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Advanced Calculus for Applications, Second Edition 2nd Edition

4.5 out of 5 stars 11 customer reviews
ISBN-13: 978-0130111890
ISBN-10: 0130111899
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Editorial Reviews

From the Publisher

This volume offers an integrated treatment of mathematical topics which can be developed from results of elementary calculus, and which are of common importance in many fields of application.
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Product Details

  • Paperback: 733 pages
  • Publisher: Prentice-Hall; 2nd edition (April 10, 1976)
  • Language: English
  • ISBN-10: 0130111899
  • ISBN-13: 978-0130111890
  • Product Dimensions: 6 x 1.6 x 8.9 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #699,943 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

Format: Paperback
This is a one of the best introductions to advanced calculus out there, in my opinion. Once you've read it, you'll have enough background to start work on serious PDEs and analysis. Further, the book has an rather extensive set of problems for the reader to work, with solutions provided.
There are several flaws, however, which is why I gave it 4 stars. In particular, the first couple chapters are an excrutiating read. It was so boring, in fact, that I quit reading the book and shelved it for three years (math was just a hobby at the time). Once you get past those initial few series-choked chapters, the book picks up the pace quite a bit; the book actually becomes quite the page turner once you get to chapter 6 and for the rest of the text --- took only three weeks to soak up the last half of the book, and that without rushing (versus three years for the first fourth ;) ).
This book is, however, an introductory text --- I'd say probably Junior level. Thus, many points are not explicitly proven. Calculus of variations, for example, only gets a couple pages, and as I recall, they only prove the necessity of d/dx(df/du') - df/du = 0, omitting any discussion of sufficiency: many other similar examples occur throughout the text. This shouldn't be a problem, however, as such issues are often discussed in the literature or in more advanced (graduate-level or advanced undergraduate) texts.
Another potential problem is that the text is fairly old. As such, it doesn't address the use of numerical methods on computers, although it does discuss numerical methods (somewhat outdated ones at times, however, as reflected in the strong emphasis on series solutions thoughout).
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Format: Paperback
This book helped me get a High Pass in Applied Mathematics here at the Thayer School of Engineering of Dartmouth College. It's not a great intro text to this material and it skips alot of details but it's a fantastic additional reference book.
For example there is a solved problem of a wave function PDE, which involves Bessel functions. Earlier sections of the text refer to how the ODE's are solved by Bessel, which many books leave out.
Later sections of the text contain an intriguing treatment of the Laplace transform.
This book is not for beginners but is a good stepping stone to more advanced concepts such as the Calculus of Variations. Beyond this you are wise to consider additional texts such as Hildebrand's Methods of Applied Mathematics which contains a more rigorous section on C of V, Bender and Orszag's Advanced Mathematical Methods for Scientists and Engineers, Wunsch's Complex Variables, and even a good review on PDE's such as Haberman's Elementary Applied PDE's is not a bad idea if you are in a review situation like I was (having spent 8 yrs in Dot Com's and then back to grad school in engineering).
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Format: Paperback
This book is definitely geared to the applied mathematics student; the topics in this book are strictly for pratical applications and not theory. It isn't too difficult but takes quite a lot of mathematical manipulation. Also, this book is quite old: to give you an idea, the first edition of this book was used by John Nash in his undergraduate calculus class in the early 1950s. Although many topics have been added in the 2nd edition, much of the material hasn't changed since its first publication in 1948. Nevertheless, you can still learn a tremendous amount from this book, even if you happen to be a 16 year old.
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Format: Paperback
I've been using this book to supplement an intense course on mathematical methods of physics that I'm currently taking correspondence in Germany, and it's been a real help to me thus far. It doesn't seem to be super mathematical (in the pure theoretical sense), but it is most definitely useful for applications, particularly for physical problems. Anyone who has had the calculus I-III sequence at a mediocre American university, along with differential equations and linear algebra, should be able to make great use of this book. It's been 17 years since I finished my undergrad math degree, and I feel that this book is just my speed!
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Format: Paperback Verified Purchase
I used this for a semester and I enjoyed learning from it. Although the book is old (1950s I think) it does show relevant data and formulas. However, the author does seem to explain things in complicated ways sometimes. Certain derivations or theories could have been simply worded or demonstrated but instead is shown with dense text. Overall, I think it is a great book. Try to get the hardcover version if you can. The softcover tends to fall apart pretty easily.
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Format: Paperback Verified Purchase
At least that is what the title of the book used to be. In that form I used it as a text in two courses at MIT. (M 351 & M 352)
So I purchased it to see what was in the new rewrite. Many of the illustrations are the same! Material has been rearranged and some new material id added. I guess that is to be expected. In general I purchased to book to be an up to date reference book and collectors item.
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