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Vector Analysis (Dover Books on Mathematics), by Louis Brand, Mathematics
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The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brought to the foreground, placing their logical structure in sharp relief.
Because the concept of a vector has been greatly generalized in geometry and mathematical physics, this text concludes with a brief introduction to abstract vector spaces, together with the ideas of linear dependence, basis, and dimension. The exposition of these abstract concepts is kept simple and clear. Numerous figures appear throughout the text.
- Sales Rank: #363276 in Books
- Published on: 2006-02-10
- Released on: 2006-02-10
- Original language: English
- Number of items: 1
- Dimensions: 8.42" h x .59" w x 5.38" l, .68 pounds
- Binding: Paperback
- 304 pages
Most helpful customer reviews
15 of 15 people found the following review helpful.
A splendid textbook
By Tomas Garza
No doubt this is an excellent introduction to the topic. Plenty of examples, interesting applications, well-organized; even though the original edition dates back to 1957, I think it is still one of the best books on the subject. The first chapter shows the power of vector methods, and once one gets familiar with them (mathematical) life becomes easier. Physical and engineering problems are illuminating. I recommend it without reservations.
5 of 5 people found the following review helpful.
A mathematician's gift to students of physics
By Jeremy Roach
L. Brand's Vector Analysis is a special book. Especially for physics students used to learning the subject from physics textbooks. There is a chapter for each of Newtonian mechanics, fluid mechanics, and electrodynamics. The postulates for each theory are clearly and explicitly stated (e.g. Maxwell's equations for electrodynamics). However those are merely applications of the mathematical theory. And the mathematics is absolutely beautiful. Much like analytic geometry, vector analysis conveys geometric information through algebraic equations. Though VA happens to be optimized for motion in 3 dimensions (e.g. a point moving along a curve).
Before purchasing this book you'll want to know basic calculus. And some basic geometric facts: two intersecting lines in space, and 3 points in space, form a plane, the Pythagorean theorem, the SAS rule for similar triangles, etc. You might have to look up what a Jacobian is as well.
3 of 3 people found the following review helpful.
Great book
By C. A. Hauer
Excellent text for review. Solutions for all problems are provided. Will be utilized in conjunction with my other studies and projects.
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