Ebook Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds, by Theodore Shifrin
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Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds, by Theodore Shifrin
Ebook Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds, by Theodore Shifrin
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Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs.
* Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts.
* Numerous exercises of varying levels of difficulty, both computational and more proof-oriented.
* Exercises are arranged in order of increasing difficulty.
- Sales Rank: #695016 in Books
- Brand: Example Product Brand
- Published on: 2004-01-26
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Dimensions: 9.39" h x .95" w x 7.72" l, 2.00 pounds
- Binding: Hardcover
- 504 pages
Most helpful customer reviews
27 of 28 people found the following review helpful.
A Very Challenging Combination of Linear Algebra and Multivariate Calculus
By JL1984
At the University of Georgia this book is used for a two semester honors course that combines linear algebra and multivariate calculus (MATH 3500 and MATH 3510) and is generally taught by Dr. Shifrin himself. The idea is to show students how the two subjects are fundamentally related while at the same time giving rigorous proofs of the underpinnings of vector calculus and linear algebra. I would say that about 80% of the work in this text is proof related, so if you're one who normally struggles with theory and proofs this is definitely not the book for you.
While Dr. Shifrin can be a bit dry with his explanations at times I can guarantee you that students will learn a lot by putting forth the effort. Again, for those of you who are not familiar with Shifrin's books or style of writing I would not recommend this book to any beginner of linear algebra and/or multivariate calculus. This book is best served for students who feel comfortable proving theorems and being able to justify their work. Nonetheless, if you're up for a good challenge I would highly recommend this book because the exercises will definitely make you think.
In conclusion, I think one of the most rewarding aspects of this book is the appreciation of linear algebra/vector calculus that one will have after having labored through the chapters. Oftentimes students take linear algebra and leave the class wondering what the point of it all was, which actually defeats the purpose of taking the class in the first place. Well, with this book those questions will be taken care of because students are exposed to the practicality of linear algebra by showing how it is related to calculus and how it is useful in and of itself. If you're looking for more than just mere formulas/generalizations to memorize to get you through the class (or if you're just curious about the subject) then by all means pick up this book because I guarantee you will not be disappointed.
4 of 4 people found the following review helpful.
This is very nice book that produces a very complete coverage of the ...
By George Hrabovsky
This is very nice book that produces a very complete coverage of the material. Why give it only 2 stars? Easy. The material is not so advanced that it is worth the ridiculous price. Hubbard and Hubbard is more cost-effective (you save $40) and has a lot more material. Alternately you can purchase Borden and Shilov from Dover together and save $125.
8 of 11 people found the following review helpful.
Beautiful but Wordy
By Amazon Customer
This book is probably best for young students who have a large amount of time on their hands.
There are some parts about it I love---such as the effort to give an intuitive explanation of every concept, the attention given to creativity, problems, typesetting, and diagrams; and there are some things I hate---the fact that sometimes the book tries too hard to explain and just ends up obfuscating the concept; the weaving, self-conscious prose; and the fact that sometimes more subtlety is better, which the text occasionally seems to forget.
If you are mature enough, I think you can probably learn the content here well from a more terse presentation.
And if you are immature, a more terse presentation might be a quicker way for you to grow up.
But in all, I can't hate this text for the sake of its effort to really make students understand the interplay and rigorous nature of mathematics.
Two books which are similar to this one are
(1) Advanced Calculus of Several Variables by CH Edwards, which I prefer and highly recommend (readable yet compact)
(2) Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms. I do not have experience with this, but have heard rave reviews. In my opinion, at 800 pages, it is probably a sprawling summary of all undergraduate mathematics, with some ingenious insights.
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