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Summary: A Mathematical Treatise of Physics
Review: One of the most elegant texts I have ever learned from and have myself used. Mary Boas is simply the best in explaining and presenting examples of ODEs, PDEs, Fourier Series, Complex Variables and a host of other topics.No serious student of budding theoretical or mathematical physics interest will be without Mary L.
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Summary: one thing to add
Review: the other reviews basically covered it, but i might add one thing. the book also contains many many problems. for example in the chapter on fourier transforms, in around 38 pages there are 155 problems, with relevant information before each set. 53 answers were given in the back. so with boas there is no need to comb other texts looking for relevant problems.
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Summary: A good book on undergrad Math Physics
Review: This book covers basic topics(vector analysis, ode, series, multivariable calculus, calculus of variations, Fourier, etc.) in a very original and understandable way. However, my only complaint, it is too classical. It doesn't go into any depth on vector spaces and other math essential to QM. But for the basics it is the best book out there.
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Summary: A book that has everything.
Review: This book has a bit of everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, ODE, PDE, Transforms just to name a few. If you get a chance to study everything from this book, you will probably learn more from this book than all your undergraduate math courses combined. Some concepts on this book may be difficult to understand due to the lack of in depth coverage. But I guess the main intention of this book is to focus on the applied side and cover as much material that is relevant to physics and engineering as possible and not go into much detail on the theory side.
If you are a graduate student in physics or engineering and want to buy this book for reference, it will be a good start for the first year courses but won't help you much after that.
Readibility of this book is excellent. You will understand most of the concepts and examples presented.
Bottomline: This is a must have book for engineers and physicists.
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Summary: Good But Not The Best!
Review: This is a math book for those in Physics and Engineering. I found the book somewhat lacking in examples. And it very often will not even provide answers to the odd numbered problems. It's almost essential to purchase the solutions manual to this if you want to understand the first several chapters (if your self studying). The text also lacks good visual examples. It totally leaves out Systems of Differential Equations (aka Dynamical Systems).
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Summary: Great review, not so good to learn from
Review: This was the textbook for my first advanced math-physics (mathsics) class. While the review of vector calc and other things I already knew was really helpful, I found it just too lacking in good examples and simpler homework problems to learn from it really well. Although I am really glad I own the book, I would rather learn from something that gives examples similar to the homework problems and gives a few lower-level homework problems to get my feet wet and THEN I can jump into the more complicated stuff.
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Summary: Great review, not so good to learn from
Review: This was the textbook for my first advanced math-physics (mathsics) class. While the review of vector calc and other things I already knew was really helpful, I found it just too lacking in good examples and simpler homework problems to learn from it really well. Although I am really glad I own the book, I would rather learn from something that gives examples similar to the homework problems and gives a few lower-level homework problems to get my feet wet and THEN I can jump into the more complicated stuff.
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Summary: indispensable Mathematical hanbook for physics students
Review: To put it quite simply, if you are a physics student, you must own this book. What does this book do for you? Consider this... In my school, we do not have a mathematical methods course for science, so I decided to take on a math minor to take all the classes neccesary to do physics "right." This included a class on ODEs, Fourier Series & PDEs, Linear Algebra, and Complex Variables. These classes, although helpful, cover a lot of stuff that is not quite useful for understanding physics concepts, often undermining or dampening the stuff that is actually applicable. What makes this book so great is that it combines all the essential math concepts into one compact, clearly written reference. If I could do it all over again, I would easily rather take a two semester Math Methods course (like they do in many schools) using a book like Boas than take all these obtuse math courses. With this book, it makes it so handy to review previously learned concepts or actually learn poorly presented topics ( for a physicist anyway) in mathematics classes... (Things like Coordinate Transformations, Tensors, Special Functions & PDEs in spherical & cylindrical coordinates, Diagonilzation, the list goes on.....) Keep this gem handy when doing homework and studying for exams, learning the math tools from this book enables you to concentrate squarely on the physics in your other textbooks... (since mathematical background information, understandably, is often cut short...)
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Summary: Clear and Understandable!!
Review: Why can't all college textbooks be like this book? Many times authors write over your head to make themselves feel superior or to ensure they will still have a job explaining things to the student. Not this book. It is extreamly clear and highly understandable. I actually read the book to understand the professor instead of the usual practice of listening to the instructor to understand the book. Mary Boas did an awesome job with this book. I am more than pleased with it. It just because the number 1 book for me to recommend and you will darn sure find it in my office from now on!!
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Summary: Do not get carried away!
Review: Yes, everyone loves the book - and so do I (see? I have given it 5 stars!). There is one little problem: this excellent book cannot replace the "real" mathematical books. When I first started using this book I was always concerned about the completness of the material. In other words, when she gave a "receipe" for solving a problem I would always think to myself "how do I know, that this solution is complete? are there not any other solutions? WHERE IS THE PROOF? etc."
You are always given the receipe, and, yes, this receipes will help you solve most problems and prepare for most examinations, but will you really understand MATHEMATICS behind the problems?
The solution in my opinion is to get hold of a few good and rigorous books on calculus, advanced calculus, variational methods, elements of complex analysis and basics of functional analysis. Once you have worked through them you can read M.Boas and really understand and appreciate the book. But the question is: will you need M.Boas then?
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