A graduate-level text introducing the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Directed primarily to graduate-level engineers and physical scientists, it has also been used successfully to introduce modern differential geometry to graduate students in mathematics. Includes 45 illustrations. Index.
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37 of 41 people found the following review helpful:
5.0 out of 5 stars
An intro to differential forms for physicists,
By A Customer
This review is from: Differential Forms with Applications to the Physical Sciences (Dover Books on Mathematics) (Paperback)
This book introduces differential forms to physicists. It is suitable for those with no advanced training in math other than multivarible calculus and linear algebra. No prior knowledge of topology is needed, although it doesn't hurt. The book starts with a good intro explaining the motivation for forms and when they might be useful over tensors and vectors. The exterior algebra is then presented in chapter 2, followed by a chapter on the exterior derivative. The rest of the book prestents a good deal of applications of forms including the statement and proof of the Newton-Leibniz-Ostrogradksy-Gauss-Green-Stokes Theorem, usually just called Stoke's Theorem. I'd recommend this book to any grad student in Theoretical physics that plans on doing research on physics in the 21st century.
22 of 24 people found the following review helpful:
4.0 out of 5 stars
Good But not the best,
By Mostafa (Iran) - See all my reviews
This review is from: Differential Forms with Applications to the Physical Sciences (Dover Books on Mathematics) (Paperback)
I was searching for a good source discussing the differential forms "from the ground up",while passing a course on GR. My motivation in studying this book was Weinberg's mentioning af it as "An extremely readable book" on the topic,in his book on GR.I belive that this is a good book if you have enough time and motivation to study differential forms from basic and without much hurry to use them operationally , but (at least in my opinion) it lacks that degree of clarity that one requires from a book on mathematical physics.To truly understand some parts (even at the early definitions)you may need to spend much more time that you could imagine at the first sight.Some basic ideas are expressed too concise.If you want to learn about differential forms in physics, this book would be some good, but not(I think) during a semester on something else (like GR), beacuse the way of presenting the material is not so stright , nor is operational enough.You may find the books by Lovelock & Rund or by Goldberg & Bishop more useful.
10 of 10 people found the following review helpful:
3.0 out of 5 stars
Concise,
By jb333333 "jb333333" (Australia) - See all my reviews
This review is from: Differential Forms with Applications to the Physical Sciences (Dover Books on Mathematics) (Paperback)
As a survey of the applications of differential forms to various aspects of the physical sciences, this book works quite well. However, for the non-mathematician, there are more intuitive texts available, although it is unlikely that they will have the same scope. The exposition is extremely concise, far more so than, for example, Lovelock and Rund, and at times this makes the text somewhat heavy going. Having said that though, the reader with a reasonable level of mathematical maturity will find the book very rewarding. A reader who is mainly focussed on differential geometry though would probably be better off with Lovelock and Rund.
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43
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- An Introduction to the Geometry and Topology of Fluid Flows (NATO Science Series II: Mathematics, Physics and Chemistry) by Renzo L. Ricca on page 133, and page 227
- Differential Geometry, Calculus of Variations, and Their Applications (Lecture Notes in Pure and Applied Mathematics) by George M. Rassias on page 377, and page 425
- A Second Course in Mathematical Analysis (Cambridge Mathematical Library) by J. C. Burkill on page 378, and Back Matter
- An Introduction to the Geometry and Topology of Fluid Flows (NATO Science Series II: Mathematics, Physics and Chemistry) by Renzo L. Ricca on page 133, and page 227
- Geometric Phases in Classical and Quantum Mechanics (Progress in Mathematical Physics) by Dariusz Chruscinski in Back Matter
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