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Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics) 2nd ed. 2009 Edition

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ISBN-13: 978-0387095035
ISBN-10: 0387095039
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Editorial Reviews

Review

From the reviews of the second edition:

"The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities." --Physics Today

"Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done." --Zentralblatt MATH

"This new edition … of Mathematical Methods is designed to be used in an upper-division undergraduate course for physics and engineering majors. … The order of presentation is particularly good. … An additional strength of the book is the inclusion of chapters on nonlinear dynamics and probability. These chapters give a good introduction to chaos theory and the basic concepts of probability for beginning statistical mechanics students. … Overall, the volume is well written … . Summing Up: Highly recommended. Upper-division undergraduates." (E. Kincanon, Choice, Vol. 46 (8), April, 2009)

"The purpose of this book is to provide a comprehensive survey of the mathematics underlying theoretical physics at the level of graduate students entering research … . It is also intended to serve the research scientist or engineer who needs a quick refresher course in the subject … . This volume is intended to help bridge the wide gap separating the level of mathematical sophistication expected of students of introductory physics from that expected of students of advanced courses of undergraduate physics and engineering." (Teodora-Liliana Radulescu, Zentrablatt MATH, Vol. 1153, 2009)

From the Back Cover

Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.

Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics.

This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.

Some praise for the previous edition:

"The book has many strengths. For example: Each chapter starts with a preamble that puts the chapters in context. Often, the author uses physical examples to motivate definitions, illustrate relationships, or culminate the development of particular mathematical strands. The use of Maxwell's equations to cap the presentation of vector calculus, a discussion that includes some tidbits about what led Maxwell to the displacement current, is a particularly enjoyable example. Historical touches like this are not isolated cases; the book includes a large number of notes on people and ideas, subtly reminding the student that science and mathematics are continuing and fascinating human activities."

--Physics Today

 

"Very well written (i.e., extremely readable), very well targeted (mainly to an average student of physics at a point of just leaving his/her sophomore level) and very well concentrated (to an author's apparently beloved subject of PDE's with applications and with all their necessary pedagogically-mathematical background)...The main merits of the text are its clarity (achieved via returns and innovations of the context), balance (building the subject step by step) and originality (recollect: the existence of the complex numbers is only admitted far in the second half of the text!). Last but not least, the student reader is impressed by the graphical quality of the text (figures first of all, but also boxes with the essentials, summarizing comments in the left column etc.)...Summarizing: Well done."

--Zentralblatt MATH

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Product Details

  • Series: Lecture Notes in Physics (Book 719)
  • Hardcover: 832 pages
  • Publisher: Springer; 2nd ed. 2009 edition (October 27, 2008)
  • Language: English
  • ISBN-10: 0387095039
  • ISBN-13: 978-0387095035
  • Product Dimensions: 10.2 x 7.3 x 2.1 inches
  • Shipping Weight: 3.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #1,621,125 in Books (See Top 100 in Books)

More About the Author

Sadri Hassani is a Professor Emeritus of physics, a title he received after 31 years of teaching at an American public university. He holds a PhD in theoretical physics from Princeton University and is the author of several books, mostly on mathematical physics. In addition to theoretical physics, he is passionate about disseminating scientific awareness to the public, a task exemplified by his book, From Atoms to Galaxies, and the blog he is maintaining at http://skepticaleducator.org.

Customer Reviews

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Most Helpful Customer Reviews

34 of 36 people found the following review helpful By K. Luey on October 13, 2000
Format: Hardcover
When I took undergraduate quantum mechanics 30 years ago, we learned a lot about Louis deBroglie, Max Planck, the photoelectric effect, then moved into wave functions, the Schroedinger equation, simple one-dimensional potentials and the hydrogen atom. Maybe there was a little angular momentum tossed in. It was not until graduate school that I learned much about
/X> = xi/x>
where /X> is a vector in an n-dimensional, linearly independent vector space and the xi's were its components in the basis /x>. A lot of things like representations might have made more sense. Anyway, Hassani's undergraduate text gives one an excellent view of vectors and coordinate systems. In particular, it trains one well to leap into the more abstract view of vectors one reads about in, say, R. Shankar's excellent book on quantum mechanics, and also gives one a good deal of exercise on how to translate between coordinate systems. In graduate school, I found the ability to roam between coordinate systems to be very, very handy and the laborious time spent learning it was worth it. I'm not done with this book yet. I'm now getting into his chapters on complex variables and differential equations, but Hassani's treatment of vectors and coordinate systems is very good indeed. Undergraduate physics students who plan to go on into graduate school will find time with this book well spent.
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21 of 26 people found the following review helpful By bergvall jonas on April 7, 2001
Format: Hardcover
This book is for those who already aquired some knowledge in mathematical analysis, linear algebra with vectors and some introduction in complex analysis. Roughly altogether about 15 University points.
Because it's surely not teaching you key things like what limits, substitution, integrand (one page according to index), asymptotics and so on really are. That knowledge is expected of you to have.
Instead the book gives a sort of enhanced recapitulation and expansion on topics and new insights on new topics as well; what these can be used for and how to use them. This is great because the reading goes intellectually much faster and get your attention right away with the stuff you already have a working knowledge of.
The boxes are great; containing important definitions which then is accompanied with instant examples clearifying the definitions by proof or otherwise gives descriptive and explanatory content for a method or definition
Hassani's book is also well written in terms of language use.
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3 of 3 people found the following review helpful By Brian on October 21, 2010
Format: Hardcover Verified Purchase
Upon taking theoretical physics last year I used the "Mathematical Methods in the Physical Sciences" by Mary Boas. While that is a fantastic book (with solutions), I find this book to build up topics in a clearer manner. This book follows the syllabus I had for that class almost to the letter, while we had to jump around a lot in Boas's book. I admit that not having any solutions to use for practice or self-study puts a damper on things, but this book is outlined so well I can't say that this book is not worth reading.

By far one of the most "easy on the eye" theoretical physics books out there, and I highly recommend it to any undergraduate who wishes to study any theoretical science.
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3 of 3 people found the following review helpful By VZ on September 6, 2009
Format: Hardcover Verified Purchase
I suppose no introductory math methods book can have everything. But this book would get six stars if it had included the matrix formulation of the eigenvalue problem with some treatment of unitary matrices. In addition, a solutions manual to aid in self study would be nice. Or at least some answers or hints to some problems. Otherwise, a neat book.
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3 of 12 people found the following review helpful By Michael G. Williams on March 21, 2006
Format: Hardcover
Helps students become familiar with complex mathematics in more applications than a standard course. Not as thorough as the books covering the same material by Mary Boas. IMHO.
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