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Mathematical Methods: For Students of Physics and Related Fields (Lecture notes in mathematics ; 719)
By Sadri Hassani
Publisher: Springer-Verlag
Number Of Pages: 783
Publication Date: 2008-09-25
ISBN-10 / ASIN: 0387095039
ISBN-13 / EAN: 9780387095035
Binding: Hardcover
Product Description:
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
Summary: Mathematical Methods for Undergraduates
Rating: 3
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.
Summary: Aquired mathematical knowledge recommended
Rating: 5
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.
Summary: A Lot has Changed
Rating: 5
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.
Code
http://www.filefactory.com/file/eb53a9/n/0387095039_rar
By Sadri Hassani
Publisher: Springer-Verlag
Number Of Pages: 783
Publication Date: 2008-09-25
ISBN-10 / ASIN: 0387095039
ISBN-13 / EAN: 9780387095035
Binding: Hardcover
Product Description:
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
Summary: Mathematical Methods for Undergraduates
Rating: 3
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.
Summary: Aquired mathematical knowledge recommended
Rating: 5
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.
Summary: A Lot has Changed
Rating: 5
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.
Code
http://www.filefactory.com/file/eb53a9/n/0387095039_rar
