich with problem sets that add insight, both theoretically and practically. It is accompanied by a solutions manual which strengthens comprehension.
I highly recommend this book. I think it deserves to be a model to follow for authorship in the digital age.
Beautiful Scaffolding.......2006-08-09
Linear algebra is the Babel language of sciences, this book helps you to get proficient in speaking it. Clear-cut presentation, mathematical rigor and historical gossip is in such an unison, that you'll crave for a sequel. This is the 18-th 5-star rating, you shouldn't hesitate any more!
One of the best introductory (modern) books I know........2006-04-27
If you need to learn Linear Algebra and Matrix Theory, your best starting point is this book.
Very well written, many examples, and many "modern" results, that are not found in classics as Gantmacher (also an excellent book).
Buy it and see for yourself.
Book Description
With meta-analysis methods playing a crucial role in health research in recent years, this important and clearly-written book provides a much-needed survey of the field.
Meta-analysis provides a framework for combining the results of several clinical trials and drawing inferences about the effectiveness of medical treatments. The move towards evidence-based health care and practice is underpinned by the use of meta-analysis. This book:
* Provides a thorough criticism and an up-to-date survey of meta-analysis methods
* Emphasises the practical approach, and illustrates the methods by numerous examples
* Describes the use of Bayesian methods in meta-analysis
* Includes discussion of appropriate software for each analysis
* Includes numerous references to more advanced treatment of specialist topics
* Refers to software code used in the examples available on the authors' Web site
Practising statisticians, statistically-minded clinicians and health research professionals will benefit greatly from the clear presentation and numerous examples. Medical researchers will grasp the basic principles of meta-analysis, and learn how to apply the various methods.
Customer Reviews:
A personal review.......2007-05-13
This book has two big advantages: In my personal view it is written well for someone who has at least some basic statistical understanding and for me there are quite enough practical examples and illustrations of the chosen methodology. The second advantage in my opinion is its wealth of references at the end of every chapter.
Overall it covers almost all of the relevant methods and thus can be considered as a reference for the experienced statistician and as an easily comprehensible introduction to the beginner.
I think to recommend this book warmly to any reader who does not need the theoretical foundations of probability in meta-analysis.
Book Description
This edition of Finite Mathematics with Applications continues to be an excellent learning tool for applied mathematics students. As always, the text includes the popular margin exercises as well as comprehensive review of algebraic topics, but with this revision comes the fresh insight of a new co-author. This new edition is all that you need and more.
Customer Reviews:
College book for finite mathematics.......2007-07-12
This is one of the worst math books I have ever had the pleasure of using.
I usually always make A's in mathematics, and am also in Honors, but this book is a fight to understand.
The answers in the back are wrong very often, about 1-3 times per exercise. There are about 4-7 exercises per chapter @ 10 chapters. This is extremely frustrating when learning new facets of mathematics. This book is being used at University I am attending, and is not worth this level of education. The instruction in the book is very confusing, by jumping from idea to idea with no flow. First the errors have to be filtered out before any learning can be done. The course I am taking is an online course, so without a live instructor to give the correct information, one leaves completely confused. I have emailed my professor at least once per chapter to confirm my correct answer against the wrong answer in the book. Or the answer key may have extra answers i.e. problem 11 may have questions a, b, and c, and the key will have answers for a, b, c, d, and e.
TO ANY EDUCATOR LOOKING TO USE THIS BOOK FOR THE CLASSROOM, PLEASE CONSIDER ANOTHER RESOURCE, THIS BOOK IS OF VERY POOR QUALITY. Pearson should be ashamed to allow such bad editing to make it to consumers. This is the 9th (Ninth) edition printed in 2007. Math does not change enough to have such bad errors. Nor should any book be so jumbled.
Average customer rating:
- Excellent Choice for the Non-Math Student
- Harvard
|
Applied Calculus
Deborah Hughes-Hallett ,
Patti Frazer Lock ,
Andrew M. Gleason ,
Daniel E. Flath ,
David O. Lomen ,
David Lovelock ,
William G. McCallum ,
Brad G. Osgood ,
Douglas Quinney ,
Karen Rhea ,
Jeff Tecosky-Feldman ,
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Otto K. Bretscher ,
Sheldon P. Gordon , and
Eric Connally
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ASIN: 0471681210 |
Book Description
APPLIED CALCULUS, 3/E brings together the best of both new and traditional curricula to meet the needs of today's students. The author team's extensive teaching experience and proven ability to write innovative and relevant problems has made this text a true bestseller. Exciting new real-world applications make this new edition even more meaningful to students in management, life and social sciences. This book will work well for those departments seeking a middle ground for their instructors.
APPLIED CALCULUS, 3/E exhibits the same strengths from earlier editions including the "Rule of Four", an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.
Customer Reviews:
Excellent Choice for the Non-Math Student.......2007-03-31
This is a magnificant calculus book. It is aimed at students in business, the social sciences, and the life sciences. This is done by first the examples and problems. But perhaps even more important the wording of the text is such that these students will understand what they are trying to convey and to clearly show them how calculus can be used to solve problems in their particular field.
At the beginning of the book, three pages of the Preface, the applications discussed in the text are listed by: Business and Economics, Life Sciences and Ecology, Social Sciences, Physical Sciences. Under these headings are subjects like: Value of a Car, AIDS, Cancer Rates, Abortion Rate and so on. These are subjects that will have some interest and applicability to students rather than the old traditional problems like water flowing into and out of a bucket that used to be the mainstream of teaching calculus.
Finally, calculus marks a transition in the study of mathematics for a student. Up until now he studied arithmetic every year in school, maybe he finally got to a bit of algebra and trig. Now he is exposed to a whole new world of ways to handle problems that go beyond anything he has seen before. This book eases the student into an understanding of how to approach these problems better than any I've seen.
Harvard.......2007-01-31
Sorry to bother you with this review. The authors of this book are distinguished professors at Harvard University (a fine school, no matter what anyone says). Professor Gleason, in particular, is a mathematician of world-historical importance. In a sense, taking lectures from Gleason is not worse than having a lecture from Laplace or Poincare or any of the other great lights of mathematics. I confess that I haven't seen the book or held it between my hands, but I couldn't just leave it here with only a one star review of a disgruntled student. Really, the book has to be better than a single star if Gleason even held it in his hand once.
Customer Reviews:
The Pinacle of Introductory Analysis.......2007-03-12
Walter Rudin's book barely needs introduction at this point. It has gained a reputation as the best text anywhere for an introduction to real analysis, and is the gold standard for many first year graduate courses in the subject. Rudin's work is a masterpiece of style and form, and his presentation is second to none. Care has been taken with every proof to make it as elegant as possible. The selection of problems typically ranges from those requiring a few minutes thought, to the fantastically difficult.
Therein does lie one of the two problems with this book, however. Occasionally Rudin relegates an important--and useful--result to the exercises where it could be overlooked by the unwary. There are some sections where more examples aimed at getting a student to practice applying fundamental concepts would be useful, instead of making them bend over backwards to find an answer.
The only other problem, which is often brought up as a criticism of the book, is that Rudin is often perhaps a bit too terse in his exposition between proofs. There isn't always a strong motivation given for a topic, which makes this book a difficult one to learn from without a good instructor.
Overall, it would be hard to do better than the so-called "baby" Rudin book. The price tag is a little steep for something so slender, but the content inside can easily outshine any other 3 similar texts in the area. This is an absolute must own for any aspiring analyst.
Solid and elegant.......2007-01-02
This book is well known for being terse. I will not refute this, but I will say that it is certainly not the tersest math book I have read (that honor might go to Samuel's algebraic number theory text). I am a graduate student in computer science, and I found this book to be enjoyable, well-structured, easy-to-read, and with excellent exercises. I probably would not attempt to use it for independent reading, though. The book develops calculus from the beginning, wasting no time, and giving almost no examples (unless you take the time to work through all the exercises). It is thus important to have a good instructor who can fill in the gaps as you go along.
The price, however, is ridiculous.
Simply the best ... .......2006-06-23
If you didn't use this classic in your first pass at elementary
analysis, you owe it to yourself to find a copy and work
through as many exercises as possible ... especially if you
plan to go further to graduate level work in mathematics.
Other books that are increasingly used for this subject still
leave readers with a 'maturity/sophistication' gap relative to
more advanced texts in real analysis, etc.
A course at MIT based on this text is presented at the link
below, with suggested coverage, exercises, solutions, etc. -
[...]
Analysis 101.......2006-05-13
Principles of Mathematical Analysis by Walter Rudin can rightly be called "the Bible of classical analysis". I have seen it cited in more books than I can count. And after a full year of working through the book in graduate school, I can see why. As many other reviewers here have pointed out, this book requires more than a little of that magical quality called "mathematical maturity". Simply defined, "mathematical maturity" is the ability to read between the lines and fill in the gaps in a given mathematical text.
While Rudin certainly provides an encyclopedic account of basic analysis in metric spaces, he does leave some gaps (many are intentional) in his proofs. So be alert when you read this book, and if anything in his super short, slick proofs is not 100% clear, be prepared to fill in the details yourself. Also, remember that Rudin's way of presenting proofs is not always the most instructive when first learning the material. There is an implicit challenge to the reader to see if he or she can provide a more expository proof. Although I can say that when the classical proof suffices, Rudin usually does not deviate from it.
Some of the highlights/weaknesses of the book are the following:
Chapter 1: The material in this chapter is of course standard. However, Rudin supplements the chapter with an appendix on the construction of the real field from the field of rationals via the notion of Dedekind cuts. After reading many, many analysis books, I can tell you that it is difficult to find an explicit construction of the reals in books on an elementary level. Thus, while certainly not required to appreciate the rest of the text, I do recommend at least a casual perusal of the appendix just to see that "it can be done".
Chapter 2: Rudin may seem to go a little overboard in his presentation on basic topology, but trust me, it will *all* be used later. So do not gloss over anything in this chapter. In particular, note how the notion of compactness is not defined a priori by any metric space ideas. However, in metric spaces, compactness does imply certain useful properties. One that is used again and again is the equivalence of compactness and sequential compactness in metric spaces. Thus, after moving on to Chapter 3 and beyond, I advise you to look back at Chapter 2 often.
Chapter 3: One notable feature is that Rudin does not attempt to discuss limits per se before discussing numerical sequences and series. This may make you a little uncomfortable at first, but it turns out that this approach works best. Again, everything in this chapter is essential to the rest of the book. My only gripe with this chapter is the material on "upper and lower limits", better known as lim sup and lim inf. I feel that he should have expanded the discussion in this section a little more. In particular, his Theorem 3.19 should have had a proof supplied in the text. One of the reasons I feel this way is because the Root and Ratio tests for convergence of infinite series of numbers use lim sup heavily.
Chapter 4: Limits are finally introduced as the reader remembers them from basic calculus. The only difference is that Rudin works with arbitrary metric spaces, which turns out to be very useful later. Take note of Theorem 4.2. Reformulating the existence of a limit of a function in terms of limits of sequences is a handy theoretical tool that makes a lot of proofs (Rudin's included) much easier to understand. That said, there are no real surprises until Theorem 4.8. You can probably omit the subsection "Discontinuities" with no loss. I say this even though some of the theorems in "Monotonic Functions" use that material in their proofs. Theorem 4.30 in particular (monotone functions on open intervals have at most a countable number of discontinuities) has a much better proof than that Rudin provides. So try and look elsewhere for the proofs of those theorems.
Chapter 5: All the derivative proofs are just like you remember from advanced calculus. The only one that merits special attention is L'Hospital's Rule. Work through it very carefully, it is more subtle than it appears.
Chapter 6: The Riemann-Stieltjes integral can be obtained by only slightly more effort, so Rudin wisely decides to base all of his proofs (through Theorem 6.19) on it. Just be aware that some of the material covered, such as the Fundamental Theorem of Calculus and integration by parts is only discussed for the original Riemann integral. Theorem 6.25 (based on the Cauchy-Schwarz inequality) acquires a special significance in the following chapters, so memorize it!
Chapter 7: By far, this is the most crucial chapter in the book. This is probably the material that you may have had limited or no exposure to in the past. The famous Weierstrass Approximation Theorem (and its generalization by Marshall Stone) is given here. Read this chapter front to back at least four times. Yes, it is that important. Otherwise, the Fourier Theory presented in Chapter 8 will seem like gibberish.
Chapter 8: Expansion of analytic functions via power series is presented here. A brisk, but complete development of the exponential, sine and cosine functions is also featured here. Problem 6 in the exercises at the end of the chapter is worth special consideration. Work it out after you read about the exponential function. The Fourier material is relatively straightforward, although awkward when divorced from measure theory. As Rudin himself notes, the hypothesis that f be Riemann integrable is often unnecessary, so you may want to peek ahead at Chapter 11 while reading many of the proofs, especially Parseval's Theorem. The material on the gamma function is cute, but not really needed.
Chapter 9: The standard treatment of multivariable functions. Rudin's coverage of linear algebra is succinct. Also, the linear algebra has more important uses than merely providing a pathway to "multivariable calculus". The theory of linear operators sketched in Theorems 9.5 to 9.8 will lead you directly to the more abstract theory of Banach spaces. The Banach spaces take a very central role in advanced analysis as can be seen by reading Royden's "Real Analysis". I also recommend supplementary reading for this chapter. A good book to look at is Charles Pugh's "Real Mathematical Analysis" which has an extensive treatment of multivariable functions. Also, you might skim over George Simmon's "Introduction to Topology and Modern Analysis", a great introduction to the abstract theory of operators. This material is only hinted at in Rudin, but comes to its full fruition in Simmons.
Chapter 10: This is Rudin's introduction to differential geometry. I honestly have not given this chapter a thorough reading, but on the surface it looks ok. Most of the deeper theorems from multivariable calculus (excepting the Implicit Function Theorem, discussed in Chapter 9) are treated here, such as the trifecta known as Stoke's, Green's, and the Divergence Theorems, respectively. This chapter is important to anyone going into fields such as partial differential equations.
Chapter 11: This chapter seems to be the one that most people criticize in the book. Rudin gives a perfunctory outline of Lebesgue theory that seems to rob the reader of much needed detail. Indeed, this chapter is a little too lean for my tastes. But in Rudin's defense, he warns the reader at the outset that "proofs are only sketched in some cases, and some of the easier propositions are stated without proof". Hence, I recommend just giving this chapter a light read, then go to another book (such as Royden) for the real proofs. As expected, Rudin discusses some of the seminal results of Lebesgue theory, including, but not limited to: the Monotone Convergence Theorem, the Dominated Convergence Theorem, and the correspondence of the Lebesgue integral with the ordinary Riemann integral (whenever the latter exists). The Riesz-Fischer Theorem from Fourier analysis appears here. Lebesgue's Dominated Convergence Theorem (Theorem 11.32) is worth a careful reading. Afterwards, look at Exercise 12 in Chapter 7 for a simpler version of the DCT using the familiar Riemann integral. The proof is not that difficult.
It goes without saying that the exercises are extremely important and should all be attempted. Unless you are brilliant, odds are that at least a few will elude you. Nonetheless, many important results and counterexamples are listed in the exercises, so you will benefit from working them. Be warned though that Rudin will intermingle easy with very difficult problems.
An obvious problem is the outrageous price. Unfortunately, this book is essential reading, so you'll just have to cough up the dough or look for it cheap elsewhere. It is a good book to learn from and a fantastic reference. I don't know if I would call it the "best analysis book ever". But its current edition was released 30 years ago, so that says something about its popularity.
P.S. Once you've finished Rudin, the book by Pugh referenced above is a good read to "pull it all together". There are some well-thought out problems that will both challenge and inspire you to learn more at the same time.
Highly recommended.
Pretty Good.......2006-05-13
I want to start by listing some of my complaints. First of all, I do not think it is entirely appropriate for a student's first exposure to analysis. The majority of students would be better off taking a an honors calculus or advanced calculus course first, so they can learn how to prove things about the continuity of specific functions or convergence of series before they start proving things and functions and series in general (a look at, say, Bartle's book over summer break would probably work just as well, but my point remains the same). Second of all, the exercises are, for the most part, extremely challenging. While this is not a bad thing by any means, the book would probably benefit by having a few extra, easier problems. Third, it could use some pictures, not that many, but they would certainly help illustrate some of the ideas. Fourth, a few of the proofs are very difficult to understand because they are perhaps too concise (for example, the Cauchy-Schwarz inequality in the first Chapter). Finally, $140 is prohibitively expensive.
That having been said, PMA is considered the classic of its genre, and for good reason. It is extremely well-written, if a bit concise, and forces the reader to do a lot of thinking. While the problems are challenging, they are very non-trivial, and again, force the reader to do a lot of thinking. You may be noticing a theme here. This is an excellent book if the student has enough experience with mathematical thought, however, many others will be lost.
Personally, I prefer Pugh's book, which I think addresses all the shortcomings I listed above, but I certainly see why many would want to stick with the tried-and-true PMA.
Book Description
This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions). Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
Customer Reviews:
Inspiring and Useful.......2000-06-13
I was turned on to this book by a friend of mine who is an expert in geometric measure theory. He recommended the book as a very nice exposition of some of the material found in Federer's "Geometric Measure Theory" as well as other material. I found the book to be beautifully designed to help the reader learn its contents. There was enough between the lines so that one needed to WORK through the book, but in contrast to parts of Federer's book, enough detail so that reasonably fast progress could be made. Unfortunately, I was interupted in my race through the book and so I have yet to work through the latter part of the book. But given the large part I did cover and my experience doing that, I am certain to finish the monograph, most likely when I start using functions of bounded variation with any frequency.
There are no explicit exercises. But as already alluded to above, there are implicit exercises that are encountered in working through the book. I found that the lack of separate exercises is actually not bad at all since the implicit exercises encountered are automatically motivated by their necessity for the understanding of the text - and are therefore relevant!
A prerequisite for the book is a course in analysis that includes measure theory and integration as well as an exposure to elementary functional analysis. The functional analysis is not actually necessary, but the added maturity that such an exposure would impart would be useful.
Very briefly, the contents via the 6 chapter titles are 1) General Measure Theory, 2) Hausdorff Measure, 3) Area and Coarea Formulas, 4) Sobolev Functions, 5) BV Functions and Sets of Finite Perimeter, and 6) Differentiability and Approximation by C^1 Functions.
I found the contents very interesting ... quoting the authors "... we packed into these notes all sorts of interesting topics that working mathematical analysts need to know, but are mostly not taught." And indeed this was the case in my experience ... both the "interesting" part and the "not taught" part.
I am disappointed in the price, but if any book is worth it, this one certainly is.
Book Description
Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.
This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the second volume.
Chapter summaries and detailed illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance.
Advanced undergraduates and Masters level students in mathematical finance and financial engineering will find this book useful.
Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.
Customer Reviews:
Good book.......2007-10-01
I agree that most concepts are clearly explained....emphasis on *most*. OK, I'll nitpick. And I admit I'm nitpicking. For example, the proof of Jensen's inequality (which he oddly dives into without defining convex functions), is rather non-intuitive, and seems to be more an appeal to the accompanying picture rather than a proof. The proof given under the Wikipedia entry for "Jensen's Inequality" is much clearer, and makes much more sense, at least to my way of thinking. Other than the occassional gaffe such as this, it is a highly readable, informative, and dare I say enjoyable text!
Nice book.......2007-03-08
I think its a very good book for fundamental concepts in stocastic calculus.
Good for finanical mathematics graduates.......2007-01-10
clear explanations on binomial models for European and American options. Abstract concepts also included such as change of measures, martingales, stopping times. Proofs in book assumed no knowledge on sigma fields or measure theory.
Very good to understand the basics of pricing-theory........2006-03-04
This book is great book about theory. Using a simple binomial tree as asset evolution model, all key notions are introduced. Neutral-risk probabilities come up in a simple, natural way, and I never found such a clear explanation of the the change of measure and its meaning in finances. Examples help to understand every ussue.
The only case in which you should not buy it: if you are looking for real-market instruments and techniques.
Interesting Read.......2006-02-17
I found this book to be a very interesting and fun read. A very helpful introduction to binomimal models and basic stopping time principals. It also provides a great refresher to Martingale principals. If you are having trouble with Shreve's volume II then have a look at this book first.
Average customer rating:
- Tan7 Calculus solution manual-red cover with Boy on it-for managerail life.
- Great Cacl text, but CD ROM not Mac compatible
- Where are the last four chapters?
- THE PAPERBACK IS THE SOLUTIONS MANUAL
- Easy to read.
|
Calculus for the Managerial, Life, and Social Sciences (with CD-ROM and Printed Access Card iLrn Tutorial, vMentor 1-Semester)
Soo T. Tan
Manufacturer: Brooks Cole
ProductGroup: Book
Binding: Hardcover
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ASIN: 0534419860 |
Book Description
In the market-leading CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Soo T. Tan provides an accurate, accessible presentation of calculus combined with just the right balance of applications, pedagogy, and technology to help students succeed in the course. The new Seventh Edition includes highly interesting current applications and exercises to help stimulate student motivation. An exciting new array of supplements, including iLrn Tutorial and the Interactive Video Skillbuilder CD-ROM, provides students with extensive learning support so instructors will have more time to focus on teaching the core concepts.
Customer Reviews:
Tan7 Calculus solution manual-red cover with Boy on it-for managerail life........2007-05-17
This book is excellent it helped me a LOt. I wold have failed if it was not for this life saving book. The answers where clear and concise. This book shows step by step how to work each problem!!
I only wish it had a calculator explaination for the problems.
Great Cacl text, but CD ROM not Mac compatible.......2007-01-08
We used this text book in an NYU continuing education program. The course was designed as a refresher course for potential MBA applicants. I was taking it because we truly use calculus in the analytics of our systems at work.
This is a great text book. The illustrations are terrific. The problem sets are very good as they truly use real-world problems and examples. The instruction is crisp, without excessive theoretical wanderings.
One of the best scientific and engineering texts I have used.
CON: The enclosed CD ROM does not work with the Mac OSX operating system, and although I contacted customer support, they did not have plans to make the software OSX compatible. :-(
Where are the last four chapters?.......2005-10-09
This solutions book only goes through chapter 8 and the actual text has 12 chapters. I found that the answers were explained fairly well but I was very disappointed that it was missing several chapters and was probably not worth the money.
THE PAPERBACK IS THE SOLUTIONS MANUAL.......2003-10-02
Unfortunately the paperback is not a a paperback edition of the textbook, but the student's solution manual.
Easy to read........2000-05-05
I thought the book explained each topic in an easy to follow manner. There are some challenging excercises at the end of each section. Some of the exercises stumped me, but I guess that's good if you're looking to be challenged. I bought the solutions manual which gives step by step solutions to the odd questions. The book doesn't cover every area of calculus, but I found it useful when I didn't understand what we covered in class.
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