Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students’ physical intuition as he guides them through the mathematical methods required to study upper-level physics.
Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material.
It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions (‘By the Ways’) as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension.
Div, Grad, Curl, and All That: An Informal Text on Vector Calculus
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The topics usually encountered in a book dealing with mathematical methods for the physicist are covered. The presentation of the topics is more "lively" than the classical books such as Arfken, Riley or even Boas. I really appreciated the fact that the author presents the mathematical notions from the point of view of physics. This approach is quite similar to the excellent book by Snieder (a guided tour of mathematical methods for the physicial sciences).
Even if the author wants to create the link between mathematics and physics, the mathematical notions are not for all that neglected and not considered as "simple" tools (for example, linear algebra concepts are clearly defined in a rigorous manner) . This approach is quite similar to the other excellent book on the same subject by Altland (mathematics for physicists) although the latter is a bit more abstract and could thus be read as complementary reading.
I highly recommend this book. It will find its place without problem in the current literature (despite the fact of the great number of works already published on this subject.
The printing quality of the books of cambrdige university press is, as always, irreproachable.
Sincerely,